Mechatronics

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Introduction to Mechatronics

MODULE - 1 INTRODUCTION TO MECHATRONICS SCOPE OF MECHATRONICS Mechatronics is considered as an application of computer based digital control technique via electric and electronic interfaces to solve mechanical engineering problems. Mechatronics is a synergic combination of mechanical and electrical engineering, computer science and information technology, which includes control systems as well as numerical methods used to design products with built-inintelligence. A mechatronic system requires multi-disciplinary approach for its design, development and implementation. In mechatronics, entire electro mechanical system is treated concurrently in an integrated manner by a multidisciplinary team of engineers and other professionals. There are many applications of mechatronics in mass production, which are used in industrial and house hold situations. Examples of mechatronics products include digital cameras, microwave oven, heating control, and automatic material conveying systems etc. A humanoid robot is another intelligent mechatronic system. It may involve many servomotors and a variety of other mechatronic components. Mechatronic components are more efficient, and cost effective, precise, accurate, reliable and flexible and have mechanically fewer complexities. A mechatronic system consists of a mechanical skeleton, actuators, sensors, controllers, signal conditioning/ modification devices, computer /digital hardware and software, interfacing device and power sources. Mechanical systems frequently consists of more than just mechanical components and may include fluid ,pneumatic, thermal, acoustic, chemical, or other elements as well . Sensor detects the quantity that is being measured (measurand), while the transducer converts the detected measurand into a convenient form for subsequent use (recording, control and actuation). The transducer signal may be filtered, amplified and suitably modified prior to this. Transfer function models (in frequency domain) are useful in representing, analyzing, designing and evaluating sensors, transducers, controllers, actuators and interfacing devices. What is mechatronics? The term mechatronics is used for the integration of microprocessor control systems, electrical systems and mechanical systems. A mechatronic system is not just a marriage of electrical and mechanical systems and is more than just a control system; it is a complete integration of all of them. In the design of cars, robots, machine tools, washing machines, cameras, and very many other machines, such an integrated and 1

Prepared by Shijin C.S.

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St.Joseph’s College of Engineering and Technology, Palai.

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interdisciplinary approach to engineering design is increasingly being adopted. The integration across the traditional boundaries of mechanical engineering, electrical engineering, electronics and control engineering has to occur at the earliest stages of the design process if cheaper, more reliable, more flexible systems are to be developed. Mechatronics has to involve a concurrent approach to these disciplines rather than a sequential approach of developing, say, a mechanical system then designing the electrical part and the microprocessor part. Definition of mechatronics A mechanical system designed to execute a desired function works under the input parameters like force torque pressure heat etc to produce respective units like translation rotation expansion and deformation .When the extraction of information’s input to a system is carried out by sensors and the output information is extracted by actuators to be processed by a controller (preferably microprocessor based) so that the desired function is executed with specified accuracy by the action of feed back process it would represent a mechatronic system. Such an arrangement is generally illustrated by the block diagram given in figure.

Fig : Definition of Mechatronics 2


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In the representation provided the mechanism is a mechanical system .The sensors are electrical/ electronic. Actuators can be mechanical/ electrical. Microprocessor based controllers are electronic. Hence the total system is the integration of mechanical, electrical and electronic sub-systems arranged to produce an accurate process or function automating the output. With the addition of computers the mechatronic system becomes more sophisticated and flexible. To define mechatronics with single sentence “Mechatronics is the synergistic integration of mechanical engineering with electronics and electrical with intelligent computer control in the design and manufacture of industrial products, processes and operations”.

SYSTEMS The mechatronic system is made of several systems like measurement system, drive and actuation system, control system, microprocessor system, and computer system. The characteristics of each system are i) System: A system can be thought of as a box which has an input and an output and where we are not concerned with what goes on inside the box but only the relationship between the output and the input. Thus, for example, a motor may be thought of as a system which has as its input electric power and as output the rotation of a shaft. Figure shows a representation of such a system.

Fig : An example of a system Any mechanical, electrical or electronic element or set of elements that can give out certain useful outputs under the understandable inputs can be named the system. The system can be purely mechanical, electrical or electronic requiring compatible inputs. But the mechatronic system is the combination of these systems. The schematic of a system is given in figure.

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ii) Measurement System: A measurement system can be thought of as a black box which is used for making measurements. It has as its input the quantity being measured and its output the value of that quantity. For example, a temperature measurement system, i.e. a thermometer, has an input of temperature and an output of a number on a scale. Figure shows a representation of such a system.

Fig: An example of a measurement system Any system that measures parameters like temperature, pressure, force, voltage, current, etc can be considered to a measurement system. For example a pressure gauge receives pressurized fluids through a pipe and the deformation of a flexible copper tube is converted to dial indication (analogue) by the rotation of a pinion. Such a system is shown below.

iii) Control System: A control system can be thought of as a black box which is used to control its output to some particular value or particular sequence of values. For example, a domestic central heating control system has as its input the temperature required in the house and as its output the house at that temperature, i.e. you set the required temperature on the thermostat or controller and the heating furnace adjusts itself to pump water through radiators and so produce the required temperature in the house. Figure shows a representation of such a system.

Fig : An example of a control system

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MEASUREMENT SYSTEMS Measurement systems can, in general, be considered to be made up of three elements (as illustrated in Fig.): 1. A sensor which responds to the quantity being measured by giving as its output a signal which is related to the quantity. For example, a thermocouple is a temperature sensor. The input to the sensor is a temperature sensor. The input to the sensor is a temperature and the output is an e.m.f. which is related to the temperature value. 2. A signal conditioner takes the signal from the sensor and manipulates it into a condition which is suitable for either display or in the case of a control system, for use to exercise control. Thus for example, the output from a thermocouple is a rather small e.m.f. and might be fed through an amplifier to obtain a bigger signal. The amplifier is the signal conditioner. 3. A display system where the output from the signal conditioner is displayed. This might, for example, be a pointer moving across a scale or a digital readout. As an example consider a digital thermometer. This has an input of temperature to a sensor, probably a semiconductor diode. The potential difference across the sensor is, at constant current, a measure of the temperature. This potential difference is then amplified by an operational amplifier to give a voltage which can directly drive a display. The sensor and operational amplifier may be incorporated to the same silicon chip.

Fig : A measurement system and its constituent elements The resistance strain gauges mounted on a loaded beam in the form of a Wheatstone’s bridge give change in voltage by change in resistance owing to change in length by deformation. The differential amplifier amplifies the voltage signal that is given to analogue or digital strain indicator to give out the strain reading as the output.

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MICROPROCESSOR BASED CONTROLS Microprocessors are now rapidly replacing the mechanical cam-operated controllers and being used in general to carry out control functions. They have the great advantage that a grater variety of programs become feasible. In many simple systems there might just an embedded microcontroller, this being a microprocessor with memory all integrated on one chip, which has been specifically programmed for the task concerned. A more adaptable form is the programmable logic controller. This is a microprocessor-based controller which uses programmable memory to

store

instructions and to implement functions such as logic, sequence, timing counting and arithmetic to control events and can be readily programmed for different tasks. Fig. shows the control action of a programmable logic controller, the inputs being signals from switches being closed and the program used to determine how the controller should respond to the inputs and the output it should then give.

Fig : Programmable Logic Controller The mechanical mechanisms like speed governors, cam actuated valves and switches, rack and pinion driven analog indicators are being replaced by microprocessor based controllers. The main features of microprocessor controllers are •

Variety of programs can process the multiple inputs to give multiple outputs.

•

The programs can be altered/ reprogrammed to change the output specifications.

•

There is programmable memory to store instructions and carry out control functions.

•

The processors being integrated chips are compact in size embedded in any circuit 6


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THE MECHATRONICS APPROACH The Domestic Washing machine that used cam-operated switches in order to control the washing cycle is now out-of-date. Such mechanical switches are being replaced by microprocessors. A microprocessor may be considered as being essentially a collection of logic gates and memory elements that are not wired up as individual components but whose logical functions are implemented by means of software. The microprocessor - controlled washing machine can be considered an example of a mechatronics approach in that a mechanical system has become integrated with electronic controls. As a consequence, a bulky mechanical system is replaced by a much more compact microprocessor system which

is

readily

adjustable to give a greater variety of programs. Mechatronics involves the bringing together of a number of technologies : mechanical engineering , electronic engineering , electrical engineering , computer technology and control engineering . This can be considered to be the application of computer based digital control techniques , through electronic and electric interfaces , to mechanical engineering problems. Mechatronics provide an opportunity to take a new look at problems with mechanical engineers not just seeing a problem in terms of mechanical principle but having to see it in terms of a range of technologies. The electronics, etc., should not be seen as bolt-on item to existing mechanical hardware. A mechatronic approach needs to be adopted right from design phase .There needs to be a complete rethink of the requirements in terms of what an item is required to do. There are many applications in the mass-produced products used in the home. The microprocessor-based controllers are to be found in domestic washing machines, dish washers, ovens, cameras, camcorders, watches, hi-fi and video recorder systems, central heating controls, sewing machines, etc. They are to be found in cars in the active suspension, antiskid brakes, engine control, speedometer display, transmission etc. A larger scale application of mechatronics is a flexible manufacturing engineering system (FMS) involving computer-controlled machines, robots, automatic material conveying and overall supervisory control.

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Advantages and Disadvantages of Mechatronics. S. No.

Advantages of Mechatronic Systems

S. No.

Disadvantages of Mechatronic Systems

1.

Serves effectively high dimensional accuracy requirements.

1.

Improves application and under utilization can result in losses.

2.

Mechatronic systems provide increased productivity on the shop floor.

2.

Maintenance and repair may workout costly.

3.

The initial cost is high.

Reconfiguration feature by pre 3.

supplied programs facilitate the low volume production.

4.

Provides higher level of flexibility required for small product cycles.

Techo-econic estimation has to be done 4.

mechatronic system.

Manufacturing lead time is reduced 5.

resulting in lowering of unit cost

carefully in the selection of

Calls for training and re-orientation of 5.

especially in mass production.

the work force, in design and manufacture. The technicians and engineers have to

6.

Results in automation in production, assembly and quality control.

6.

be given basic knowledge of two domain disciplines viz. Precision mechanics and electronics.

Plays major role in total 7.

manufacturing solutions rather than

The concurrent integration of 7.

stand alone machines.

mechatronic design needs expertise of multidisciplinary knowledge.

Production of parts and products of 8.

international standards gives better reputation and return. Higher life is expected by proper

9.

maintenance and timely diagnosis of the fault.

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SENSORS AND TRANSDUCERS The term sensor is used for an element which produces a signal relating to the quantity being measured. Thus in the case of an electrical resistance temperature element, the quantity being measured is temperature and sensor transforms an input of temperature into a change in resistance. The term transducer is often used in place of the term sensor. They are defined as elements that when subject to some physical change experience a related change. Thus sensors are transducers. However a measurement system may use transducers, in addition to the sensor, in other parts of the system to convert signals from one form to another form. Definition of sensor “It is a part of the measurement system that provides response to the particular measurable physical parameter, which can be one of the input energy domain transformed into another form of energy domain with or without aid of modulating energy domain”. The six energy domains identified to accept, transfer and modulate by a sensor are v Mechanical. Distance, velocity, force, acceleration or size etc. are covered in this domain. v Electrical. Current, resistance, voltage, inductance, capacitance form the basis of this domain. v Magnetic. Field strength and flux density can be considered in this domain. v Thermal. The effect of temperature like heat capacity, latent heat, phase changes, sensible heat, superheating can be identified in this domain. v Radiant. The frequency, phase, intensity, polarity of electromagnetic radiation fall in this domain. v Chemical. The concentration of the chemical substances crystal structure, and aggregation of state concerning the behaviors of the matter exemplify this domain.

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Classification of Sensors The static and dynamic performance characteristics play important role in the selection of the type of sensors needed for the applications suitable to the mechatronic system. The range, error, accuracy, sensitivity, repeatability, stability and resolution are some of the static performance parameters to be looked into before selecting a right sensor. Response time, rise time, settling time and time constant are the main dynamic characteristics usually considered in mechatronic application of sensors.

i) Pressure Sensors The mechanical pressure gauge with collapsible tube and analogue indication is the most beginning in pressure measurement which still finds application in mechanical industries. In fluid power systems with dynamic fluctuations electrical pressure sensors are preferred. In these the elastic deformations depending upon the materials physical properties, are transformed into electrical signal. The strain gauges find the frequent usage in pressure measurements. Piezoelectric sensors are most suitable for dynamic pressure measurements and small in size. For both static and dynamic pressure signals best solutions are piezoresistive sensors. Vapour deposited thick film sensors on silicon wafers constitute the measuring element. The signal gets amplified by the integrated differential amplifier. This has the disadvantage of being sensitive to temperature changes.

ii) Flow Sensors The result of flow management is influenced by the parameters like pressure pulsation, temperature, and viscosity of the flow medium. The principle of flow measurement is fraught with the effects of flow captured via physical properties and then transformed into a signal proportional to volume flow. Knowing the cross-section of the medium at a point where the velocity of the stream is measured to obtain the flow rate. Gear pump can be used for measure flow with high accuracy. But they have the drawbacks of higher pressure loss and are prone to seizing due to contaminations. Measuring turbine is another mechanical application of flow measurement in which the flow drives the turbine wheel that induces an electrical impulse for each blade.

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iii) Hall Effect Sensors E.R. Hall in 1879 discovered the Hall Effect. “A beam of charged particles passing through a magnetic field experience a force that defect the beam from the straight line path”. This is known as Hall Effect. Electrons (negative charged particles) are made to pass through a plate of rectangular cross section and a magnetic field is applied at right angle to the plane of the plate as shown in fig. The electrons are deflected towards one side of the plate, making that side negatively charged and the other side becomes positively charged. The force due to the applied magnetic field is called Lorentz force. The mechanism of deflection is governed by the balance in Lorentz force and the force on the charged particle due to electric field.

Fig : Principle of Hall effect The potential difference, V, created in between the transverse face of the plate, is given by

V = Hc Where,

FL T t

HC = Hall’s co-efficient FL = Magnetic flux density due to Lorentz force I = Current flowing through the plate t = Thickness of the plate V = Hall voltage

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iv) Light Sensors Any radiation of appropriate wavelength fall on the depletion layer of p-n junction develops a potential difference between the junctions. The voltage across the layer is proportional to the illumination of the incident radiation. Figure (a) shows the incidence on light rays on the n layer of the p n junction. Figure (b) is the characteristic curve showing the variation of voltage with wavelength of radiation.

Type of Light sensors 1. Photo diodes 2. Photo transistors 3. Photo conductors Photo Diodes: The reverse bias is applied against the p-n junction that results in a very high resistance. The light ray is made to fall on n-layer (depletion layer). This results in decrease in resistance of diode, developing a reverse current due to the sweep up of the electron-hole pair. The reverse current is the measure of intensity of the incident radiation. The response of photo diodes is quick and they can be used as variable resistance devices.

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Photo Transistors: A base-collector arranged in parallel to the photo diode a bipolar transistor is formed. In this PN junction collector-base is photo sensitive. The incident radiation on the base results in reverse current of photodiode, which is base current of the transistor. The base current is proportional to the intensity of light. The internal signal processing amplifies the base current to give higher sensitivity to the photo transistors.

Photo Conductors: By coating a layer of indium antimonide (InSb) or cadmium sulphide (CdS) on a layer of silicon dioxide (SiO2) the photo resistors are produced. The base is the p-type material (SiO2) and n-type materials (In or CdS) are diffused on it. The incident light ray illuminating the n-type layer results in change of conductivity. The bridge circuit arrangement detects this change by the change in output voltage proportional to the intensity of incident light. The photo resistor design and the required circuitry are shown in figure.

Fig: Photo conductor, structure and bridge

v) Optical Sensor The proximity of the object is detected by the action of the travelling light move. The light emitted by the transmitter focuses on the object which reflects to be received by the receiver photo diode. The constructional feature of the optical sensor is shown in figure. The light from the emitting diode is focused by the transmitter lens, on to the 13


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object surface. The reflected light waves travel back and received by the solid state photodiode through the receiver lens. The object within the range of sensor can detect the presence. The focal length of the sensor lenses decide the range within which the proximity of the object is detected.

Fig: Optical Sensor

Transducers Transducer is a pedantic word formed from two Latin words. By definition the transducer is that part of a system that transfers information or data in the form of energy from one part of the system to another with or without changing the form of energy containing the informations. Some of the Parameters transduced by electro-mechanical devices are as follows: Force, Pressure, Temperature, Displacement, Proximity, Viscosity, Flow, Frequency, Time, Vibration and Chemical composition. Transducers are classified as 1. Electrical

(Resistive, Capacitive, Inductive, Thermo electric, Resonant etc.)

2. Solid State

(Magnetic, Thermal, Mechanical, Chemical etc.)

3. Optical (Radian energy, Photo detector, Vision system, Laser scanning, Fiber optic etc.) 4. Piezo-electric (Accelerometer, Humidity meter, Light Modulators, Actuators, Acoustic devices etc.) 5. Ultrasonic 14

(Flow measurement, Distance, Velocity, Ultrasonic imaging etc.).


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DISPLACEMENT, POSITION AND PROXIMITY Displacement sensors are concerned with the measurement of the amount by which some object has been moved; position sensors are concerned with the determination of the position of some object with reference to some reference point. Proximity sensors are a form of position sensor and are used to determine when an object has moved to within some particular critical distance of the sensor. They are essentially devices which give on-off outputs. In selecting a displacement, position or proximity sensor, consideration has to be given to: 1. The size of displacement. 2. Whether the displacement is linear or angular. 3. The resolution required. 4. The accuracy required. 5. What material the measured object is made of. 6. The cost. Displacement and position sensors can be grouped into two basic types: contact sensors in which the measured object comes into mechanical contact with the sensor or non-contacting where there is no physical contact between the measured object and the sensor. The following are the examples of commonly used displacement sensors. 1. Potentiometer sensor A potentiometer consists of a resistance element with a sliding contact which can be moved over the length of the element. Such elements can be used for linear or rotary displacements, the displacement being converted into potential difference. The rotary potentiometer consists of a circular wire-wound track or a film of conductive plastic over which a rotatable sliding contact can be rotated. The track may be single turn or helical. with a constant input voltage Vs, between the terminals1 and 3, the output voltage Vo between terminals 2 and 3 is a fraction of the input voltage, the fraction depending on the ratio of the resistances R23 between terminals 2 and 3 compared with the total resistance R13 between terminals 1 and 3, i.e. Vo/Vs=R23/R13. If the track has a constant resistance per unit length, i.e. per unit angle, then the output is proportional to the angle through which the slider has rotated. Hence the angular displacement can be converted into potential difference. 15


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Fig : Rotary Potentiometer With a wire-wound track the slider in moving from one turn to the other will change the voltage output in steps, each step being a movement of one turn. If the potentiometer has N turns then the resolution, as a percentage, is 100/N. Thus the resolution of a wide track is limited by the diameter of the wire used and typically ranges from about 1.5 mm for a coarsely wound track to 0.5 mm for a finely wound one. Errors due to non-linearity of the track tend to range from less than 0.1% to about 1%. The track resistance tends to range from about 20 Ω to 200 kΩ. Conductive plastic has ideally infinite resolution, errors due to non-linearity of track of the order of 0.05% and resistance values from about 500 Ω to 80 kΩ. The conductive plastic has a higher temperature coefficient of resistance than the wire and so temperature changes have a greater effect on accuracy. 2. Strain-gauged element The electrical resistance strain gauge (in fig) is a metal wire, metal foil strip, or a strict of semiconductor material which is water-like and can be stuck onto surfaces like a postage stamp.

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Fig: Strain gauges: (a) metal wire, (b) metal foil, (c) semiconductor When subjected to strain, its resistance R changes, the fractional change in resistance ∆R/R being proportional to the strain ε, i.e. ΔR = Gε R

Where G, the constant of proportionality, is termed the gauge factor. Since strain is the ratio (change in length/ original length) then the resistance change of a strain gauge is a measurement of the change in length of the element to which the strain gauge is attached. The gauge factor of the metal wire or foil strain gauges with the metals generally used is about 2.0. silicon p-type and n-type semiconductor strain gauges have gauge factors of about +100 or more for p-type silicon and -100 or more for n-type silicon. The gauge factor is normally supplied by the manufacturer of the strain gauges from the calibration made of a sample of strain gauges taken from a batch. The calibration involves subjecting the sample gauges to known strains and measuring their changes in resistance. A problem with all strain gauges is that their resistance not only changes with strain but also with temperature. Semiconductor strain gauges have a much greater sensitivity to temperature than metal strain gauges. 3. Capacitive element The capacitance c of a parallel capacitor is given by

C=

εr εo A d

Where εr is the relative permittivity of the dielectric between the plates, εo a constant called the permittivity of free space, A the area of overlap between the two plates and d the plate separation. Capacitive sensors for the monitoring of linear displacements might thus take the forms shown in figure. In (a) one of the plates is moved by 17


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displacement so that the plate separation changes; in (b) the displacement causes the area of overlap to change; in (c) the displacement causes the dielectric between the plates to change.

Fig : Forms of Capacitive sensing element For the displacement changing the plate separation (Fig. (a)), if the separation d is increased by a displacement x then the capacitance becomes:

C - ΔC =

ε r εo A d+x

4. Differential transformers The linear variable differential transformer, generally referred to by the abbreviation LVDT, consists of three coils symmetrically spaced along an insulated tube. The central coil is the primary coil and the other two are identical secondary coils which are connected in series such a way that their outputs oppose each other. A magnetic core is moved through the central tube as a result of displacement being monitored.

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Fig : LVDT When there is an alternating voltage input to the primary coil, alternating emf’s are introduced in the secondary coils. With the magnetic core central, the amount of magnetic material in each of the secondary coils is the same. Thus the emf’s induced in each coil are the same. Since they are so connected their outputs oppose each other, the net result is zero output. However, when the core is displaced from the central position there is a greater amount of magnetic core in one coil than the other, e.g. more in secondary coil 2 than coil 1. The result is that a greater e.m.f. is induced in one coil than the other. There is then a net output from the two coils. Since greater displacement means even more core in one coil than the other, the output, the difference between the two emf’s increases the greater the displacement being monitored.

Fig : LVDT output 19


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The emf induced in a secondary coil by a changing current i in the primary coil is given by:

e=M

di dt

Where M is the mutual inductance, its value depending on the number of turns on the coils and the ferromagnetic core. Thus, for a sinusoidal input current of i = I sinωt to the primary coil, the emf’s induced in the two secondary coils 1 and 2 can be represented by:

v1 = k1 sin(ωi - Φ) and v2 = k 2 sin(ωi - Φ) where the values of k1, k2 and φ depend on the degree of coupling between the primary and secondary coils for a particular core position. φ is the phase difference between the primary alternating voltage and the secondary alternating voltages. Because the two outputs are in series, their difference is the output :

Output voltage = v1 -v2 = (k1 -k 2 ) sin (ωt-Φ) when the core is equally in both the coils, k1 equals k2 and so the output voltage is zero. When the core is more in 1 than in 2 we have k1 > k2 and:

Output voltage = (k1 -k 2 ) sin (ωt-Φ) when the core is more in 2 than in 1 we have k1 < k2. A consequence of k1 being less than k2 that there is a phase change of 1800 in the output when the core moves from more in 1 to more in 2. Thus:

Output voltage = -(k1 -k 2 ) sin (ωt-Φ)

= (k 2 -k1 ) sin [ ωt + (π-Φ)]

A rotary variable differential transformer (RVDT) can be used for the measurement of rotation; it operates on the same principle as that of an LVDT. The core is a cardioid-shaped piece of magnetic material and rotation causes more of it to pass into one secondary coil than the other. The range of operation is typically ± 400 degree with a linearity error of about ± 0.5% of the range.

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VELOCITY & MOTION The following are the examples of sensors that can be used to monitor linear angular velocities and detect motion. The application of motion detectors includes security systems used to detect intruders and interactive toys and appliances, e.g. the cash machine screen which becomes active when you get near to it. 1. Incremental encoder The incremental encoder described in the previous section can be used for a measurement as angular velocity, the number of pulses produced per second being determined. 2. Tachogenerator The tachogenerator is used to measure angular velocity. One form, the variable reluctance tachogenerator, consists of a toothed wheel of ferromagnetic material which is attached to the rotating shaft (in fig.). A pick-up coil is wound on a permanent magnet. As the wheel rotates, so the teeth move past the coil and the air gap between the coil and the ferromagnetic material changes. We have a magnetic circuit with an air gap which periodically changes. Thus the flux linked by a pick-up coil changes. The resulting cyclic change in the flux linked produces an alternating e.m.f in the coil.

Fig : Variable Reluctance Tachogenerator If the wheel contains n teeth and rotates with an angular velocity ω, then the flux change with time for the coil can be considered to be of the form:

Φ = Φ 0 + Φ a cos nωt where Ф0 is the mean value of the flux and Фa the amplitude of the flux variation. The induced e.m.f 'e' in the N turns of the pick-up coils is thus:

e=-N 21

dΦ d = - N (Φ 0 + Φ a cos nωt ) = N Φ a nω sin nωt dt dt


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FORCE A spring balance is an example of a force sensor in which a force, a weight, is applied to the scale pan and causes a displacement, i.e. the spring stretches. The displacement is then a measure of the force. Forces are commonly measured by the measurement of displacements, the following method illustrating this. 1. Strain gauge load cell A very commonly used form of force-measuring transducer is based on the use of electrical resistance strain gauges to monitor the strain produced in some member when stretched, compressed or bent by the application of the force. The arrangement is generally referred to as a load cell. Figure shows an example of such a cell.

Fig : Strain gauge load cell This is a cylindrical tube to which strain gauges have been attached. When forces are applied to the cylinder to compress it, then the strain gauges give a resistance change which is a measure of the strain and hence the applied forces. Since temperature also produces a resistance change, the signal conditioning circuit used has to be able to eliminate the effects due to temperature. Typically such load cells are used for forces up to about 10 MN, the non-linearity error being about ± O.03 % of full range, hysteresis error ± O.02 % of full range and repeatability error ± 0.02 % of full range. Strain gauge load cells based on the bending of a strain-gauged metal element tend to be used for smaller forces, e.g. with ranges varying from 0 to 5 N up to 0 to 50 kN. Errors are typically a non-linearity error of about ± 0.03 % of full range, hysteresis error ± 0.02 % of full range and repeatability error ± 0.02 % of full range. 22


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FLUID PRESSURE Many of the devices used to monitor fluid pressure in industrial processes involve the monitoring of the elastic deformation of diaphragms, capsules, bellows and tubes. The types of pressure measurements that can be required are: absolute pressure where the pressure is measured relative to zero-pressure, i.e. a vacuum, differential pressure where a pressure difference is measured and gauge pressure where the pressure is measured relative to the barometric pressure.

Fig : Diaphragms: (a) flat, (b) corrugated For a diaphragm (Fig.(a) and (b)), when there is a difference in pressure between the two sides then the centre of the diaphragm becomes displaced. Corrugations in the diaphragm result in a greater sensitivity. This movement can be monitored by some form of displacement sensor, e.g. a strain gauge, as illustrated in figure given below. A specially designed strain gauge is often used, consisting of four strain gauges with two measuring the strain in a circumferential direction while two measure strain in a radial direction. The four strain gauges are then connected to form the arms of a Wheatstone bridge. While strain gauges can be stuck on a diaphragm, an alternative is to create a silicon diaphragm with the strain gauges as specially doped areas of the diaphragm.

Fig : Diaphragm Pressure Gauge

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TEMPERATURE Changes that are commonly used to monitor temperature are the expansion or contraction of solids, liquids or gases, the change in electrical resistance of conductors and semiconductors and thermoelectric e.m.f.s. The following are some of the methods that are commonly used with temperature control systems. 1. Bimetallic strips This device consists of two different metal strips bonded together. The metals have different coefficients of expansion and when the temperature changes the composite strip bends into a curved strip, with the higher coefficient metal on the outside of the curve. This deformation may be used as a temperature-controlled switch, as in the simple thermostat which was commonly used with domestic heating systems. The small magnet enables the sensor to exhibit hysteresis, meaning that the switch contacts close at a different temperature from that at which they open.

Fig : Bimetallic Thermostat 2. Resistance temperature detectors (RTDs) The resistance of most metals increases, over a limited temperature range, in a reasonably linear way with temperature (Fig.).

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Fig : Variation of Resistance with temperature for metals For such a linear relationship:

Rt = Ro (l + αt) where Rt is the resistance at a temperature t0 C, Ro the resistance at 0°C and α a constant for the metal termed the temperature coefficient of resistance. Resistance temperature detectors (RTDs) are simple resistive elements in the form of coils of wire of such metals as platinum, nickel or nickel-copper alloys; platinum is the most widely used. Thin film platinum elements are often made by depositing the metal on a suitable substrate, wirewound elements involving a platinum wire held by a high temperature glass adhesive inside a ceramic tube. Such detectors are highly stable and give reproducible responses over long periods of time. They tend to have response times of the order of 0.5 to 5 s or more. 3. Thermistors Thermistors are small pieces of material made from mixtures of metal oxides, such as those of chromium, cobalt, iron, manganese and nickel. These oxides are semiconductors. The material is formed into various forms of element, such as beads, discs and rods (in Fig.).

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Fig : Thermistor The resistance of conventional metal-oxide thermistors decreases in a very nonlinear manner with an increase in temperature, as illustrated in Figure.

Fig : Variation of Resistance with temperature for a typical thermistor Such thermistors having negative temperature coefficients (NTC). Positive temperature coefficient (PTC) thermistors are, however, available. The change in resistance per degree change in temperature is considerably larger than that which occurs with metals. The resistance-temperature relationship for a thermistor can be described by an equation of the form

R t = K eβ/t where Rt is the resistance at temperature t, with K and β being constants. Thermistors have many advantages when compared with other temperature sensors. They are rugged and can be very small, so enabling temperatures to be monitored at virtually a point. Because of their small size they respond very rapidly to changes in temperature. They give very large changes in resistance per degree change in temperature. Their main disadvantage is their non-linearity. 26


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INPUTTING DATA BY SWITCHES Mechanical switches consist of one or more pairs of contacts which can be mechanically closed or opened and in doing so make or break electrical circuits. Thus 0 or 1 signals can be transmitted by the act of opening or closing a switch. Mechanical switches are specified in terms of their number of poles and throws. Poles are the number of separate circuits that can be completed by the same switching action and throws are the number of individual contacts for each pole. Figure (a) shows a single pole-single throw (SPST) switch, Figure (b) a single pole-double throw (DPDT) switch and Figure (c) a double pole-double throw (DPDT) switch.

Fig : Switches (a) SPST, (b) SPDT, (c) DPDT 1. Debouncing A problem that occurs with mechanical switches is switch bounce. When a mechanical switch is switched to close the contacts, we have one contact being moved towards the other. It hits the other and, because the contacting elements are elastic, bounces. It may bounce a number of times (Fig.) before finally settling to its closed state after, typically, some 20 ms. Each of the contacts during this bouncing time can register as a separate contact. Thus, to a microprocessor, it might appear that perhaps two or more separate switch actions have occurred. Similarly, when a mechanical switch is opened, bouncing can occur. To overcome this problem either hardware or software can be used.

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Fig : Switch bounce on closing With software, the microprocessor is programmed to detect if the switch is closed and then wait, say, 20 ms. After checking that bouncing has ceased and the switch is in the same closed position, the next part of the program can take place. The hardware solution to the bounce problem is based on the use of a flip-flop. Figure shows a circuit for debouncing a SPDT switch which is based on the use of a SR flipflop.

Fig : Debouncing a SPDT switch As shown, we have S at 0 and R at 1 with an output of 0. When the switch is moved to its lower position, initially S becomes 1 and R becomes 0. This gives an output of 1. Bouncing in changing S from 1 to 0 to 1 to 0, etc. gives no change in the output. Such a flip-flop can be derived from two NOR or two NAND gates. A SPDT switch can be debounced by the use of a D flip-flop. The output from such a flip-flop only changes when the clock signal changes. Thus by choosing a clock period which is greater than the time for which the bounces last, say 20 ms, the bounce signals will be ignored. 28


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SIGNAL CONDITIONING The output signal from the sensors of a measurement system has generally to be processed in some way to make it suitable for the next stage of the operation. The signal may be, for e.g., too small and have to be amplified, contain interference which has to be removed, be non-linear and require linearization, be analogue and have to be made digital, be digital and have to be made analogue, be a resistance change and have to be made into a current change, be a voltage change and have to be made into a suitable size current change, etc. All these changes can be referred to as signal conditioning. For example, the output from a thermocouple is a small voltage, a few millivolts. A signal conditioning module might then be used to convert this into a suitable size current signal, provide noise rejection, linearization, and cold junction compensation (i.e. compensating for the cold junction not being at 00C). The signal handled by microprocessors need to be conditioned for effective processing. The signals from the sensors/transducers may be non linear, noise filled or weak in magnitude.

Such signals should be modified and magnified to suit the

specification rating of the microprocessor and micro controllers. There may be need to convert the signal from one form to another. These signal conditioning functions are most

commonly,

done

using

operational

amplifiers

of

various

types.

The

microprocessors are to be protected from excessive voltage and reverse polarity of the signal proper electronic protection circuit. The signal conditioning and protection are accomplished by the interface systems inserted between sensors/actuators and the microprocessors. Certain parameters like speed, position, force etc., are sensed before measurement, to give some form of signal to be processed. Such signal before being input to the next stage of processing may have to be conditioned for under lying reasons. The signal can be weak and has to be magnified. It may have interface as a noise which is to be filtered. The non-linear signal has to be manipulated. The signal may have to be converted for the change in resistance and voltage. Analogue form may be required in the digital form. The digital form may need conversion to analogue form. 29


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Hence the signal which may be weak, non-linear, noise filled, and certain form is transformed to an amplified signal, linear, noise free and some other required form through an amplifier, signal manipulator, a filter and a converter before being supplied to a processor is known as “signal conditioning”. CONCEPT OF SIGNAL CONDITIONING

Fig : Signal conditioning concept INTERFACING WITH A MICROPROCESSOR

Input and output devices are connected to a microprocessor system through ports. The term interface is used for the item that is used to make connections between devices and a port. Thus there could be inputs from sensors, switches and keyboards and output to displays and actuators. The simplest interface could be just a piece of wire. However, the interface often contains signal conditioning and protection, the protection being to prevent damage to the microprocessor system. For example inputs needing to be protected against excessive voltages or signals of the wrong polarity.

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Microprocessor requires input s which are digital, thus a conversion of analogue to digital signal is necessary if the output from a sensor is analogue. However, many sensors generates only a very small signal, perhaps a few mill volts. Such a signal is insufficient to be directly converted from analogue to digital without first being amplified. Signal conditioning might also be needed with digital signals to improve their quality. The interface may thus contain a number of elements. There is also the output from a microprocessor, perhaps to operate an actuator. A suitable interface is also required here. The actuator might require an analogue signal and so the digital output from the microprocessor needs converting to an analogue signal. There can also be a need for protection to stop any signal becoming inputted back through the output port to damage the microprocessor. NEED FOR SIGNAL CONDITIONING

The signal required by the microprocessor or the microcontroller cannot be in the raw form from the input devices like sensors. The signals need transformation which is accomplished by the interface systems, connected between input devices and processors, and processor and output devices. The need for conditioning signal arises for the following aspects: The processor is to be protected from the erratic input signals of excessive voltage and wrong polarity. The protection from the sudden output signal. The processor can process the signal that is in the compatible form with the system characteristics. The processing system can receive the signals that have ratings suitable to their specifications. The processors are capable of handling noise free and disturbance free signals to perform correctly. The non-linearity in the signals output from the input devices needed to be manipulated to transform into linear signals. The interface systems between input devices like sensors switches, keyboards, and the microprocessors is first being amplified, then being converted from analogue form to digital form and then protected for excessive voltage and wrong polarity.

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OPERATIONAL AMPLIFIERS The Operational Amplifier is a high gain d.c. amplifier, the gain typically being of the order of 100, 000 or more, that is supplied as an integrated circuit on a silicon chip. By definition, operational amplifier is a high gain d.c. device that magnifies the input signal (current or voltage) up to an order of 106 or more. It is supplied as a silicon chip with integrated circuit in it. A typical chip with op-amp is shown in fig. The op-amp has mainly two inputs, known as the inverting input (-) and the non-inverting input (+). The types of inputs to an operational amplifier are: 1.

Negative inverting input

2.

Positive non-inverting input

3.

Negative voltage supply

4.

Positive voltage supply

5.

Two offset null inputs for extracting non-ideal behaviors from op-amps.

Fig : Operational Amplifier Depending on the inputs and connections of impedance, the op-amps perform as: • Voltage to current or current to voltage converter • The signal adder • Signal magnifier • Non-linear to linear manipulator • A filter for noise reduction 32


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1. INVERTING AMPLIFIER

The input is taken to the inverting input through a resistor R1 with the noninverting input being connected to ground. A feedback path is provided from the output, via the resistor R2 to the inverting input. The operational amplifier has a voltage gain of about 100 000 and the change in out put voltage is limited to about +_ 10 V . The input voltage then must be between +0.0001 V and -0.0001 V. This is virtually zero and so point X is at virtually earth potential. For this reason it is called a virtual earth. The potential difference across R1 is (Vin -Vx). Hence, for an ideal operational amplifier with an infinite gain, and hence Vx = 0, the input potential Vin can be considered to be across R1.

Thus

Vin = I 2 R 1

Fig: Inverting amplifier The operational amplifier has very high impedance between its input terminals; for a 741 about 2 MΩ. Thus virtually no current flows through X into it. For an ideal operational amplifier the input impedance is taken to be infinite and so there is no current flow through X. Hence the current I1 through R1 must be the current through R2. The potential difference across R2 is (Vx - Vout) and thus, since Vx is zero for the ideal amplifier, the potential difference across R2 is –Vout.

Thus

- Vout = I 2 R 2

Dividing these two equations:

Voltage gain of circuit =

Vout R =- 2 Vin R1

Thus the voltage gain is determined solely by the relative values of R1 and R2. The negative sign indicates that the output is inverted, i.e. 1800 out of phase, with respect to the input.

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2. NON-INVERTING AMPLIFIER

The output can be considered to be taken from across a potential divider circuit consisting of R1 in series with R2. The voltage Vx is then the fraction R1/ (R1+R2) of the output voltage.

Vx =

R1 Vout (R 1 + R 2 )

Since there is virtually no current through the operational amplifier between the two inputs there can be virtually no potential difference between them. Thus, with the ideal operational amplifier, we must have Vx =Vin. Hence

Voltage gain of circuit =

Vout (R 1 + R 2 ) R = = 1+ 2 Vin R1 R1

Fig : Non- inverting amplifier 3. SUMMING AMPLIFIER

As with the inverting amplifier, X is a virtual earth. Thus the sum of the currents entering X must equal that leaving it. Hence

I = IA + IB + IC But IA = VA/RA, IB = VB/RB and IC = VC/RC. Also we must have the same current I passing through the feedback resistor. The potential difference across R2 is (VX – Vout). Hence, since Vx can be assumed to be zero, it is –Vout and so I = -Vout/R2. Thus 34


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-

Vout V V V = A + B + C R2 RA RB RC

The output is thus the scaled sum of the inputs, i.e.

R  R R Vout = -  2 VA + 2 VB + 2 Vc  Rc RB  RA  If RA= RB=RC=R1 then

Vout = -

R1 (VA + VB + VC ) R2

Fig : Summing amplifier

FILTERING The term filtering is used to describe the process of removing a certain band of frequencies from a signal and permitting others to be transmitted. The range of frequencies passed by a filter is known as the pass band, the range not passed as the stop band and the boundary between stopping and passing as the cut-off frequency. Filters are classified according to the frequency ranges they transmit or reject. A low-pass filter has a pass band which allows all frequencies from 0 up to some frequency to be transmitted.

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Fig : Characteristics of ideal low pass filter A high pass filter has a pass band which allows all frequencies from some value up to infinity to be transmitted.

Fig : Characteristics of ideal high pass filter A band pass filter allows all the frequencies within a specified band to be transmitted.

Fig : Characteristics of ideal band pass filter A band stop filter stops all frequencies with a particular band from being transmitted.

Fig : Characteristics of ideal band stop filter In all cases the cut-off frequency is defined as being that at which the output voltage is 70.7% of that in the past band. The term attenuation is used for the ratio of input and output powers, this being written as the ratio of the logathirm of the ratio and so gives the attenuation in units of bels. Since this is a rather large unit, decibels (dB) are 36


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used and then attenuation in dB = 10 lg (input power /output power). Since the power through an impedance is proportional to the square of the voltage the attenuation in dB = 20 1g (input voltage /output voltage). The output voltage of 70.7% of that in the pass band is thus an attenuation of 3dB. The term passive is used to describe a filter made up using only resistors, capacitors and inductors, the term active being used when the filter also involves an operational amplifier. Passive filters have the disadvantage that the current that is drawn by the item that follows can change the frequency characteristics of the filter. This problem does not occur with an active filter. Low-pass filters are very commonly used as a part of signal conditioning. This is because most of the useful information being transmitted is low frequency. Since noise tends to occur at higher frequencies, a low-pass filter can be used to block it off. Thus a low-pass filter might be selected with a cut-off frequency of 40 Hz, thus blocking off any inference signals from the A.C mains supply and noise in general. Low pass passive filters are characterized to operate in the lower frequencies and are generally used to filter the noise occurring in the higher frequencies as in case of interferences in an a.c. mains supply. They are termed passive because they make use of only resistors, inductors and capacitors to make the filters.

Fig : Low-pass passive filter Low pass active filters: An integrating operational amplifier using a capacitor in its feedback loop acts as a low pass active filter that removes noise in the high frequency range. Figure shows the basic form of low pass filter.

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Fig : Low-pass active filter High pass passive filters: Passive high pass filter that filters the noises at lower frequencies and transmits of higher frequencies is shown in figure. Two capacitors arranged in series between input and output with a parallel inductor functions as high pass passive filter.

Fig : Passive high pass filter A high pass active filter using operational amplifier is shown in fig. The feedback output is given to both inverting and non-inverting inputs through a resistor. Two capacitors in series with inverting input do the filtering of noise at high frequencies.

Fig : High pass active filter 38


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MULTIPLEXERS There are situations common in practical circuits that a processor has to receive and process in sequence the data from multiple sources. A multiplexer is a circuit that is able to have inputs of data from a number of sources and then, by selecting an input channel, give an output from just one of them. The multiplexer enables to share single data channel between multiple input sources. In applications where there is need for measurements to be made at a number of different locations, rather than use a separate ADC and microprocessor for each measurement, a multiplexer can be used to select each input in turn and switch it through a single ADC and microprocessor. The multiplexer is essentially an electronic switching device enables each of the inputs to be sampled in turn.

Fig : Multiplexer There are two types of multiplexers: Time Division Multiplexing (TDM) Frequency Division Multiplexing (FDM) 1. In Time Division Multiplexing (TDM), each of the data sources is connected to data channel transmitting the data. In this the data is made available to the processor at different time. Often there is a need for a number of peripheral devices to share the same input/output lines from a microprocessor. So that each peripheral can be supplied with different data it is necessary to allocate each a particular time slot during which data is transmitted. This is termed time division multiplexing. When large data slowly varying with time TDM is useful. The examples of data source for measurement are pressure, temperature and static strain. These data have discrete values in series useful to TDM. Figure shows the time division multiplexing. 39


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Fig : TDM concept 2. The Frequency Division Multiplexer (FDM) is particularly suited for analogue signals. In this each data source is modulated to subcarrier frequency. All the subcarriers are combined in a mixer and modulated to higher frequency carriers. Then the information is transmitted to the receiver. Receiver after demodulation separates into such carriers and filtered to contain the individual information data. This uses both amplitude modulation systems. A block diagram of operation of FDM is shown in figure.

Fig : FDM concept

DATA ACQUISITION

- -

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Fig : DAQ System

- -

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DATA ACQUISITION SYSTEMS

Automated data acquisition systems can take the form of a dedicated instrument termed a data logger or a personal computer using plug-in DAQ boards.

Data loggers Figure shows the basic elements of a data logger. Such a unit can monitor the inputs from a large number of sensors. Inputs from individual sensors, after suitable signal conditioning, are fed into the multiplexer. The multiplexer is used to select one signal which is then fed, after amplification, to the analogue-to-digital convertor. The digital signal is then processed by a microprocessor. The microprocessor is able to carry out simple arithmetic operations, perhaps taking average of a number of measurements. The output from the system might be displayed on a digital meter that indicates the output and channel number, used to give a permanent record with a printer, stored on a floppy disc or transferred to perhaps a computer for analysis.

Fig : Data logger system

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PULSE MODULATION A problem that is often encountered with dealing with the transmission of lowlevel d.c. signals from sensors is that the gain of an operational amplifier used to amplify them may drift and so the output drifts. This problem can be overcome if the signal is a sequence of pulses rather than a continuous-time signal. One way this conversion can be achieved is by chopping the d.c. signal in the way suggested in fig. The output from the chopper is a chain of pulses, the heights of which are related to the d.c. level of the input signal. This process is called pulse amplitude modulation. After amplification and any other signal conditioning, the modulated signal can be demodulated to give a d.c. output. With pulse amplitude modulation, the height of the pulses is related to the size of the d.c. voltage.

Fig : Pulse Amplitude Modulation An alternative to this is pulse width modulation (PWM) where the width, i.e. duration, of a pulse rather than its amplitude depends on the size of the voltage.

Fig : Pulse Width Modulation 43


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DISPLAYS Measurement systems consist of three elements: sensor, signal conditioner and display or data presentation element. There are a very wide range of elements that can be used for the presentation of data. Traditionally they have been classified into two groups: indicators and recorders. Indicators give an instant visual indication of the sensed variable while recorders record the output signal over a period of time and give automatically a permanent record. The recorder will be the most appropriate choice if the event is high speed or transient and cannot be followed by an observer, or there are large amounts of data, or it is essential to have a record of the data. Both indicators and recorders can be subdivided into two groups of devices, analogue and digital. An example of an analogue indicator is a meter which has a pointer moving across a scale, while a digital meter would be just a display of a series of numbers. An example of an analogue recorder is a chart recorder which has a pen moving across a moving sheet of paper, while a digital recorder has the output printed out on a sheet of paper as a sequence of numbers. Data Presentation Elements The most commonly used examples of data presentation elements are 1. Analogue and digital meters The moving coil meter is an analogue indicator with a pointer moving across a scale. The basic instrument movement is a d.c. micro ammeter with shunts, multipliers and rectifiers being used to convert it to other ranges of direct current and measurement of alternating current, direct voltage, and alternating voltage. With alternating current and voltages, the instrument is restricted to between about 50 Hz and 10 kHz. The accuracy of such a meter depends on a number of factors, among which are temperatures, the presence of nearby of magnetic fields or ferrous materials, the way the meter is mounted, bearing friction, inaccuracies in scale marking during manufacture, etc. In addition there are errors involved in reading the meter, e.g. parallax errors when the position of the pointer against the scale is read from an angle other than directly at right angles to the scale and errors arising from estimating the position of the pointer between scale markings. The overall accuracy is generally of the order of ± 0.1 to ± 5%. The time taken for a moving coil meter to reach a steady deflection is typically in the region of a few seconds. The low resistance of the meter can present loading problems. 44


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The digital voltmeter gives its reading in the form of a sequence of digits. Such a form of display eliminates parallax and interpolation errors and can give accuracies as high as ± 0.005%. The digital voltmeter is essentially just a sample and hold unit feeding an analogue-to-digital converter with its output counted by a counter (in fig.).

Fig : Principle of digital voltmeter It has a high resistance, of the order of 10 MΩ, and so loading effects are less likely than with the moving coil meter with its lower resistance. Thus, if a digital voltmeter specification includes the statement ‘sample rate approximately 5 readings per second’ then this means that every 0.2 s the input voltage is sampled. It is the time taken for the instrument to process the signal and give a reading. Thus, if the input voltage is changing at a rate which results in significant changes during 0.2 s then the voltmeter reading can be in error. A low cost digital voltmeter has typically a sample rate of 3 per second and an input impedance of 100 MΩ. 2. Analogue chart recorders There are three basic types of analogue chart recorders: the direct reading recorder, the galvanometric recorder and the potentiometric or closed-loop recorder. The data can be recorded on paper by fibre-tipped ink pens, by the impact of a pointer pressing a carbon ribbon against the paper, by the use of thermally sensitive paper which changes color when a heated pointer moves across it, by a beam of ultraviolet light falling on paper sensitive to it and by a tungsten wire stylus moving across the surface of specially coated paper, a thin layer of aluminium over coloured dye, and the electrical discharge removing the aluminium and exposing the dye. The direct reading recorder (in Fig.) has a pen or stylus directly moved by the displacement action of the measurement system. For temperature measurement this might be the displacement of a bimetallic strip, for a pressure gauge the displacement of a Bourdon tube. A circular chart is used and rotates at a constant rate, typically one revolution in 12 hours, 24 hours or 7 days. The pen moves along curved radial lines and 45


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thus paper with curved lines has to be used for the plotting. This makes interpolation difficult. Simultaneous recording with up to four separate variables is possible with four separate pens. The instrument is fairly robust with accuracy of the order of ± 0.5% of the full-scale deflection.

Fig : Direct reading recorder The galvanometric type of chart recorder (Fig.) works on the same principle as the moving coil meter movement. The coil is suspended between two fixed points by a suspension wire. When a current passes through the coil a torque acts on it, causing it to rotate and twist the suspension. The coil rotates to an angle at which the torque is balanced by the opposing torque resulting from the twisting of the suspension. The rotation of the coil results in a pen being moved across a chart. If R is the length of the pointer and θ the angular deflection of the coil, then the displacement y of the pen is y = R sin θ. Since θ is proportional to the current i through the coil, then y is proportional to sin i. This is a non-linear relationship. However, if the angular deflections are restricted to less than ±100, then the relationship is reasonably linear, the non-linearity error being less than 0.5%. A greater problem is, however, the fact that the pen moves in an arc rather than a straight line and thus curvilinear paper (Fig.) has to be used for the plotting. With such forms of chart there are difficulties in interpolation for points between the lines.

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Fig : Galvanometric recorder 3. Printers Printers provide a record of data on paper. There are a number of versions of such printers: the dot matrix printer, the ink/bubble jet printer and the laser printer. The dot matrix printer has a print head (Fig.) which consists of either 9 or 24 pins in a vertical line. Each pin is controlled by an electromagnet which when turned on propels the pin onto the inking ribbon. This transfers a small blob of ink onto the paper behind the ribbon. A character is formed by moving the print head in horizontal lines back-and-forth across the paper and firing the appropriate pins.

Fig : Dot matrix print head mechanism 47


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The ink jet printer uses a conductive ink which is forced through a small nozzle to produce a jet of very small drops of ink of constant diameter at a constant frequency. With one form a constant stream of ink passes along a tube and is pulsed to form fine drops by a piezoelectric crystal which vibrates at a frequency of about 100 kHz (in fig.).

Fig : Producing a stream of drops Another form uses a small heater in the print head with vaporized ink in a capillary tube, so producing gas bubbles which push out drops of ink (shown in figure given below).

Fig : Principle of the bubble jet In one printer version each drop of ink is given a charge as a result of passing through a charging electrode and the charged drops are deflected by passing between plates between which an electric field is maintained; in another version a vertical stack of nozzles is used and each jet is just switched on or off on demand. Inkjet printers can give colour prints by the use of three different colour ink jet systems. The fineness of the drops is such that prints can be produced with more than 600 dots per inch.

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MEASUREMENT SYSTEMS The following examples illustrate some of the points involved in the design of measurement systems for particular applications.

1. Load cell for use as a link to detect load lifted A link-type load cell has four strain gauges attached to its surface and can be inserted in between the cable lifting a load and the load to give a measure of the load being lifted. Two of the strain gauges are in the longitudinal axis direction and two in a transverse direction. When the link is subject to tensile forces, the axial gauges will be in tension and the transverse gauges in compression. Suppose we have the design criteria for the load cell of sensitivity such that there is an output of about 30 mV when the stress applied to the link is 500 MPa. We will assume the strain gauges may be assumed to have gauge factor of 2.0 and resistance of 100Ω.

Fig : Load cell When a load F is applied to the link then, since the elastic modulus E is stress/strain and stress is force per unit area, the longitudinal axis strain εl is F/AE and the transverse strain εt is –υF/AE, where A is the cross-sectional area and υ is Poisson’s ratio for the link material. The responses of the strain gauges to the strain are

δ R1

δ R4

GF R1 R4 AE δ R3 δ R2 -ν GF = = G ε2 = R3 R2 AE 49


=

= G ε1 =

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The output voltage from the Wheatstone bridge is given by

Vo =

Vs R 1 R 4 (R 1 + R 2 ) (R 3 + R 4 )

 δ R1 δ R 2 δ R 3 δ R 4    + R R R R 2 3 4   1

With R1 = R2 = R3 = R4 = R, and with δR1 = δR4 and δR2 = δR3,

then

Vs (δ R 1 − δ R 2 ) 2R V GF (1 + ν ) = s 2AE

Vo =

2. Temperature alarm system A measurement system is required which will set off an alarm when the temperature of the liquid rises above 400 C. The liquid is normally at 300 C. The output from the system must be a 1V signal to operate the alarm. Since the output is to be electrical and the reasonable speed of response is likely to be required, an obvious possibility is an electrical response element. To generate a voltage output the resistance element could be used with a Wheatstone bridge .The output voltage will probably be less than 1V for a change from 30 to 400 C but a differential amplifier could be used to enable the required voltage to be obtained. A comparator can then be used to compare the value with the set of value for the alarm. Suppose a nickel element is used. Nickel has a temperature of coefficient of resistance of 0.0067 /K. Thus if the resistance element is taken as being 100 Ω at 00 C then its resistance at 300 C will be

R 30 = R 0 (1 + at) = 100 (1 + 0.0067× 30) = 120.1 Ω and at 400 C

R 40 = 100 (1 + 0.0067× 40) = 126.8 Ω Thus there is a change in resistance of 6.7 Ω. If this element forms one arm of a Whetstone bridge which is balanced at 300 C, then the output voltage V0 is given by

δ Vo =

Vs δ R 1 R1 + R 2

With the bridge balanced at 300 C and, say, all the arms the same value and a supply voltage at 4 V, then

δ Vo =

50

4 X 6.7 = 0.109 126.8 + 120.1


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CALIBRATION Calibration consists of comparing the output of a measurement system and its sub systems against standards of known accuracy. The standards may be other instruments which are kept specially for calibration duties or some means of defining standard values. The relationship between the calibration of an instrument in everyday use and national standards is likely to be: 1. National standards are used to calibrate standards for calibration centers. 2. Calibration centre standards are used to calibrate standards for instrument manufacturers. 3. Standardized instruments from instrument manufacturers are used to provide in-company standards. 4. In-company standards are used to calibrate process instruments. The following are some examples of calibration procedures that must be used incompany: 1.

Voltmeters : These can be checked against standard voltmeters or standard cells giving standard e.m.f.s.

2. Ammeters : These can be checked against standard ammeters. 3.

Gauge factor of strain gauges : This can be checked by taking a sample of gauges from a batch and applying measured strains to them when mounted on some test piece. The resistance changes can be measured and hence the gauge factor computed.

4. Wheat stone bridge circuits : The output from a wheat stone bridge can be checked when a standard resistance is introduced into one of the arms. 5. Load cells : For low-capacity load cells, dead-weight loads using standard weights can be used. 6. Pressure sensors : Pressure sensors can be calibrated by using a dead-weight tester. The calibration pressures are generated by adding standard weights W to the piston tray. After the weights are placed on the tray, a screw-driven plunger is forced into the hydraulic oil in the chamber to lift the piston weight assembly. The calibration pressure is then W/A, where A is the cross-sectional area of the piston. Alternatively the dead-weight tester can be used to calibrate a pressure gauge and this gauge can be used for the calibration of other gauges. 51


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PNEUMATIC AND HYDRAULIC ACTUATION SYSTEMS Pneumatic signals are often used to control final control elements, even when the control system is otherwise electrical. This is because such systems can be used to actuate large valves and other high power control devices and so move significant loads. The main drawback with pneumatic systems is, however, the compressibility of air. Hydraulic signals can be used for even higher power control devices but are more expensive than pneumatic systems and there are hazards associated with oil leaks which do not occur with air leaks. Power supplies With a hydraulic system, pressurized oil is provided by a pump driven by an electric motor. The pump pumps oil from a sump through a non-return valve and an accumulator to the system, from which it returns to the sump. Figure illustrates the arrangement.

Fig : Hydraulic power supply A pressure relief valve is included, this being to release the pressure if it rises above a safe level, the non-return valve is to prevent the oil being back driven to the pump and the accumulator is to smooth out any short-term fluctuations in the output oil pressure. Essentially the accumulator is just a container in which the oil is held under pressure against an external force, figure showing the most commonly used form which is gas pressurized and involves gas within a bladder in the chamber containing the hydraulic fluid, an older type involved a spring-loaded piston. If the oil pressure rises then the bladder contracts, increases the volume the oil can occupy and so reduces 52


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the pressure. If the oil pressure falls, the bladder expands to reduce the volume occupied by the oil and so increase its pressure.

Fig : Accumulator With a pneumatic power supply (in fig.) an electric motor drives an air compressor. The air inlet to the compressor is likely to be filtered and via a silencer to reduce the noise level. A pressure relief valve provides protection against pressure in the system rising above a safe level. Since the air compressor increases the temperature of the air there is likely to be a cooling system and to remove contamination and water from the air a filter with water trap. An air receiver increases the volume of air in the system and smoothes out any short-term pressure fluctuations.

Fig : Pneumatic power supply 53


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VALVES To affect various functions in a hydraulic power pack to control the operations of the actuators the hydraulic valves are used. The following subjective aspects are needed to be controlled in the hydraulic circuits according to the application requirements. §

The pressure control.

§

The flow control.

§

The direction control. The system pressure should not exceed certain limit for the safety of the pump.

The different branches in the circuit need different pressure in the hydraulic oil supplied to the actuators. The pressure should be retained in certain actuator function without exhibiting drift in the position. The actuators are to be sequenced by pressure control to operate in a required order. The relief, regulation, balancing and sequencing are the pressure control aspects carried out by pressure control valves. The amount of oil specified by volumetric flow rate reaching the actuator is regulated by the flow control valves. For an actuator of given geometrical configuration the speed of actuation has a direct bearing on the rate of flow of oil. The position of flow control valve in different segment of the circuit executes different flow control action needed for the suitable application. The actuators (linear or rotary) are to be reversed in operation or stopped at certain stage for idling. The reversal in direction is effected by the direction control valves. Different aspects and duty, different configurations in directional valve exist. DIRECTIONAL CONTROL VALVES

Pneumatic and hydraulic systems use directional control valves to direct the flow of fluid through a system. They are not intended to vary the rate of flow of fluid, but are either completely open or completely closed, i.e. on/off devices. Such on/off valves are widely used to develop sequenced control systems. They might be activated to switch the fluid flow direction by means of mechanical, electrical or fluid pressure signals. A common type of directional control valve is the spool valve. A spool moves horizontally within the valve body to control the flow. The fig shows a particular form. In (a), the air supply is connected to port 1 and port 3 is closed. Thus the device connected to port 2 can be pressurized. When the pool is moved to the left, as in (b), the air supply is cut off and port 2 is connected to port 3. Port 3 is a vent to the atmosphere and so the air pressure in the system attached to port 2 is vented. Thus the movement of the spool has allowed the air to firstly flow into the system and then be reversed and 54


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flow out of the system. Rotary spool valves have a rotating spool which, when it rotates, opens and closes ports in a similar way.

Fig : Spool Valve Another common form of directional control valve is the poppet valve. The figure shows 1 form. This valve is normally in the closed condition, there being no connection between port1 to which the pressure supply is connected and port 2 to which the system is connected. In poppet valves, balls, discs or cones are used in conjunction with valve seats to control the flow. When the push button is depressed, the ball is pushed out of its seat and flow occurs as a result of port 1 being connected to port 2. When the button is released, the spring forces the ball back up against its seat & so closes off the flow.

Fig : Poppet Valve 55


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ACTUATORS Actuation systems are the elements of control systems, which are responsible for transforming the output, of a microprocessor or control system into a controlling action on a machine or a device. Thus, or e.g., we might have an electrical output from the controller which has to be transformed into a linear motion to move a lode. Another e.g. might be where an electrical output from the controller has to be transformed into an action which controls the amount of liquid passing along a pipe. DEFINITION OF ACTUATOR AND ACTUATOR SYSTEM

Any mechanical, electrical or electro mechanical system that produces linear or rotary motion to drive mechanical events like shafts, screws, slide or a manipulator can be termed as actuator. Along with the actuator other elements like connecting parts, fixtures, attachments and hardware that serve the purpose of generation of motion either linear or rotational can be termed as actuator system. Examples. A hydraulic cylinder with connecting yoke or clevis and mounting flange or trunnion can be treated as actuator system. An electrical motor with output shaft provided with key or flanged coupling and mounting plate, forms an actuator system. The purpose of actuator is to convert one form of energy into mechanical work in the form of motion. The energy comes in the form of electrical energy or mechanical energy. Electrical conductors are the transfer elements for the electrical energy. The hydraulic oil or air is the medium to carry the mechanical energy. The actuator that works on the pressure energy supplied by the hydraulic oil is called the "Hydraulic Actuator". CLASSIFICATION OF ACTUATORS

The first level of classification is based on the type of motion produced by an actuator, i.e., linear or rotational. In the next level of classification the type of energy and the energy medium is taken as the basis. In the third level the configuration of design forms the basis of classification. In the first level of classification the type of motion bifercates the actuators into linear and rotary actuators. Translation is the function of linear actuators where as rotation is the function of rotary actuators. Sometimes the rotatory actuators with the 56


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aid of mechanical elements produce translatory motion in the mechatronic system. In some mechanical systems the reciprocatory motion is converted to rotary motion by cranking action. The output of translation is the displacement and force exertion. The rotary actuation results in the output of angular displacement and torque. Both type of actuations are responsible for some form of power development that can do work. The types of medium conveying energy to the actuating system further classify each actuator in this level. The electrical energy is most commonly used form of energy that directly and indirectly assists the function of actuation. The pressurized hydraulic oil and compressed air are other kinds of media that help in carrying energy to the hydraulic and pneumatic actuators. It is the electrical energy that is used to create the pressure in hydraulic and pneumatic media. The third level of classification has the design configurations as the basis. The functional requirements, the output specifications, the characteristic performance indicators are taken as the base to configure various designs. This base of classification is application dependent. The style, the manufacturing considerations, cost considerations, the reliability consideration and size consideration form the basis.

Fig : Tree diagram of classification of actuators 57


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MECHANICAL ACTUATION SYSTEMS These are consideration of mechanisms; mechanisms are devices which can be considered to be motion converters in that they transform motion from one form to some other required form. They might, for example, transform linear motion into rotational motion, or motion in one direction into a motion in a direction at right angles, or perhaps a linear reciprocating motion into rotary motion, as in the internal combustion engine where the reciprocating motion of the pistons is converted into rotation of the crank and hence the drive shaft. Mechanical elements can include the use of linkages, cams, gears, rack-andpinion, chains, belt drives, etc. For example, the rack-and-pinion can be used to convert rotational motion to linear motion. Parallel shaft gears might be used to reduce a shaft speed. Bevel gears might be used for the transmission of rotary motion through 90°. A toothed belt or chain drive might be used to transform rotary motion about one axis to motion about another. Cams and linkages can be used to obtain motions which are prescribed to vary in a particular manner. Many of the actions which previously were obtained by the use of mechanisms are, however, often nowadays being obtained by the use of microprocessor systems. For example, cams on a rotating shaft were previously used for domestic washing machines in order to give a timed sequence of actions such as opening a valve to let water into the drum, switching the water off, switching a heater on, etc. Modern washing machines use a microprocessor-based system with the microprocessor programmed to switch on outputs in the required sequence. Mechanisms still, however, have a role in mechatronics systems. For example, the mechatronics system in use in an automatic camera for adjusting the aperture for correct exposures involves a mechanism for adjusting the size of the diaphragm. While electronics might now be used often for many functions that previously were fulfilled by mechanisms, mechanisms might still be used to provide such functions as: 1. Force amplification, e.g. that given by levers. 2. Change of speed, e.g. that given by gears. 3. Transfer of rotation about one axis to rotation about another. e.g. a timing belt. 4. Particular types of motion, e.g. that given by a quick-return mechanism. The term kinematics is used for the study of motion without regard to forces. When we consider just the motions without any consideration of the forces or energy involved then we are carrying out a kinematic analysis of the mechanism. 58


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FREEDOM AND CONSTRAINTS

An important aspect in the design of mechanical elements is the orientation and arrangement of the elements and parts. A body that is free in space can move in three, independent, mutually perpendicular directions and rotate in three ways about those directions (Fig.). It is said to have six degrees of freedom.

Fig: Types of motion The number of degrees of freedom is the number of components of motion that are required in order to generate the motion. If a joint is constrained to move along a line then its translational degrees of freedom are reduced to one. Figure (a) shows a joint with just this one translational degree of freedom. If a joint is constrained to move on a plane then it has two translational degrees of freedom. Figure (b) shows a joint which has one translational degree of freedom and one rotational degree of freedom.

Fig: Joints with: (a) one, (b) two degrees of freedom GEAR TRAINS

Gear trains are mechanisms which are very widely used to transfer and transform rotational motion. They are used when a change in speed or torque of a rotating device is needed. For example, the car gearbox enables the driver to match the speed and torque requirements of the terrain with the engine power available. 59


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Rotary motion can be transferred from one shaft to another by a pair of rolling cylinders (Fig.); however, there is a possibility of slip. The transfer of the motion between the two cylinders depends on the frictional forces between the two surfaces in contact. Slip can be prevented by the addition of meshing teeth to the two cylinders and the result is then a pair of meshed gear wheels.

Fig: Rolling Cylinders Gears can be used for the transmission of rotary motion between parallel shafts and for shafts which have axes inclined to one another. RATCHET AND PAWL

Ratchets can be used to lock a mechanism when it is holding a load. Figure shows a ratchet and pawl. The mechanism consists of a wheel, called a ratchet, with saw-shaped teeth which engage with an arm called a pawl. The arm is pivoted and can move back and forth to engage the wheel. The shape of the teeth is such that rotation can occur in only one direction. Rotation of the ratchet wheel in a clockwise direction is prevented by the pawl and can only take place when the pawl is lifted. The pawl is normally spring loaded to ensure that it automatically engages with the ratchet teeth. Thus a winch used to wind up a cable on a drum may have a ratchet and pawl to prevent the cable unwinding from the drum when the handle is released.

Fig : Ratchet and Pawl 60


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ELECTRICAL ACTUATION SYSTEMS The linear and rotary actuation is also effectively done using electrical medium. Certain advantages over hydraulic actuators make the extensive usage in mechatronic systems. The switching and control of electrical actuators form the part of mechatronics systems. The electric systems used as actuators for control are: 1. Switching devices such as mechanical switches, e.g. relays,or solid-state switches, e.g. diodes, thyristors, and transistors, where the control signal switches on or off some electrical device, perhaps a heater or a monitor. 2. Solenoid type devices where a current through a solenoid is used to actuate a soft iron core, as, for example, the solenoid operated hydraulic/ pneumatic valve where a control current through a solenoid is used to actuate a hydraulic/ pneumatic flow. 3. Drive systems, such as d.c. and a.c. motors, where a current through a motor is used to produce rotation.

MECHANICAL SWITCHES Mechanical switches are often used as sensors to give inputs to systems, e.g. keyboards. The electrical relay is an example of a mechanical switch used in control as an actuator. Mechanically opening and closing of electrical circuits by breaking or making through one or more contact pairs is done by ‘Mechanical switches’. The opening is transmitted by ‘0’ signal and closing is transmitted by ‘1’. The terminals of separate electrical circuits that are to be switched by same action are termed as “poles”. The numbers of individual contacts for each pole are named as “throws”. Based on number of throws and poles in a switching action, they are classified into the following.

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Table : Mechanical Switches

DESIGN VARIETIES IN MECHANICAL SWITCHES

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RELAYS Relays are electrically operated switches in which changing a current in one electrical circuit switches a current on or off in another circuit. For the relay shown in fig(a), when there is a current through the solenoid of the relay, a magnetic field is produced which attracts the iron armature ,moves the push-rode, and so closes the normally open (NO) switch contacts and opens the normally closed (NC) switch contacts. Relays are often used in control systems, the output from the controller is a relatively small current and a much larger current is needed to switch on or off the final correction element, e.g. the current required by the electric heater in a temperature control system or a motor. In such a situation they are likely to be used in conjunction with transistors and fig (b) shows the type of circuit that might be used. Because relays are inductances they can generate a back voltage when the energizing current is switched off or when their input switches from a high to low signal. As a result damage can occur in connecting circuit. To overcome this problem a diode is connected across the relay. When back e.m.f. occurs the diode conducts and shorts it out.

Fig: (a) A relay and (b) a driver circuit As an illustration of the ways relays can be used in control systems, fig shows how two relays might be used to control the operation of pneumatic valves which in turn control the movement of pistons in three cylinders A, B and C.

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Fig : Relay Controlled System The sequence of operation is: 1. When the start switch is closed, the current is applied to the A and B solenoids and results in both A and B extending, i.e. A+ and B+. 2. The limit switches a+ and b+ are then closed;

a+ closure results in current

flowing through relay oil 1 which then closes its contacts and so supplies current to the C solenoid and then results in the extending, i.e. C+. 3. Its extension causes limit switch C+ to close and so current to switch the A and B control valves and hence retraction of the cylinders A and B, i.e. A- and B-. 4. Closing limit switch a- passes a current through the relay coil 2, its contacts close and allows a current to valve C and cylinder C to retract, i.e. C-. The sequence thus given by this system is A+ and B+ concurrently, then C+, followed by A- and B- concurrently and finally C-. Time delay relays are control relays that have a delayed switching action. The time delay is usually adjustable and can be initiated when a current flows through the relay coil or when it ceases to flow through the coil.

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SOLID STATE SWITCHES There are a number of solid-state devices which can be used to electronically switch circuits. These include: 1 2 3 4

Diodes. Thyristors and triacs. Bipolar transistors. Power MOSFETs.

1. Diodes The diode has the characteristics as shown in figure and so allows a significant current in one direction only.

Fig : Diode Characteristic A diode can thus be regarded as a ‘directional element’, only passing a current when forward biased, i.e. with the anode being positive with respect to the cathode. If the diode is sufficiently reversed biased, i.e. a very high voltage, it will break down. If an alternating voltage is applied across a diode, it can be regarded as only switching on when the direction of the voltage is such as to forward bias it and being off in the reverse biased direction. The result is that the current through the diode is half-rectified to become just the current due to the positive halves of the input voltage as shown in Fig.

Fig : Half-wave rectification 66


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2. Thyristors and triacs The thyristor, or silicon-controlled rectifier (SCR), can be regarded as a diode which has a gate controlling the conditions under which the diode can be switched on. Figure shows the thyristor characteristic.

Fig : Thyristor characteristic With the gate current zero, the thyristor passes negligible current when reverse biased (unless sufficiently reverse biased, hundreds of volts, when it breaks down). When forward biased the current is also negligible until the forward breakdown voltage is exceeded. When this occurs the voltage across the diode falls to a low level, about 1 to 2 V, and the current is then only limited by the external resistance in a circuit. Thus, for example, if the forward breakdown is at 300 V then when this voltage is reached the thyristor switches on and the voltage across it drops to 1 or 2 V. If the thyristor is in series with a resistance of, say, 20 Ω then before breakdown we have a very high resistance in series with the 20 Ω and so virtually all the 300 V is across the thyristor and there is negligible current. When forward breakdown occurs, the voltage across the thyristor drops to, say, 2 V and so there is now 300 - 2 = 298 V across the 20 Ω resistor, hence the current rises to 298/20 = 14.9 A. Once switched on the thyristor remains on until the forward current is reduced to below a level of a few milliamps. The voltage at which forward breakdown occurs is determined by the current entering the gate, the higher the current the lower the breakdown voltage. The power-handling capability of a thyristor is high and thus it is widely used for switching high power applications.

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3. Bipolar Transistors Bipolar transistors come in two forms, the npn and the pnp. Figure shows the symbol for each. For the npn transistor, the main current flows in at the collector and out at the emitter, a controlling signal being applied to the base. The pnp transistor has the main current flowing in at the emitter and out at the collector, a controlling signal being applied to the base.

Fig : Transistor symbols: (a) npn, (b) pnp For a npn transistor connected as shown in Figure (a), the so-termed commonemitter circuit, the relationship between the collector current Ic and the potential difference between the collector and emitter VCE is described by the series of graphs shown in Figure (b). When the base current IB is zero the transistor is cut off; in this state both the base-emitter and the base-collector junctions are reverse biased. When the base current is increased, the collector current increases and VCE decreases as a result of more of the voltage being dropped across Rc. When VCE reaches a value VCE(sat), the basecollector junction becomes forward biased and the collector current can increase no further, even if the base current is further increased. This is termed saturation. By switching the base current between 0 and a value that drives the transistor into saturation, bipolar transistors can be used as switches. When there is no input voltage Vin then virtually the entire Vcc voltage appears at the output. When the input voltage is made sufficiently high the transistor switches so that very little of the Vcc voltage appears at the output (Fig. (c)).

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Fig : Transistor Switch 4. MOSFETs MOSFETS (metal-oxide field-effect transistors) come in two types, the n-channel and the p-channel. Figure shows the symbols. The main difference between the use of a MOSFET for switching and a bipolar transistor is that no current flows into the gate to exercise the control. The gate voltage is the controlling signal. Thus drive circuitry can be simplified in that there is no need to be concerned about the size of the current.

Fig: MOSFETs: (a) n-channel, (b) p-channel With MOSFETs, very high frequency switching is possible, up to 1 MHz, and interfacing with a microprocessor is simpler than with bipolar transistors.

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SOLENOIDS Solenoids can be used to provide electrically operated actuators. Solenoid valves are an example of such devices, being used to control fluid flow in hydraulic or pneumatic systems. When a current passes through a coil a soft iron core is pulled into the coil and, in doing so, can open or close ports to allow the flow of a fluid. Construction Solenoid has a fixed ferrous body with a coil for excitation. The centrally positioned is the plunger which is a movable element. The body and the plunger (armature) are made of ferro magnetic material for flux carrying. Tube carries a conical stopper plate at one end, which is also magnetic.

Fig : Construction of a solenoid Principle of Working Switching on the current the body and the conical stopper get magnetized because of which the plunger is attracted towards the stopper. On switching off current to the coil plunger returns back to the free position. Solenoids are basically short stroke (up to 25 mm) unidirectional linear electrical actuators in which the action is always to pull the plunger into the coil irrespective of the polarity of the current. The force· of actuation supplied by the simple solenoid of the type shown in figure is given by

1  N2 I2  F =  2  A μ 0 2 x  70


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N = number of turns on the coil I = the current through the coil x = length of air gap A = Area of cross-section of air gap. μ0 = permeability of air.

Characteristic of Solenoid The force exerted by the plunger is maximum in the beginning and varies nonlinearly as the stroke progresses. The plunger force decreases with the stroke, as shown in figure

Fig : Force stroke current.

REFERENCES 1) Mechatronics

- W. Bolton

2) Mechatronics

- Ganesh S. Hegde

3) Control Systems and Mechatronics

- J.Srinivas

4) Mechatronics

- Dan S. Necsuleseu

5) Understanding Electro Mechanical Engineering

- Lawrence J. Kamm

6) Mechatronics - Principles, Concepts & Applications - Nitaigour Premchand Mahalik

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Input/output Systems

MODULE - 2 INPUT/OUTPUT SYSTEMS INPUT/OUTPUT SYSTEMS When a microprocessor is used to control some system it has to accept input information, respond to it and produce output signals to implement the required control action. Thus there can be inputs from sensors to feed data in and outputs to such external devices as relays and motors. The term peripheral is used for a device, such as a sensor, keyboard, actuator, etc. which is connected to a microprocessor. It is however, not normally possible to connect directly such peripheral devices to a microprocessor bus system due to a lack of compatibility in signal forms and levels. Because of such incompatibility, a circuit known as an interface is used between the peripheral items and the microprocessor. Figure illustrates the arrangement. The interface is where this incompatibility is resolved.

Fig : The interfaces

INPUT/OUTPUT PORTS In computer hardware, a 'port' serves as an interface between the computer and other computers or peripheral devices. Physically, a port is a specialized outlet on a piece of equipment to which a plug or cable connects. Electronically, the several conductors making up the outlet provide a signal transfer between devices. Computer ports in common use cover a wide variety of shapes such as round (PS/2, etc.), rectangular (FireWire, etc.), square (telephone modem), trapezoidal (D-Sub—the old printer port was a DB-25), etc. There is some standardization to physical properties and function. For instance, most computers have a keyboard port (currently a round DIN-like outlet referred to as PS/2), into which the keyboard is connected. 72


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Electronically, hardware ports can almost always be divided into two groups based on the signal transfer: •

Serial ports send and receive one bit at a time via a single wire pair (Ground and +/-). Parallel ports send multiple bits at the same time over several sets of wires.

•

After ports are connected, they typically require "handshaking", which is a similar concept to the negotiation that occurs when two fax machines make a connection, where transfer type, transfer rate, and other necessary information is shared even before data are sent. Plug-and-play ports are designed so that the connected devices automatically start handshaking as soon as the hot-plugging is done. USB ports and FireWire ports are plug-and-play. Auto-detect or auto-detection ports are usually plug-and-play, but they offer another type of convenience. An auto-detect port may automatically determine what kind of device has been attached, but it also determines what purpose the port itself should have. For example, some sound cards allow plugging in several different types of audio speakers, then a dialogue box pops up on the computer screen asking whether the speaker is left, right, front, or rear for surround sound installations. The user's response determines the purpose of the port, which is physically a 1/8" tipsleeve-ring (TRS connector) mini jack. Some auto-detect ports can even switch between input and output based on context. FireWire ports used with video equipment (among other devices) can be either 4-pin or 6-pin. The two extra conductors in the 6-pin connection carry electrical power. This is why a self-powered device such as a camcorder often connects with a cable that is 4-pins on the camera side and 6-pins on the computer side, the two power conductors simply being ignored. This is also why laptop computers usually only have 4-pin FireWire ports, since they cannot provide enough power to meet requirements for devices needing the power provided by 6-pin connections. Note that optical (light) fiber, microwave, and other technologies (i.e., quantum) have different kinds of connections, since metal wires aren't effective for signal transfers with these technologies. Optical connections are usually a polished glass or plastic interface, possibly with oil that lessens refraction between the two interface surfaces. Microwaves are conducted through a pipe, which can be seen on a large scale by examining microwave towers with "funnels" on them leading to pipes. 73


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Hardware port trunking (HPT) is a technology that allows multiple hardware ports to be combined into a single group, effectively creating a single connection with a higher bandwidth, sometimes referred to as a double-barrel approach. This technology also provides a higher degree of fault tolerance since a failure on one port may just mean a slow-down rather than a dropout. Compare this to Software Port Trunking (SPT) where two agents (websites, channels, etc.) are bonded into one with the same effectiveness, i.e., ISDN B1 (64K) plus B2 (64K) equals data throughput of 128K. The figures of commonly used Input/output Ports are

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INTERFACE REQUIREMENTS The following are some of the actions that are often required of an interface circuit: 1. Electrical buffering/isolation This is needed when the peripheral operates at a different voltage or current to that on the microprocessor bus system or there are different ground references. The term buffer is used for a device that provides isolation and current or voltage amplification. For example, if the output of a microprocessor is connected to the base of a transistor, the base current required to switch the transistor is greater than that supplied by the microprocessor and so a buffer is used to step up the current. There also has often to be isolation between the microprocessor and the higher power system. 2. Timing control Timing control is needed when the data transfer rates of the peripheral and the microprocessor are different, e.g. when interfacing a microprocessor to a slower peripheral. This can be achieved by using special lines between the microprocessor and the peripheral to control the timing of data transfers. Such lines are referred to as handshake lines and the process as handshaking. The peripheral sends a DATA READY signal to the input/output section. The CPU then determines that the DATA READY signal is active. The CPU then reads the data from the input/output section and sends an INPUT ACKNOWLEDGED signal to the peripheral. This signal indicates that the transfer has been completed and thus the peripheral can send more data. For an output, the peripheral sends an OUTPUT REQUEST or PERIPHERAL READY signal to the input/output section. The CPU determines that the PERIPHERAL READY signal is active and sends the data to the peripheral. The next PHERIPHERAL READY signal may be used to inform the CPU that the transfer has been completed. 3. Code conversion This is needed when the codes used by the peripherals differ from those used by the microprocessor. For e.g., an LED display might require a decoder to convert the BCD output from a microprocessor into the code required to operate the seven display elements. 75


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PERIPHERAL INTERFACE ADAPTERS Interfaces can be specifically designed for particular inputs/outputs; however, programmable input/output interface devices are available which permit various different input and output options to be selected by means of software. Such devices are known as Peripheral interface adapters (PIAs). A commonly used PIA parallel interface is Motorola MC 6821. It is part of MC6800 family and thus can be directly attached to Motorola MC6800 & MC68HC11 buses. The device can be considered to be essentially just two parallel input/output ports, with their control logic, to link up with the host microprocessor. Figure shows the basic structure of the MC6821 PIA and the pin connections.

Fig : MC6821 PIA

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The PIA contains two 8-bit parallel data ports, termed A and B. Each port has: 1. A peripheral interface register. An output has to operate in a different way to an input port because the data must be held for the peripheral. Thus for output a register is used to temporarily store data. The register is said to be latched, that is connected, when a port is used for output and unlatched when used for input. 2. A data direction register that determines whether the input/output lines are inputs or outputs. 3. A control register that determines the active logical connections in the peripheral. 4. Two control lines, CA1 and CA2 or CB1 or CB2. Two microprocessor address lines connect the PIA directly through the two register select the lines RS0 and RS1. This gives the PIA four addresses for the six registers. When RS1 is low, side A is addressed and when high it is side B. RS0 addresses registers on a particular side, i.e. A or B. When RS0 is high, the control register is addressed, when low the data register or the data direction register. For a particular side, the data register and the data direction register have the same address. Which of them is addressed is determined by bit 2 of the control register. Each of the bits in the A and B control registers is concerned with some features of the operation of the ports. Thus for the A control register we have the bits shown in figure. A similar pattern is used for the B control register.

Fig : Control register Bits 0 to 1 The first two bits control the way that CA1 or CB1 input control lines operate. Bit 0 determines whether the interrupt output is enabled. BO = 0 disables the IRQA(B) microprocessor interrupt, BO = 1 enables the interrupt. CA1 and CB1 are not set by the static level of the input but are edge triggered, i.e. set by a changing signal. Bit 1 determines whether bit 7 is set by a high-to-low transition (a trailing edge) or a low tohigh transition (a leading edge). B1 = 0 sets a high-to-low transition, B1 = 1 sets a low-to-high transition. 77


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Bit 2 Bit 2 determines whether data direction register or peripheral data registers are addressed. With B2 sets to 0 data direction registers are addressed, with B2 sets set to 1 peripheral data registers are selected. Bit 3, 4 and 5 These bits allow the PIA to perform a variety of functions. Bit 5 determines whether control line 2 is an input or an output. If bit 5 is set to 0 control line 2 is an input, if set to1 it is an output. In input mode, both CA2 and CB2 operate in the same way. Bit 3 and 4 determine whether the interrupt output is active and which transitions set bit 6. With B5 = 0, i.e. CA2(CB2) set as an input: B3 = 0 disables IRQA(B) microprocessor interrupt by CA2(CB2); B3 = 1 enables IRQA(B) microprocessor interrupt by CA2(CB2); B4 = 0 determines that the interrupt flag IRQA(B), bit B6, is set by high-to-low transition on CA2(CB2), B4 = 1 determines that it is set by a low-tohigh transition. B5 = 1 sets CA2(CB2) as an output. In output mode CA2 and CB2 behave differently. For CA2: with B4 = 0 and B3 = 0, CA2 goes low on the first high-to-low ENABLE (E) transition following a microprocessor read of peripheral data register A and is returned high by the next CA1 transition; B4 = 0 and B3 = 1, CA2 goes low on the first high-to-low ENABLE transition following a microprocessor read of the peripheral data register A and is returned high by the next high-to-low ENABLE transition. Bit 6 This is the CA2(CB2) interrupt flag, being set by transitions on CA2(CB2). With CA2(CB2) as an input (B5 = 0), it is cleared by a microprocessor read of the data register A(B). With CA2(CB2) as an output (B5 = 1), the flag is 0 and is not affected by CA2(CB2) transitions. Bit 7 This is the CA1(CB1) interrupt flag, being cleared by a microprocessor read of data register A(B). The process of selecting which options are to be used is termed configuring or initializing the PIA. The RESET connection is used to clear all the registers of the PIA. The PIA must then be initialized. 78


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PROGRAMMABLE LOGIC CONTROLLERS A programmable logic Controller (PLC) is a digital electronic device that uses a programmable memory to store instructions and to implement functions such as logic, sequencing, timing, counting and arithmetic

in order

to control machines and

processes and has been specifically designed to make programming easy.

Fig : Programmable logic controller The term logic is used because the programming is primarily concerned with implementing logic and switching operations. Inputs devices, e.g. switches, and output devices, e.g. motors, being controlled are connected to the PLC and then the controller monitors the inputs and outputs according to the program stored in the PLC by the operator and so controls the machine or process. Originally they were designed as a replacement for hard-wired relay and timer logic control systems. PLCs have the great advantage that it is possible to modify a control system without having to rewire the connections to the input and output devices, the only requirement being that an operator has to key in a different set of instructions. Also they are much faster than relay-operated systems. The result is a flexible system which can be used to control systems which vary quite widely in their nature and complexity. Such systems are widely used for the implementation of logic control functions because they are easy to use and program. PLCs are similar to computers but have certain features which are specific to their use as controllers. These are: 1. They are rugged and designed to withstand vibrations, temperature, humidity and noise. 2. The interfacing for inputs and outputs is inside the controller. 3. They are easily programmed and have an easily understood programming language. Programming is primarily concerned with logic and switching operations. 79


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PLCs were first conceived in 1968. They are now widely used and extend from small self-contained units for use with perhaps 20 digital input/outputs to modular systems which can be used for large numbers of inputs/outputs, handle digital or analogue inputs/outputs, and also carry out PID control modes. The next section is a discussion of the basic structure of PLCs and how they can be used to control machines or processes.

BASIC STRUCTURE It consists of a central processing unit (CPU), memory, and input/output circuitry. The CPU controls and processes all the operations within the Programmable Logic Controller (PLC). It is supplied with a clock with a frequency of typically between 1 and 8 MHz. This frequency determines the operating sped of the PLC and provides the timing and synchronization for all elements in the system. A bus system carries information and data to and from the CPU, memory and input/output units. There are several memory elements: a system ROM to give permanent storage for the operating system and fixed data, RAM for the user’s program, and temporary buffer stores for the input/output channels. The programs in RAM can be changed by the user. However, to prevent the loss of these programs when the power supply is switched off, a battery is likely to be used in the PLC to maintain the RAM contents for a period of time. After a program has been developed in RAM it may be loaded into an EPROM memory chip and so made permanent. Specifications for small PLCs often specify the program memory size in terms of the number of program steps that can be stored. A program step is an instruction for some event to occur. A program task might consist of a number of steps and could be, for example: examine the state of switch A, examine the state of switch B , if A and B are closed then energise solenoid P which then might result in the operation of some actuator. When this happens another task might be started. Typically, the number of steps that can be handled by a small PLC is of the order of 300 to 1000, which is generally more than adequate for most of the control situations.

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Fig : Architecture of a PLC

PLC PROGRAMMING PLC programming based on the use of ladder diagrams involves writing a program in a similar manner to drawing a switching circuit. The ladder diagram consists of two vertical lines representing the power rails. Circuits are connected as horizontal lines, i.e. the rungs of the ladder, between these two verticals. Fig. shows the basic standard symbols that are used and an example of rungs in a ladder diagram. In drawing the circuit line for a rung, inputs must always precede outputs and there must be at least one output on each line. Each rung must start with an input or a series of inputs and end with an output.

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Fig : Ladder diagram The inputs and outputs are numbered, the notation used depending on the PLC manufacturer, e.g. the Mitsubishi F series of PLCs precedes input elements by an X and output elements by a Y and uses the following numbers: Inputs

X400-407, 410-413 X500-507, 510-513

Outputs

(24 possible outputs)

Y430-437 Y530-537

(16 possible inputs)

To illustrate the drawing of a ladder diagram, consider a situation where the output from the PLC is to energise a solenoid when a normally open start switch connected to the input is activated by being closed shown in fig (a). The program required is shown in fig (b). Starting with the input, we have the normally open symbol

. This might have an input address Y400. The line terminates with the

output, the solenoid; with the symbol O. this might have the output address Y430. To indicate the end of the program the end rung is marked. When the switch is closed the solenoid is activated. This might, for example, be a solenoid valve which opens to allow water to enter the vessel. 82


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Fig : Switch controlling a solenoid

LOGIC FUNCTIONS The logic functions can be obtained by combinations of switches and the following shows how we can write ladder program for such combinations. 1. AND Following figure (a) shows a situation where a coil is not energized unless two, normally open, switches are both closed. Switch A and switch B have both to be closed, which thus gives an AND logic situation. The ladder diagram starts with , labelled Input 1, to represent switch A and in series with it

, labelled Input

2, to represent switch B. The line then terminates with O to represent the output. Figure (b) shows the line.

Fig : An AND system 2. OR Figure (a) shows a situation where a coil is not energized until either, normally open, switched A or B is closed. The situation is an OR logic gate. The ladder diagram starts with it

, labelled Input 1, to represent switch A and in parallel with

, labelled Input 2, to represent switch B. The line then terminates with O to

represent the output. Figure (b) shows the line.

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Fig : An OR system 3. NOR Figure (a) shows how we can represent the ladder program line for a NOR gate. Since there has to be an output when neither A nor B have an input and when there is an input to A or B the output ceases, the ladder program shows Input 1 in parallel with Input 2, with both being represented by normally closed contacts .

Fig : A NOR system 4. NAND Figure shows a NAND gate. There is no output when A and B have an input. Thus for a ladder program line to obtain an output we require no inputs to Input 1 and to Input 2.

Fig : A NAND system

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DATA HANDLING With the exception of the shift register, the previous parts of this module have been concerned with the handling of individual bits of information, eg. a switch being closed or not. There are, however, some control tasks where it is useful to deal with related groups of bits, e.g. a block of eight inputs, and so operate on them as a data word. Such a situation can rise when a sensor supplies an analogue signal which is converted to, say, an 8-bit word before becoming an input to a PLC. The operations that may be carried out with a PLC on data word normally include: 1. Moving data. 2. Comparison of magnitudes of data, i.e. greater than, equal to, or less than. 3. Arithmetic operations such as addition and subtraction. 4. Conversions between binary coded decimal (BCD), binary and octal. As discussed earlier, individual bits have been stored in memory locations specified by unique addresses. For example, for the Mitsubishi PLC, input memory addresses have been preceded by an A, output by a Y, timers by a T, auxiliary relays by an M, etc. Data instructions also require memory addresses and the locations in the PLC memory allocated for data are termed data registers. Each data register can store a binary word of, usually, 8 or 16 bits and is given an address such as D0, D1, D2 etc. An 8- bit word means that a quantity is specified to a precision of 1 in 256, a 16-bit a precision of 1 in 65 536. Each instruction has to specify the form of the operation, the source of the data used in terms of its data register and the destination data register of the data. 1. DATA MOVEMENT For data movement the instructions will contain the move data instruction, the source addresses of the data and the destination address of the data. Thus the ladder rung could be of the form shown in figure and the instructions could be, when data is to be moved from data register D1 to data register D2:

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Such data transfers might be to move a constant into a data register, a time or count value to a data register, data from a data register to a timer or counter, data from a data register to an output, input data to a data register, etc.

Fig : Move data 2. DATA COMPARISON PLCs can generally make the data comparisons of less than (usually denoted by < or LES), equal to (= or EQU), less than or equal to (≤ or <= or LEQ), greater than (> or GRT), greater than or equal to (≥, >= or GEQ) and not equal to ( ≠ or <> or NEQ). To compare data, the program instruction will contain the comparison instruction, the source address of the data and the destination address. Thus to compare the data in register D1 to see if it is greater than data in data register D2, the ladder program rung would be of the form shown in figure

Fig : Compare data 86


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The instructions would be:

Such a comparison might be used when the signals from two sensors are to be compared by the PLC before action is taken. For example, an alarm might be required to be sounded if a sensor indicates a temperature above 800C and remain sounding until the temperature falls below 700C. Figure shows the ladder program that could be used.

Fig : Temperature alarm The input temperature data is inputted to the source address and the destination addresses contains the set value. When the temperature raises to 800C, or higher, the data value in the source address becomes ≥ the destination address value and there is an output to the alarm which latches the input. When the temperature falls below 700C, or lower, the data value in the source address becomes ≤ to the destination address value and there is an output to the relay which then opens its contacts and so switches the alarm off. 3. ARITHMETIC OPERATIONS Some PLCs can carry out just the arithmetic operations of addition and subtraction, others have even more arithmetic functions. The instruction to add or subtract generally states the instruction, the register containing the address of the 87


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value to be added or subtracted, the address of the value to which the addition or from which the subtraction is to be made and the register where the result is to be stored. Figure shows the form used for the ladder symbol for addition with OMRON.

Fig : Add data Addition or subtraction might be used to alter the value of some sensor input value, perhaps a correction or offset term, or alter the present values of timers or counters. 4. CODE CONVERSIONS All the internal operation in the CPU of a PLC are carried out using binary numbers. Thus, when the input is a signal which is decimal, conversion to binary coded decimal (BCD) is used. Likewise, where a decimal output is required, conversion to decimal is required. Such conversion are provided with most PLCs. For example, with Mitsubishi, the ladder rung to convert BCD to binary is of the form shown in figure. The data at the source address is in BCD and converted to binary and placed at the destination address.

Fig : BCD to binary

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COMMUNICATION SYSTEMS DIGITAL COMMUNICATIONS An external bus is a set of signal lines that interconnects microprocessors, microcontrollers, computers and PLCs and also connects them with peripheral equipment. Thus a computer needs to have a bus connecting it with a printer if its output is to be directed to the printer and printed. Multiprocessor systems are quite common. For example, in a car there are likely to be several microcontrollers with each controlling a different part of the system, e.g. engine management, braking and instrument panel, and communication between them is necessary. In automated plant there is not only a need for data to pass between programmable logic controllers, displays, sensors, and actuators and allow for data and programs to be inputted by operator , but they can also be data communications with other computers. There may, for example, be a need to link a PLC into a control system involving a number of PLCs and computers. Computer integrated manufacturing (CIM) is an example of a large network which can involve large numbers of machines linked together. This chapter is a consideration how such data communications between computers can take place, whether it is just simply machine-to-machine or a large network involving large numbers of machines linked together, and the forms of standard communication interfaces.

CENTRALISED, HIERARCHIAL AND DISTRIBUTED CONTROL Centralized computer control involves the use of one central computer to control an entire plant. This has the problem that failure of the computer results in the loss of control of the entire plant. This can be avoided by the use of dual computer systems. If one computer fails the other one takes over. Such centralized systems were common in the 1960s and 1970s. The development of the microprocessor and the ever reducing costs of computers have led to multi-computer systems becoming more common and the development of hierarchical and the distributed systems. With the hierarchical system, there is a hierarchical system of computers according to the tasks they carried out. The computers handling the more routine tasks are supervised by computers which have a greater decision-making role. For example, the computers which are used for direct digital control of systems are subservient to a computer which performs supervisory control of the entire system. The work is divided between the computers according to the function involved. There is a specialization of computers with some computers only receiving some information and others different information. 89


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With the distributed system, each computer system carries out essentially similar tasks to all the other computer systems. In the event of a failure of one, or over loading of a particular computer, work can be transferred to other computers. The work is spread across all the computers and not allocated to specific computers according to the function involved. There is no specialization of computers. Each computer thus needs access to all the information in the system. In most modern systems there is generally a mixture of distributed and hierarchical systems. For example, the work of measurement and actuation may be distributed among a number of microcontrollers/computers which are linked together and provide the data base for the plant. These may be overseen by a computer used for direct digital control or sequencing and this in turn may be supervised by one used for supervisory control of the plant as a whole. Typical levels in such a scheme are: Level 1: Measurement and actuators Level 2: Direct digital and sequence control Level 3: Supervisory control Level 4: Management control and design Distributed/ Hierarchical systems have advantage of allowing the task of measurement scanning and signal conditioning in control systems to be carried out by sharing it between a number of microprocessors. This can involve a large number of signals with a high frequency of scanning. If extra measurement loops are required, it is a simple matter to increase the capacity of the system by adding microprocessors. The units can be quite widely dispersed, being located near the source of the measurements. Failure of one unit does not result in failure of the entire system. 1. PARALLEL AND SERIAL DATA TRANSMISSION Data communication can be via parallel or serial transmission links. A. PARALLEL DATA TRANSMISSION

With in computers, data transmission is usually by parallel data paths. Parallel data buses transmit 8, 16 or 32 bits simultaneously, having a separate bus wire for each data bit and the control signals. Thus, if there are 8 data bits to be transmitted, e.g. 11000111, then 8 data wires are needed. The entire 8 data bits are transmitted in the same time as it takes to transmit 1 data bit because each bit is on a parallel wire. 90


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Handshaking lines are also needed, handshaking being used for each character transmitted with lines needed to indicate that data is available for transmission and that the receiving terminal is ready to receive. Parallel data transmission permits high data transfer rates but is expensive because of the cabling and interface circuitry required. It is thus normally only used over short distances or where high transfer rates are essential. SERIAL DATA TRANSMISSION This involves the transmission of data which, together with control signals, is sent bit by bit in sequence along a single line. Only two conductors are needed, to transmit data and to receive data. Since the bits of a word are transmitted sequentially and not simultaneously, the data transfer rate is considerably less than with parallel data transmission. However, it is cheaper since far fewer conductors are required. For example, with a car when a number of microcontrollers are used, the connections between them are by serial data transmission. Without the use of serial transmission the number of wires involved would be considerable. In general, serial data transmission is used for all but the shortest peripheral connections. Consider the problem of sending a sequence of characters along a serial link. The receiver needs to know where one character starts and stops. Serial data transmission can be either asynchronous or synchronous transmission. Asynchronous transmission implies that both the transmitter and receiver computers are not synchronized, each having its own independent clock signals. The time between the transmitted characters is arbitrary. Each character transmitted along the link is thus preceded by a start bit to indicate to the receiver the start of a character, and followed by a stop bit to indicate its completion. This method has the disadvantage of requiring extra bits to be transmitted along with each character and thus reduces the efficiency of the line for data transmission. With synchronous transmission there is no need for start and stop bits since the transmitter and receiver have a common clock signal and thus characters automatically start and stop always at the same time in each cycle. The rate of data transmission is measured in bits per second. If the group of n bits forms a single symbol being transmitted and the symbol has duration of T seconds then the data rate of transmission is n/T .The baud is the unit used. The baud rate is only the same as the number of bits per second transmitted if each character is represented by just one symbol. Thus a system which does not use start and stop pulses have a baud rate equal to the bit rate, but this will not be the case when there are such bits.

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2. SERIAL DATA COMMUNICATION MODES Serial data transmission occurs in one of the three modes: 2.1. SIMPLEX MODE

Transmission is only possible in one direction, from device A to device B, where device B is not capable of transmitting back to device A. You can think of the connection between the devices being like a one-way road. This method is usually only used for transmission to devices such as printers which never transmit information.

2.2. HALF-DUPLEX MODE

Data is transmitted in one direction at a time but the direction can be changed. Terminals at each end of the link can be switched from transmit to receive. Thus device A can transmit to device B and device B to device A but not at the same time. You can think of this being like two lane road under repair with traffic from one lane being stopped by a traffic control to allow the traffic for the other lane through. Citizens Band (CB) radio is an example of half-duplex mode, a person can receive or talk but not do both simultaneously.

2.3. FULL-DUPLEX MODE

Data may be transmitted simultaneously in both directions between devices A and B. This is like a two lane high way in which traffic can occur in both directions simultaneously. The telephone system is an example of full-duplex mode in that a person can talk and receive at the same time.

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NETWORKS The term Network is used for a system which allows two or more computers/ microprocessors to be linked for the interchange of data. The logical form of the links is known as the network topology. The term node is used for a point in a network where one or more communication lines terminate or a unit is connected to the communications lines. Commonly used forms are: 1. Data Bus: This has a linear bus (shown in figure) into which all the stations are plugged. This system is often used for multipoint clusters. It is generally the preferred method for distances between nodes of more has 100 m.

2. Star: This has dedicated channels between each station and a central switching hub (shown in figure) through which all communications must pass. This is the type of network used in the telephone systems (private branch exchanges (PBXs)) in many companies, all the lines passing through a central exchange. This system is also often used to connect remote and local terminals to a central mainframe computer. There is a major problem with this system in that if the central hub fails then the entire system fails.

3. Hierarchy or Tree: This consists of a series of branches converging indirectly to a point at the head of the tree (shown in figure). With this system there is only one transmission path between any two stations. This arrangement may be formed from a number of linked data bus systems. Like the bus method, it is often used for distances between nodes of more than 100 m.

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4. Ring: This is very popular method for local area networks, involving each station being connected to a ring (shown in figure). The distances between nodes are generally less than 100 m. Data put into the ring system continuous to circulate round the ring until some system removes it. The data is available to all the stations.

5. Mesh: This method (shown in figure) has no formal pattern to the connections between stations and there will be multiple data path between them.

The term local area network (LAN) is used for a network over a local geographic area such as a building or a group of buildings on one site. The topology is commonly bus, star or ring. A wide area network is one that interconnects computers, terminals and local area networks over a national or international level.

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PROTOCOLS Transmitted data will contain two types of information. One is the data which one computer wishes to send to another, the other is information termed protocol data and is used by the interface between a computer and the network to control the transfer of the data into the network or from the network into the computer. A protocol is a formal set of rules governing data format, timing, sequencing, access control and error control. The three elements of a protocol are: 1. Syntax, which defines data format, coding and signal levels. 2. Semantics, which deals with synchronisation, control and error handling. 3. Timing, which deals with the sequencing of data and the choice of data rate. When a sender communicates with a receiver then both must employ the same protocol, e.g. two microcontrollers with data to be serially transmitted between them. With simplex communication the data block can be just sent from sender to receiver. However, with half-duplex, each block of transmitted data, if valid, must be acknowledged (ACK) by the receiver before the next block of data can be sent (shown in figure (a)); if invalid a NAK, negative acknowledgement, signal is sent. Thus a continuous stream of data cannot be transmitted. The CRC bits, cyclic redundancy checks, are a means of error detection and are transmitted immediately after a block of data. The data is transmitted as a binary number and at the transmitter the data is divided by a number and the remainder is used as the cyclic check code. At the receiver the incoming data, including the CRC, is divided by the same number and will give zero remainder if the signal is error free. With full-duplex mode (shown in figure (b)), data can be continuously sent and received.

Fig : Protocols: (a) half-duplex, (b) full-duplex 95


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Within a package being sent, there is a need to include protocol information. For example, with asynchronous transmission there may be characters to indicate the start and end of data. With synchronous transmission and the Bisync protocol, a data block is preceded by a synchronising sequence of bits, usually the ASCII character SYN (shown in figure (a)) The SYN characters are used by the receiver to achieve character synchronisation, preparing the receiver to receive data in 8-bit groupings. The Motorola MC6852 is a synchronous serial data adapter (SSDA) that is designed for use with 6800 microprocessors to provide a synchronous serial communications interface using the Bisync protocol. It is similar to the asynchronous communications interface adapter.

Fig : Bisync Another protocol is the High-level Data Link Control (HDLC). This is a fullduplex protocol with the beginning and end of a message being denoted by the bit pattern 01111110. Address and control fields follow the start flag. The address identifies the address of the destination station, the control field defines whether the frame is supervisory, information or unnumbered. Following the message is a 16-bit frame check sequence which is used to give a cyclic redundancy check (CRC). The Motorola 6854 is an example of a serial interface adapter using this HDLC protocol.

Fig : HDLC 96


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OPEN SYSTEM INTERCONNECTION COMMUNICATION MODEL Communication protocols have to exist on a number of levels. The International Organization for Standardisation (ISO) has defined a seven-layer standard protocol system known as the Open Systems Interconnection (OSI) model. The model is a framework for developing a co-ordinated system of standards. The layers are: 1. Physical layer This layer describes the means for bit transmission to and from physical components of the network. It deals with hardware issues, e.g. the types of cable and connectors to be used, synchronising data transfer and signal levels. Commonly used LAN systems defined at the physical layer is Ethernet and token ring. 2. Data link layer: This layer defines the protocols for sending and receiving messages, error detection and correction and the proper sequencing of transmitted data. It is concerned with packaging data into packets and placing them on the cable and then taking them off the cable at the receiving end. Ethernet and token ring are also defined at this level. 3. Network layer: This deals with communication paths and addressing, routing and control of messages on the network and thus making certain that the messages get to the right destinations. Commonly used network layer protocol layers are Internet Protocol (IP) and Novell’s Internetwork Packet Exchange (IPX). 4. Transport layer; This provides for reliable end-to-end message transport. It is concerned with establishing and maintaining the connection between transmitter and receiver. Commonly used transport layer protocols are Internet Transmission Control Protocols (TCP) and Novell’s Sequenced Packet exchange (IPX). 5. Session layer: This layer is concerned with the establishment of dialogues between application processes which are connected together by the network. It is responsible for determining when to turn a communication between two stations ON or OFF. 6. Presentation layer: This layer is concerned with allowing the encoded data transmitted to be presented in a suitable form for user manipulation. 7. Application layer: This layer provides the actual user information processing function and application specific services. It provides such functions as file transfer or electronic mail which a station can use to communicate with other systems on the network. 97


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COMMUNICATION INTERFACES Digital data can be communicated between devices by serial or parallel communication. With serial communications the main standard is RS-232. With parallel communications commonly used standards are the Centronics parallel interface and the general purpose interface bus (GPIB) (IEEE-488).

1. SERIAL COMMUNICATION INTERFACE The most popular serial interface is RS-232; this was first defined by the American Electronics Industries Association (EIA) in1962. The standard relates to data terminal equipment (DTE) and data circuit-terminating equipment (DCE). Data terminal equipment can send or receive data via the interface, e.g. a microcontroller. Data circuit-terminating equipment is devices which facilitate communication; a typical example is a modem. This forms an essential link between a microcomputer and a conventional analog telephone line. RS-232 signals can be grouped into three categories: a. Data RS-232 provides two independent serial data channels, termed primary and secondary. Both these channels are used for full-duplex operation. b. Handshake Control Handshaking signals are used to control the flow of serial data over the communication path. c. Timing For synchronous operation it is necessary to pass clock signals between transmitters and receivers. The connector to a RS-232C serial port is via a 25-pin D-type connector; usually a male plug is used on cable and a female socket on the DCE or DTE. For the simplest bi-directional link only the two lines 2 and 3 for transmitted data and received data, with signal ground for the return path of these signals, are needed (shown in figure (a)). Thus the minimum connection is via a three-wire cable. For a simple set-up involving a personal computer (PC) being linked with a visual display unit (VDU) pins 1, 2, 3, 4, 5, 6, 7 and 20 are involved (shown in figure (b)). The signal send through pins 4, 5, 6 and 20 are used to check that the receiving end is ready to receive a signal; a transmitting end is ready to send and the data is ready to be sent. 98


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Fig : RS-232 connections: (a) minimum configuration, (b) PC connection RS-232 is limited concerning the distance over which it can be used as noise limits the transmission of high numbers of bits per second when the length of the cable is more than about 15 m. The maximum data rate is about 20 kbits/s. Other standards such as RS-422 and RS-485 are similar to RS-232 and can be used for higher transmission rates and longer distances. RS-422 uses a pair of lines for each signal and can operate up to about 1220 meters or at higher transmission speed up to 100 bits/s and in noisier environments; maximum speed and maximum distance cannot, however, be achieved simultaneously. RS-485 can be used up to about 1220 m with speed of 100 kbits/s.

2. GENERAL PURPOSE INSTRUMENTATION BUS The standard interface commonly used for general parallel communications is the General purpose instrument bus (GPIB), the IEEE-488 standard, originally developed Hewlett Packard to link their computers and instruments and thus often referred to as the Hewlett Packard instrumentation bus. Each of the devices connected to the bus is termed a listener, talker or controller. Listeners are devices that accept data from the bus, talkers place data, on request, on the bus and controllers manage the flow of data on the bus by sending command to talkers and listeners and carries out polls to see which devices are active. The GPIB bus structure is shown below. 99


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Fig : GPIB bus structure There are a total of 24 lines with the interface. 1. Eight bi-directional lines to carry data and commands between the various devices connected to the bus. 2. Five lines for control and status signals. 3. Three lines for handshaking between devices. 4. Eight lines are ground return lines. Up to 15 devices can be attached to the bus at any one time, each device having its own address. The 8-bit parallel data bus can transmit data as one 8-bit byte at a time. Each time a byte is transferred the bus goes through a handshake cycle. Each device on the bus has its own address. Commands from the controller are signalled by taking the Attention Line (ATN) low. Commands are then directed to individual devices by placing address on the data lines; device addresses are sent via the data lines as a parallel 7-bit word with the lowest 5 bits providing the device address and the other 2 bits control information. If both these are zero then the commands are sent to all address; if bit 6 is 1 and bit 7 is 0 the addressed device is switched to be a listener; if bit 6 is 0 and bit 7 is 1 then the device is switched to be talker. Handshaking uses the lines DAV, NRFD, and NDAC, the three lines ensuring that the talker will only talk when it being listened by the listeners (in figure). When a listener is ready to accept data, NRFD is made high. When data has been placed on the line, DAV is made low to notify devices that data is available. When a device accepts a data word it sets NDAC high to indicate that it has accepted the data and NRFD low to indicate that it is now not ready to accept data. When all the listeners have set NDAC high, then the talker cancels the data valid signal, DAV going high. 100


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This then results in NDAC being set low. The entire process can then be repeated for another word being put on the data bus.

Fig : Handshaking The GPIB is a bus which is used to interface a wide range of instruments, e.g. digital multimeters and digital oscilloscopes, via plug-in boards (shown in figure) to computers with standard cables used to link the board o the instruments via interfaces.

Fig : GPIB Hardware 101


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FAULT FINDING This section is a brief consideration of the problems of fault detection with measurement, control and data communication systems. For details of the faultfinding checks required for specific systems or components, the manufacturer’s manuals should be used. There are a number of techniques that can be used to detect faults: 1. Replication checks This involves duplicating or replicating an activity and comparing the results. In the absence of faults it is assumed that the results should be the same. It could mean, with transient errors, just repeating an operation twice and comparing the results or it could involve having duplicate systems and comparing the results given by the two. This can de an expensive option. 2. Expected value checks Software errors are commonly detected by checking whether an expected value is obtained when a specific numerical input is used. If the expected value is not obtained there is a fault. 3. Timing checks This involves the use of timing checks that some function has been carried out within a specified time. These checks are commonly referred as watchdog timers. For example, with a PLC, when an operation starts a timer is also started and if the operation is not completed within a specified time a fault is assumed to have occurred. The watchdog timer trips, sets off an alarm and closes down part or the entire plant. 4. Reversal checks Where there is direct relationship between input and output values, the value of the output can be taken and the input which should have caused it computed. This can then be compared with the actual input. 5. Parity and error coding checks This form of checking is commonly used for detecting memory and data transmission errors. Communication channels are frequently subject to interference which can affect data being transmitted. To detect whether data has 102


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been corrupted a parity bit is a bit added to the transmitted data word. The parity bit is chosen to make the resulting number 1s in the group either odd (odd parity) or even (even parity). If odd parity then the word can be checked after transmission to see if it is still odd. Other forms of checking involve codes added to transmitted data in order to detect corrupt bits. 6. Diagnostic checks Diagnostic checks are used to test the behaviour of components in a system. Inputs are applied to a component and the outputs compared with those which should occur. I. COMMON HARDWARE FAULTS The following are some of the commonly encountered faults that can occur with specific types of components and systems. 1. Sensors If there are faults in a measurement system then the sensor might be at fault. A simple test is to substitute the sensor with a new one and see what effect this has on the results given by the system. If the results change then it is likely that the original sensor was faulty; if the results do not change then the fault is elsewhere in the system. It is also possible to check that the voltage/current sources are supplying the correct voltages/currents, whether there is electrical continuity in connecting wires, which the sensor is correctly mounted and used under the conditions specified by the manufacturer’s data sheet, etc. 2. Switches and relays Dirt and particles of waste material between switch contacts is a common source of incorrect functioning of material switches. A voltmeter used across a switch should indicate the applied voltage when the contacts are open and very nearly zero when they are closed. Mechanical switches used to detect the position of some item, e.g. the presence of a work piece on a conveyor, can fail to give the correct responses if the alignment is incorrect or if the actuating lever is bent. Inspection of a relay can disclose evidence of arcing or contact welding. The relay should then be replaced. If a relay fails to operate then a check can be made for the voltage across the coil. If the correct voltage is present then coil continuity can be checked with an ohmmeter. If there is no voltage across the coil then the fault is likely to be the switching transistor used with the relay. 103


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3. Motors Maintenance of both d.c. and a.c. motors involves correct lubrication. With d.c. motors the brushes wear and can require changing. Setting of new brushes needs to be in accordance with the manufacturer’s specification. A single-phase capacitor start a.c. motor that is sluggish in starting probably needs a new starting capacitor. The threephase induction motor has no brushes, commutator, slip rings or starting capacitor and short of a severe overload, the only regular maintenance that is required is periodic lubrication. 4.

Hydraulic and pneumatic systems

A common cause of faults with hydraulic and pneumatic systems is dirt. Small particles of dirt can damage seals, block orifices, cause valve spools to jam, etc. Thus filters should be regularly checked and cleaned, components should only be dismantled in clean conditions, and oil should be regularly checked and changed. FAULT FINDING TECHNIQUES Fault-finding techniques that are used with microprocessor-based systems include: 1. Visual inspection Just carefully looking at a faulty system may reveal the source of a fault, e.g. an integrated circuit which is loose in its holder or surplus solder bridging tracks on a board. 2. Multimeter This is of limited use with microprocessor systems but can be used to check for short-or open-circuit connection and the power supplies. 3. Oscilloscope The oscilloscope is essentially limited to where respective signals occur and the most obvious such signal is the clock signal. Most of the other signals with a microprocessor system are not repetitive and depend on the program being executed. 4. Logic probe The logic probe is a hand-held device shaped like a pen, which can be used to determine the logic level at any point in the circuit to which it is connected. 104


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5. Logic pulsar The logic pulsar is a hand-held pulse generator, shaped like a pen, which is used to inject controlled pulse in to circuits. The pulsar probe tip is pressed against a node in the circuit and the button on the probe pressed to generate a pulse. It is often used with the logic probe to check the functions of logic gates. 6. Current tracer The current tracer is similar to the logic probe but it senses the pulsing current in a circuit rather than voltage levels. The tip of the current tracer is magnetically sensitive and is used to detect the changing magnetic field near a conductor carrying a pulsing current. The current tracer tip is moved along printed circuit tracks to trace out the low-impendence path along which current is flowing. 7. Logic clip A logic clip is a device which clips to an integrated circuit and makes contact with each of the integrated circuit pins. The logic state of each pin is then shown by LED indicators, there being one for each pin. 8. Signature analyser With analogue systems, fault finding usually involves tracing through the circuitry and examining the waveforms at various nodes, comparison of the waveforms with what would be expected enabling faults in to be identified and located. With digital systems the procedure is more complex since trains of pulses at nodes all look very similar. To identify whether there is a fault the sequence of pulse is converted into a more readily identifiable form, this being termed the signature. The signature obtained at a node can then be compared with that which should occur. When using the signature analyzer with a circuit, it is often necessary for the circuit to have been designed so that the data bus feedback paths can be broken easily for the test to stop faulty digital sequences being fed back during the testing. A short program, which is stored in ROM, is activated to stimulate nodes and enable signatures to be obtained. The microprocessor itself can be tested if the data bus is broken to isolate it from memory and it is then made to ‘free run’ and give a ‘no operation’ (NO) instruction to each of its addresses in turn. The signatures for the microprocessor bus in this state can then be compared with those expected.

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MECHATRONICS DESIGNS The design process for any system can be considered as involving a number of stages: 1. The need The design process begins with a need from, perhaps, a customer or client. This may be identified by market research being used to establish the needs of potential customers. 2. Analysis of the problem The first stage in developing a design is to find out the true nature of the problem, i.e. analysing it. This is an important stage in that not defining the problem accurately can lead to wasted time on designs that will not fulfill the need. 3. Preparation of a specification Following the analysis a specification of the requirements can be prepared. This will state the problem, any constraints placed on the solution, and the criteria which may be used to judge the quality of the design. In stating the problem, all the functions required of the design, together with any desirable features, should be specified. Thus there might be a statement of mass, dimensions, types and range of motion required, accuracy, input and output requirements of elements, interfaces, power requirements, operating environment, relevant standards and codes of practice, etc. 4. Generation of possible solutions This is often termed the conceptual stage. Outline solutions are prepared which are worked out in sufficient detail to indicate the means of obtaining each of the required functions, e.g. approximate sizes, shapes, materials and costs. It also means finding out what has been done before for similar problems; there is no sense in reinventing the wheel. 5. Selection of a suitable solution The various solutions are evaluated and the most suitable one selected. 6. Production of a detailed design The detail of the selected design has now to be worked out. This might require the production of prototypes or mock-ups in order to determine the optimum details of a design. 7. Production of working drawings The selected design is then translated into working drawings, circuit diagrams, etc. so that the item can be made. 106


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MECHATRONICS DESIGN SOLUTIONS Consider possible solutions to the following requirements for systems to carry out simple tasks. Timed Switch Consider a simple requirement for a device which switches on some actuator, e.g. a motor, for some prescribed time. A mechanical solution could involve a rotating cam shown in figure. The cam would be rotated at a constant rate and the cam follower used to actuate a switch, the length of time for which the switch is closed depending on the shape of cam.

Fig : Cam-operated switch A PLC solution could involve the arrangement shown in figure, given below, with the given ladder program.

Fig : PLC timer system 107


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This would have the advantage over the rotating cam of having off and on times which can be adjusted by purely changing the timer present values in the program whereas a different cam is needed if the times have to be changed with the mechanical solution. The software solution is much easier to implement than the hardware one. A microprocessor-based solution could involve a microprocessor with a memory chip and input/output interfaces. The program is then used to switch an output on and then off after some time delay with the time delay being produced by a block of program in which there is a timing loop. This generates a time delay by branching round a loop the number of cycles required to generate the requisite time. Thus in assembly language we might have:

DEX decrements the index register, and this and BNE, branch if not equal, each take 4 clock cycles. The loop thus take 8 cycles and there will be n such loops until 8n + 3 + 5 gives the number F424 (LDX takes 3 cycles and RTS takes 5 cycles). In C we would write the program lines using the while function.

ELECTROMECHANICAL SYSTEMS COMPACT DISC (CD) A Compact Disc (also known as a CD) is an optical disc used to store digital data, originally developed for storing digital audio. The CD, available on the market since late 1982, remains the standard playback medium for commercial audio recordings to the present day. Standard CDs have a diameter of 120 mm and can hold up to 80 minutes of audio. There is also the Mini CD, with diameters ranging from 60 to 80 mm; they are sometimes used for CD singles, storing up to 24 minutes of audio. The technology was later adapted and expanded to include data storage CDROM, write-once audio and data storage CD-R, rewritable media CD-RW, Super Audio CD (SACD), Video Compact Discs (VCD), Super Video Compact Discs (SVCD), 108


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Photo CD, Picture CD, CD-i, and Enhanced CD. CD-ROMs and CD-Rs remain widely used technologies in the computer industry. The CD and its extensions have been extremely successful: in 2004, worldwide sales of CD audio, CD-ROM, and CD-R reached about 30 billion discs. By 2007, 200 billion CDs had been sold worldwide. Physical details A Compact Disc is made from a 1.2 mm thick disc of almost pure polycarbonate plastic and weighs approximately 16 grams. A thin layer of aluminium or, more rarely, gold is applied to the surface to make it reflective, and is protected by a film of lacquer. The lacquer is normally spin coated directly on top of the reflective layer. On top of that surface, the label print is applied. Common printing methods for CDs are screen-printing and offset printing. CD data is stored as a series of tiny indentations (pits), encoded in a tightly packed spiral track molded into the top of the polycarbonate layer. The areas between pits are known as "lands". Each pit is approximately 100 nm deep by 500 nm wide, and varies from 850 nm to 3.5 µm in length. The spacing between the tracks, the pitch, is 1.6 µm. A CD is read by focusing a 780 nm wavelength (near infrared) semiconductor laser through the bottom of the polycarbonate layer. The change in height between pits and lands results in a difference in intensity in the light reflected. By measuring the intensity change with a photodiode, the data can be read from the disc. Main physical parameters The main parameters of the CD are as follows: •

• • • • • •

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Scanning velocity: 1.2–1.4 m/s (constant linear velocity) – equivalent to approximately 500 rpm at the inside of the disc, and approximately 200 rpm at the outside edge. (A disc played from beginning to end slows down during playback.) Track pitch: 1.6 µm Disc diameter 120 mm Disc thickness: 1.2 mm Inner radius program area: 25 mm Outer radius program area: 58 mm Center spindle hole diameter: 15 mm Prepared by Shijin C.S.

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The program area is 86.05 cm² and the length of the recordable spiral is (86.05 cm² / 1.6 µm) = 5.38 km. With a scanning speed of 1.2 m/s, the playing time is 74 minutes, or around 650 MB of data on a CD-ROM. If the disc diameter were only 115 mm, the maximum playing time would have been 68 minutes, i.e., six minutes less. A disc with data packed slightly more densely is tolerated by most players (though some old ones fail). Using a linear velocity of 1.2 m/s and a track pitch of 1.5 µm leads to a playing time of 80 minutes, or a capacity of 700 MB. Even higher capacities on non-standard discs (up to 99 minutes) are available at least as recordable, but generally the tighter the tracks are squeezed the worse the compatibility. Manufacture Replicated CDs are mass-produced initially using a hydraulic press. Small granules of raw polycarbonate plastic are fed into the press while under heat. A screw forces the liquefied plastic into the mold cavity. The mold closes with a metal stamper in contact with the disc surface. The plastic is allowed to cool and harden. Once opened, the disc substrate is removed from the mold by a robotic arm, and a 15 mm diameter center hole (called a stacking ring) is removed. The cycle time, the time it takes to "stamp" one CD, is usually 2–3 seconds. This method produces the clear plastic blank part of the disc. After a metallic reflecting layer (usually aluminum, but sometimes gold or other metals) is applied to the clear blank substrate, the disc goes under a UV light for drying and it is ready to go to press. To prepare to press a CD, a glass master is made using a high-power laser on a device similar in principle to a CD writer. The glass master is a positive image of the desired CD surface (with the desired microscopic pits and lands). After testing, it is used to make a die by pressing it against a metal disc. The die is a negative image of the glass master: several are typically made, depending on the number of pressing mills that are to be making the CD. The die then goes into a press and the physical image is imposed onto the blank CD, leaving a final positive image on the disc. A small amount of lacquer is then applied as a ring around the center of the disc, and a fast spin spreads it evenly over the surface. Edge protection lacquer is also applied before the disk is finished. The disc can then be printed and packed.

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DIGITAL VERSATILE DISC (DVD) DVD (also known as "Digital Versatile Disc" or "Digital Video Disc") is a popular optical disc storage media format. Its main uses are video and data storage. Most DVDs are of the same dimensions as compact discs (CDs) but store more than six times as much data. Variations of the term DVD often describe the way data is stored on the discs: DVD-ROM has data which can only be read and not written, DVD-R and DVD+R can only record data once and then function as a DVD-ROM. DVD-RW and DVD+RW can both record and erase data multiple times. The wavelength used by standard DVD lasers is 650 nm, and thus has a red color. DVD-Video and DVD-Audio discs respectively refer to properly formatted and structured video and audio content. Other types of DVDs, including those with video content, may be referred to as DVD-Data discs. As next generation High definition optical formats also use a disc identical in some aspects yet more advanced than a DVD, such as Blue-ray Disc, the original DVD is occasionally given the retronym SD DVD.

READ ONLY MEMORY Read-only memory (usually known by its acronym, ROM) is a class of storage media used in computers and other electronic devices. Because data stored in ROM cannot be modified (at least not very quickly or easily), it is mainly used to distribute firmware (software that is very closely tied to specific hardware, and unlikely to require frequent updates). In its strictest sense, ROM refers only to mask ROM (the oldest type of solid state ROM), which is fabricated with the desired data permanently stored in it, and thus can never be modified. However, more modern types such as EPROM and flash EEPROM can be erased and re-programmed multiple times; they are still described as "read-only memory" because the reprogramming process is generally infrequent, comparatively slow, and often does not permit random access writes to individual memory locations. Despite the simplicity of mask ROM, economies of scale and fieldprogrammability often make reprogrammable technologies more flexible and inexpensive, so that mask ROM is rarely used in new products as of 2007. 111


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Types of ROMs Classic mask-programmed ROM chips are integrated circuits that physically encode the data to be stored, and thus it is impossible to change their contents after fabrication. Other types of non-volatile solid-state memory permit some degree of modification: •

Programmable read-only memory (PROM), or one-time programmable ROM (OTP), can be written to or programmed via a special device called a PROM programmer. Typically, this device uses high voltages to permanently destroy or create internal links (fuses or antifuses) within the chip. Consequently, a PROM can only be programmed once.

•

Erasable programmable read-only memory (EPROM) can be erased by exposure to strong ultraviolet light (typically for 10 minutes or longer), then rewritten with a process that again requires application of higher than usual voltage. Repeated exposure to UV light will eventually wear out an EPROM, but the endurance of most EPROM chips exceeds 1000 cycles of erasing and reprogramming. EPROM chip packages can often be identified by the prominent quartz "window" which allows UV light to enter. After programming, the window is typically covered with a label to prevent accidental erasure. Some EPROM chips are factory-erased before they are packaged, and include no window; these are effectively PROM.

•

Electrically erasable programmable read-only memory (EEPROM) is based on a similar semiconductor structure to EPROM, but allows its entire contents (or selected banks) to be electrically erased, then rewritten electrically, so that they need not be removed from the computer (or camera, MP3 player, etc.). Writing or flashing an EEPROM is much slower (milliseconds per bit) than reading from a ROM or writing to a RAM (nanoseconds in both cases), since available densities are not as great and the cost per bit is higher. o

Electrically alterable read-only memory (EAROM) is a type of EEPROM that can be modified one bit at a time. Writing is a very slow process and again requires higher voltage (usually around 12 V) than is used for read access. EAROMs are intended for applications that require infrequent and only partial rewriting. EAROM may be used as non-volatile storage for critical system setup information; in many applications, EAROM has been supplanted by CMOS RAM supplied by mains power and backed-up with a lithium battery.

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Flash memory (or simply flash) is a modern type of EEPROM invented in 1984. Flash memory can be erased and rewritten faster than ordinary EEPROM, and newer designs feature very high endurance (exceeding 1,000,000 cycles). Modern NAND flash makes efficient use of silicon chip area, resulting in individual ICs with a capacity as high as 16 GB as of 2007; this feature, along with its endurance and physical durability, has allowed NAND flash to replace magnetic in some applications (such as USB flash drives). Flash memory is sometimes called flash ROM or flash EEPROM when used as a replacement for older ROM types, but not in applications that take advantage of its ability to be modified quickly and frequently.

OPTICAL CHARACTER RECOGNITION (OCR) Optical character recognition, usually abbreviated to OCR, is the mechanical or electronic translation of images of handwritten, typewritten or printed text (usually captured by a scanner) into machine-editable text. OCR is a field of research in pattern recognition, artificial intelligence and machine vision. Though academic research in the field continues, the focus on OCR has shifted to implementation of proven techniques. Optical character recognition (using optical techniques such as mirrors and lenses) and digital character recognition (using scanners and computer algorithms) were originally considered separate fields. Because very few applications survive that use true optical techniques, the OCR term has now been broadened to include digital image processing as well. Early systems required training (the provision of known samples of each character) to read a specific font. "Intelligent" systems with a high degree of recognition accuracy for most fonts are now common. Some systems are even capable of reproducing formatted output that closely approximates the original scanned page including images, columns and other non-textual components. Optical Character Recognition (OCR) is sometimes confused with on-line character recognition. OCR is an instance of off-line character recognition, where the system recognizes the fixed static shape of the character, while on-line character recognition instead recognizes the dynamic motion during handwriting. For example, on-line recognition, such as that used for gestures in the Penpoint OS or the Tablet PC 113


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can tell whether a horizontal mark was drawn right-to-left, or left-to-right. On-line character recognition is also referred to by other terms such as dynamic character recognition, real-time character recognition, and Intelligent Character Recognition or ICR. On-line systems for recognizing hand-printed text on the fly have become wellknown as commercial products in recent years. Among these are the input devices for personal digital assistants such as those running Palm OS. The Apple Newton pioneered this product. The algorithms used in these devices take advantage of the fact that the order, speed, and direction of individual lines segments at input are known. Also, the user can be retrained to use only specific letter shapes. These methods cannot be used in software that scans paper documents, so accurate recognition of hand-printed documents is still largely an open problem. Accuracy rates of 80% to 90% on neat, clean hand-printed characters can be achieved, but that accuracy rate still translates to dozens of errors per page, making the technology useful only in very limited applications. Recognition of cursive text is an active area of research, with recognition rates even lower than that of hand-printed text. Higher rates of recognition of general cursive script will likely not be possible without the use of contextual or grammatical information. For example, recognizing entire words from a dictionary is easier than trying to parse individual characters from script. Reading the Amount line of a cheque (which is always a written-out number) is an example where using a smaller dictionary can increase recognition rates greatly. Knowledge of the grammar of the language being scanned can also help determine if a word is likely to be a verb or a noun, for example, allowing greater accuracy. The shapes of individual cursive characters themselves simply do not contain enough information to accurately (greater than 98%) recognize all handwritten cursive script. It is necessary to understand that OCR technology is a basic technology also used in advanced scanning applications. For more complex recognition problems, intelligent character recognition systems are generally used, as artificial neural networks can be made indifferent to both affine and non-linear transformations.

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PRINTERS One of the most commonly used computer peripherals is the printer. a printer is a peripheral which produces a hard copy (permanent human-readable text and/or graphics) of documents stored in electronic form, usually on physical print media such as paper or transparencies. Many printers are primarily used as local peripherals, and are attached by a printer cable or, in most new printers, a USB cable to a computer which serves as a document source. Some printers, commonly known as network printers, have built-in network interfaces (typically wireless or Ethernet), and can serve as a hardcopy device for any user on the network. Individual printers are often designed to support both local and network connected users at the same time. In addition, a few modern printers can directly interface to electronic media such as memory sticks or memory cards, or to image capture devices such as digital cameras, scanners; some printers are combined with a scanners and/or fax machines in a single unit, and can function as photocopiers. Printers that include non-printing features are sometimes called Multifunction Printers (MFP), Multi-Function Devices (MFD), or All-In-One (AIO) printers. Most MFPs include printing, scanning, and copying among their features. Printers are designed for low-volume, short-turnaround print jobs; requiring virtually no setup time to achieve a hard copy of a given document. However, printers are generally slow devices (30 pages per minute is considered fast), and the cost-per-page is relatively high. The world's first computer printer was a 19th century mechanically driven apparatus invented by Charles Babbage for his Difference Engine. TYPES OF PRINTERS Impact printers place characters on the page by causing a hammer device to strike an inked ribbon. The ribbon, in turn, strikes the printing surface (paper). Several nonimpact methods of printing are used in computer printers. Older, nonimpact printers relied on special heat-sensitive or chemically reactive paper to form characters on the page. Newer methods of nonimpact printing use ink droplets, squirted from a jet nozzle device (ink-jet printers), or a combination of laser/xerographic print technologies (laser printers) to place characters on a page. Currently, the most popular nonimpact printers use ink-jet or laser technologies to deliver ink to the page. 115


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Basically, there are two methods of creating characters on a page. One method places a fully shaped and fully filled-in character on the page. This type of character is called a fully formed character. The other method involves placing dots on the page in strategic patterns to fool the eye into seeing a character. This type of character is referred to as a dot-matrix character. Over time, printer technology has improved so that they can produce photolike images. However, a number of printer technologies are still in use, due to cost and quality differences between them. The three most common printer technologies are dot matrix, inkjet or bubble jet, and laser.

MODERN PRINT TECHNOLOGY The following printing technologies are routinely found in modern printers 1. TONER BASED PRINTERS Toner-based printers work using the Xerographic principle that is used in most photocopiers: by adhering toner to a light-sensitive print drum, then using static electricity to transfer the toner to the printing medium to which it is fused with heat and pressure. The most common type of toner-based printer is the laser printer, which uses precision lasers to cause toner adherence. Laser printers are known for high quality prints, good print speed, and a low (Black and White) cost-per-copy. They are the most common printer for many general-purpose office applications, but are much less common as consumer printers due to their high initial cost-although this cost is dropping. Laser printers are available in both color and monochrome varieties. LASER PRINTERS A laser beam projects an image of the page to be printed onto an electrically charged rotating drum coated with selenium. Photoconductivity removes charge from the areas exposed to light. Dry ink (toner) particles are then electrostatically picked up by the drum's charged areas. The drum then prints the image onto paper by direct contact and heat, which fuses the ink to the paper.

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2. LIQUID INKJET PRINTERS Inkjet printers operate by propelling variably-sized droplets of liquid or molten material (ink) onto almost any sized page. They are the most common type of computer printer for the general consumer due to their low cost, high quality of output, capability of printing in vivid color, and ease of use. The emerging ink jet material deposition market also uses ink jet technologies, typically piezoelectric jets, to deposit materials directly on substrates. The idea is that because the head need not be replaced every time the ink runs out, consumable costs can be made lower and the head itself can be more precise than a cheap disposable one, typically requiring no calibration. On the other hand, if the head is damaged, it is usually necessary to replace the entire printer.

TECHNOLOGIES There are three main technologies in use in contemporary inkjet printers: thermal, piezoelectric, and continuous. 1. Thermal inkjets Most consumer inkjet printers (Lexmark, Hewlett-Packard, and Canon) use print cartridges with a series of tiny electrically heated chambers constructed by photolithography. To produce an image, the printer runs a pulse of current through the heating elements causing a steam explosion in the chamber to form a bubble, which propels a droplet of ink onto the paper. The ink's surface tension as well as the condensation and thus contraction of the vapour bubble, pulls a further charge of ink into the chamber through a narrow channel attached to an ink reservoir. The ink used is known as aqueous (i.e. water-based inks using pigments or dyes) and the print head is generally cheaper to produce than other inkjet technologies. The principle was discovered by Canon engineer Ichiro Endo in August 1977. 2. Piezoelectric inkjets Most commercial and industrial ink jet printers use a piezoelectric material in an ink-filled chamber behind each nozzle instead of a heating element. When a voltage is applied, the piezoelectric material changes shape or size, which generates a 117


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pressure pulse in the fluid forcing a droplet of ink from the nozzle. This is essentially the same mechanism as the thermal inkjet but generates the pressure pulse using a different physical principle. Piezoelectric (also called Piezo) ink jet allows a wider variety of inks than thermal or continuous ink jet but the print heads are more expensive. Piezo inkjet technology uses stationary heads, which are built with robust construction and are designed for high volume production, faster print speeds, and lower costs. There is a drop-on-demand process, with software that directs the heads to apply between zero to eight droplets of ink per dot and only where needed. 3. Continuous ink jet The continuous ink jet method is used commercially for marking and coding of products and packages. The idea was first patented in 1867, by Lord Kelvin and the first commercial devices (medical strip chart recorders) were introduced in 1951 by Siemens. In continuous ink jet technology, a high-pressure pump directs liquid ink from a reservoir through a gunbody and a microscopic nozzle, creating a continuous stream of ink droplets via the Plateau-Rayleigh instability. A piezoelectric crystal creates an acoustic wave as it vibrates within the gunbody and causes the stream of liquid to break into droplets at regular intervals – 64,000 to 165,000 drops per second may be achieved. The ink droplets are subjected to an electrostatic field created by a charging electrode as they form, the field varied according to the degree of drop deflection desired. This results in a controlled, variable electrostatic charge on each droplet. Charged droplets are separated by one or more uncharged “guard droplets” to minimize electrostatic repulsion between neighbouring droplets. The charged droplets pass through an electrostatic field and are directed (deflected) by electrostatic deflection plates to print on the receptor material (substrate), or allowed to continue on undeflected to a collection gutter for re-use. The more highly charged droplets are deflected to a greater degree. Only a small fraction of the droplets is used to print, the majority being recycled. Continuous ink jet is one of the oldest ink jet technologies in use and is fairly mature. One of its advantages is the very high velocity (50 m/s) of the ink droplets, which allows for a relatively long distance between print head and substrate. Another advantage is freedom from nozzle clogging as the jet is always in use, therefore allowing volatile solvents such as ketones and alcohols to be employed, giving the ink the ability to "bite" into the substrate and dry quickly. 118


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The ink system requires active solvent regulation to counter solvent evaporation during the time of flight (time between nozzle ejection and gutter recycling) and from the venting process whereby air that is drawn into the gutter along with the unused drops is vented from the reservoir. Viscosity is monitored and a solvent (or solvent blend) is added in order to counteract the solvent loss. Advantages of Inkjet Printer: Compared to earlier consumer-oriented colour printers, inkjets have a number of advantages. They are quieter in operation than impact dot matrix or daisywheel printers. They can print finer, smoother details through higher printhead resolution, and many consumer inkjets with photographic-quality printing are widely available. In comparison to more expensive technologies like thermal wax, dye sublimations, and laser printers, inkjets have the advantage of practically no warm up time and lower cost per page (except when compared to laser printers). Disadvantages of Inkjet Printer: Inkjet printers may have a number of disadvantages 1. The ink is often very expensive. (For a typical OEM cartridge priced at $15, containing 5 mL of ink, the ink effectively costs $3000 per liter--or $8000 per gallon.) 2. Many "intelligent" ink cartridges contain a microchip that communicates the estimated ink level to the printer; this may cause the printer to display an error message, or incorrectly inform the user that the ink cartridge is empty. In some cases, these messages can be ignored, but some inkjet printers will refuse to print with a cartridge that declares itself empty, in order to prevent consumers from refilling cartridges. 3. The lifetime of inkjet prints produced by inkjets using aqueous inks is limited; they will eventually fade and the color balance may change. On the other hand, prints produced from solvent-based inkjets may last several years before fading, even in direct sunlight, and so-called "archival inks" have been produced for use in aqueous-based machines which offer extended life. 4. Because the ink used in most consumer inkjets is water-soluble, care must be taken with inkjet-printed documents to avoid even the smallest drop of water, which can cause severe "blurring" or "running." Similarly, water-based highlighter markers can blur inkjet-printed documents.

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3.DOT-MATRIX PRINTERS A dot matrix printer or impact matrix printer is a type of computer printer with a print head that runs back and forth on the page and prints by impact, striking an ink-soaked cloth ribbon against the paper, much like a typewriter. Unlike a typewriter or daisy wheel printer, letters are drawn out of a dot matrix, and thus, varied fonts and arbitrary graphics can be produced. Because the printing involves mechanical pressure, these printers can create carbon copies and carbonless copies. Each dot is produced by a tiny metal rod, also called a "wire" or "pin", which is driven forward by the power of a tiny electromagnet or solenoid, either directly or through small levers (pawls). Facing the ribbon and the paper is a small guide plate (often made of an artificial jewel such as sapphire or ruby) pierced with holes to serve as guides for the pins. The moving portion of the printer is called the print head, and when running the printer as a generic text device generally prints one line of text at a time. Most dot matrix printers have a single vertical line of dot-making equipment on their print heads; others have a few interleaved rows in order to improve dot density. These machines can be highly durable. When they do wear out, it is generally due to ink invading the guide plate of the print head, causing grit to adhere to it; this grit slowly causes the channels in the guide plate to wear from circles into ovals or slots, providing less and less accurate guidance to the printing wires. Eventually, even with tungsten blocks and titanium pawls, the printing becomes too unclear to read. Although nearly all inkjet, thermal, and laser printers produce dot matrices, in common parlance these are seldom called "dot matrix" printers, to avoid confusion with dot matrix impact printers. Dot matrix printers can either be character-based or line-based (that is, a single horizontal series of pixels across the page), referring to the configuration of the print head. Dot matrix printers were one of the more common types of printers used for general use - such as for home and small office use. Such printers would have either 9 or 24 pins on the print head. 24-pin print heads were able to print at a higher quality. Once the price of inkjet printers dropped to the point where they were competitive with dot matrix printers, dot matrix printers began to fall out of favor for general use.

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BIOMEDICAL ENGINEERING Biomedical engineering (BME) is the application of engineering principles and techniques to the medical field. It combines the design and problem solving skills of engineering with medical and biological sciences to help improve patient health care and the quality of life of individuals.

MEDICAL DEVICES A medical device is an object which is useful for diagnostic or therapeutic purposes. Examples of medical devices include medical thermometers, blood sugar meters, and X-ray machines. Definition : A medical device as any instrument, apparatus, appliance, software, material or other article, whether used alone or in combination, including the software intended by its manufacturer to be used specifically for diagnostic and/or therapeutic purposes and necessary for its proper application, intended by the manufacturer to be used for human beings. Devices are to be used for the purpose of: •

Diagnosis, prevention, monitoring, treatment or alleviation of disease.

•

Diagnosis, monitoring, treatment, alleviation of or compensation for an injury or handicap.

•

Investigation, replacement or modification of the anatomy or of a physiological process

•

Control of conception

This includes devices that do not achieve its principal intended action in or on the human body by pharmacological, immunological or metabolic means, but which may be assisted in its function by such means. List of medical devices a. High risk devices High risk devices are life supports, critical monitoring, energy emitting and other devices whose failure or misuse is reasonably likely to seriously injure patient or staff. Examples includes • • • • • • •

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Anesthesia ventilators Anesthesia units Electrosurgical units Incubators Pulse oximeters External pacemaker Heart Lung Machine etc. Prepared by Shijin C.S.

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b. Medium risk devices These are devices including many diagnostic instruments whose misuse, failure or absence (e.g. out of service with no replacement available would have a significant impact on patient care, but would not be likely to cause direct serious injury. Examples are •

ECG • EEG • Ultrasound sensors • Phototherapy units • Phonocardiograph’s etc. c. Low risk devices Devices in this category are those whose failure or misuse is unlikely to result in serious consequences. Some examples for such equipments include • • • • • • • •

Electronic thermometer, Breast pumps Surgical microscope Sphygmomanometers Surgical table Surgical lights. Temperature monitor X-rays diagnostic equipment etc.

ARTIFICIAL INTERNAL ORGANS An artificial organ is a man-made device that is implanted into, or integrated onto, a human to replace a natural organ, for the purpose of restoring a specific function or a group of related functions so the patient may return to as normal a life as possible. The replaced function doesn't necessarily have to be related to life support, but often is. Reasons to construct and install an artificial organ, an extremely expensive process initially, which may entail many years of ongoing maintenance services not needed by a natural organ, might include: • • • •

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Life support to prevent imminent death while awaiting a transplant (e.g. artificial heart) Dramatic improvement of the patient's ability for self care (e.g. artificial limb) Improvement of the patient's ability to interact socially (e.g. cochlear implant) Cosmetic restoration after cancer surgery or accident Prepared by Shijin C.S.

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Some of the artificial internal organs are Pacemakers Artificial Heart Valves Heart Lung Machine I. PACEMAKERS Pacemaker is an electrical pulse generator for starting and/or maintaining the normal heart beat. The output of the pacemaker is applied either externally to the chest or internally to the heart muscle. In the case of cardiac stand still, the use of the pacemaker is temporary - just long enough to start a normal heart rhythm. In case's requiring long term pacing, the pacemaker is surgically implanted in the body and its electrodes are in direct contact with the heart. In cardiac diseases, where the ventricular rate is too low, it can be increased to normal rate by using pacemaker. The various arrhythmias (rhythm disturbances) that result in heart block and Adams stokes attacks represent a serious pathological condition. During that time, the patient becomes invalid because of the constant risk of sudden losing consciousness. By fixing the artificial electronic pacemakers, the above defects in the heart can be eliminated. With conventional drug therapy, the failure within a year is about 50%. Pacemaker therapy lowers this figure to 15% and leads to a considerable improvement in the patient’s mental and physical wellbeing. Methods of stimulation There are two types of stimulation or pacing: External stimulation and Internal stimulation. External stimulation is employed to restart the normal rhythm of the heart in the case of cardiac stand still. Stand still can occur during open heart surgery or whenever there is a sudden physical shock or accident. The paddle shaped electrodes are applied on the surface of the chest and currents in the range of 20 – 150 mA are employed. Internal stimulation is employed in cases requiring long term pacing because of permanent damage that prevents normal self triggering of the heart. The electrodes are in the form of fine wires of Teflon coated stainless steal. In some cases, during restarting of the heart after open heart surgery, spoon like electrodes are used. The currents in the range of 2 – 15 mA are employed. The bipolar and unipolar electrodes are used. In the bipolar electrode, there are stimulating electrode and contact electrode which serves as a return path for current to the pacemaker. In the unipolar electrode, there is only stimulating electrode and the return path for current to the pacemaker is made through body fluids. 123


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Even though the internal stimulation is adopted in most cases, based on the placement of the pacemaker; there are two types, external pacemaker and implanted pacemaker. Implanted pacemaker No.

External pacemaker

(internal pacemaker)

1.

The pacemaker is placed outside the body. It may be in the form of wrist watch or in the pocket, from that one wire will go into the heart through the vein.

The pacemaker is miniaturized and is surgically implanted beneath the skin near the chest or abdomen with its output leads are connected directly to the heart muscle.

2.

The electrodes are called endocardiac electrodes and are applied to the heart by means of an electrode catheter with electrode’s tip situated in the apex of the right ventricle. These are in contact with the inner surface of the heart chamber.

The electrodes are called myocardiac electrodes and are in contact with the outer wall of the myocardium (heart muscle). Endocardiac electrodes are also used.

3.

It does not necessitate the open chest It requires an open chest minor surgery. surgery to place the circuit.

4.

The battery can be easily replaced and any defect or adjustment in the circuit can be easily attended without getting any help from a medical doctor.

The battery can be replaced only by minor surgery. Further any defeat or adjustment in the circuit cannot be easily attended. Doctor’s help is necessary to rectify the defeat in the circuit.

5.

During placement, swelling and pain During placement swelling and pain do not arise due to maintain foreign arise due to foreign body reaction. body reaction.

6.

Here there is no safety for the Here there is a cent percent safety for pacemaker particularly in the case of the circuit from the external children carrying the pacemaker. disturbances.

7.

Mostly these are used for temporary Mostly these are used for permanent heart irregularities. heart irregularities.

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II. ARTIFICIAL HEART VALVES An artificial heart valve is a device which is implanted in the heart of patients who suffer from valvular diseases in their heart. When one or two of the four heart valves (human heart contains four valves: tricuspid valve, pulmonic valve, mitral valve and aortic valve) of the heart have a malfunction, the choice is normally to replace the natural valve with an artificial valve. This requires open-heart surgery. Valves are integral to the normal physiological functioning of the human heart. Natural heart valves are structures which have evolved a form which meets their functional requirements, which is to induce largely unidirectional flow through themselves. Natural heart valves may become dysfunctional due to a variety of pathological causes. Certain heart valve pathologies may necessitate the complete surgical replacement of the natural heart valves with heart valve prostheses. Different Natural Heart Valves Since the left side of the heart is the one which normally functions with much higher pressure differentials, the left heart valves are usually failed to function properly. The mitral valve is located between the left atrium and the left ventricle and the aortic valve is located between the left ventricle and aorta. Occasionally the tricuspid valve which is located between the right ventricle and right atrium will fail. The procedure in valve replacement involves opening the chest (thoracotomy), placing the heart on bypass using a heart-lung machine, cutting through the heart muscle to expose the valve, excising the diseased valve and the surrounding tissue and attaching a prosthetic valve in its place. Different Types of Artificial Heart Valves Most of the artificial heart valves are check valves of the caged-ball (Scandanavian type) or caged-disc (Alaskan type) variety. The ball or disc is made from silicone rubber. A metal ring surrounded by either Dacron or Teflon forms the connecting surface which is sewn to the natural seat from which the pathologic valve is removed. Starr and Edwards devised a mitral valve using a ball made of silastic 372

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rubber (Figure (a)). The Starr-Edwards aortic valve has large orifice and small regurgitation. It has large opening resistance. The closure of that valve is in a very slow manner. The Magovern-Cromie aortic valve (Figure (b )) differs from others such that there is a series of needle like projections which are screwed out during the installation procedure. These attach themselves to the ring of tissue around the valve and form the fixation. Its main advantage is that time consuming sewing of the valve to the tissue is eliminated and the operation can be performed in much less time. In the Kay Shiley mitral valve (Figure (c)) a caged disc replaces the silastic ball. This type is anatomically more suitable than other types. Gott butterfly mitral valve (Figure (d)) has quick opening and closing and large orifice. It has a disadvantage that it has great regurgitation. Similarly the leaflet valve (Figure (e)) used as mitral valve has the same functioning of Gott butterfly valve. Now-a-days the ball or disc is made of hollowed solid polymers (polypropylene, polyoxymethylene, polychlorotrifluro ethylene, etc.), metals (titanium and vitallium alloys) and pyrolytic carbon.

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III. HEART-LUNG MACHINE During open heart surgery for installation of a valve prosthesis or correction of a congenital mal function, the heart cannot maintain the circulation. It is then necessary to provide extra-corporeal circulation with a special machine called heart lung machine. Further this is also used to provide circulatory assistance to support a faulty heart. While doing open heart surgery, it is necessary to bypass the heart to enable the surgeon to work in a bloodless field under direct vision. The heart-lung machine replaces the functions of heart and lungs thereby providing the rest of the body with a continuous supply of oxygenated blood while the heart is stopped. Eventhough the heart is to be bypassed for the repair itself, for technical reasons both the heart and lungs are bypassed by present day methods. Mechanical Functions of the Heart i. In an intact heart, venous or unoxygenated blood is returned to the right side of the heart at a pressure of 0 to 5 mm Hg and oxygen saturation below 75%. ii. From the right side of the heart, the blood is pumped into lungs through pulmonary arteries. iii. In the lungs the blood is oxygenated to about 95 to 98% saturation and then it is going to the left atrium of the heart, which acts as a receiving chamber. iv. From there, the blood flows into the left ventricle through the mitral valve. The left ventricle is called the more powerful chamber of the heart. v. The ventricle ejects the blood into the aorta with peak pressures ranging from 100 to 150 mm Hg. vi. Since the contraction of the left ventricle is rhythmic, the resultant flow in the aorta is pulsatile, reaching a systolic peak pressure of about 90 to 140 mm Hg with 120 mm Hg as the mean and a low point or diastolic of about 60 to 90 mm Hg with 80 mm Hg as the mean. Systole is the period of contraction of the ventricular muscles during that time blood is pumped into the pulmonary artery and the aorta. Diastole is the period of dilation of the heart chambers as they fill with blood. vii. The heart pumps about 5 liters of blood per minute. At any time, the veins contain 75 to 80% of the blood volume and arteries contain 20 to 25% of blood volume. viii. The pressures in different areas of the heart are given as follows:

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Following figure shows the systematic cardiovascular circulation procedure. All the arteries, (except pulmonary artery) carry pure blood from heart to different parts of the body. Similarly all the veins (except pulmonary vein) carry the impure blood from different parts of the body to the heart.

Fig: Systematic Cardiovascular circulation 128


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THERAPEUTIC ELECTROMECHANICAL DEVICES (EMD’s) Therapeutic EMD’s are those instruments which are used for the treatment of human diseases. Widely used Therapeutic EMD’s are Kidney Machine, Ventilators, and Anesthesia Machine. I. KIDNEY MACHINE Kidney machine is an equipment used a s a substitute for a kidney. Although hemo dialysis, a process for removing impurities from blood was first achieved in 1944, a clinically useful device was developed only in 1960 by B.H.Scribner and his group. Renal function The natural kidneys in our body are used to eliminate the waste products formed during bodily metabolism and regulate the concentration of the body fluid constituents. Eventhough there are two kidneys in each body, a single kidney is capable of clearing all waste products in the blood. Figure shows the formation of urine from blood by the smallest functional units of the kidneys, called nephrons. The urine is formed by three processes, namely, filtration of blood plasma, active secretion of urea, uric acid and phosphates and reabsorption of water, glucose and sodium chloride so that they are restored to the blood. Each kidney contains about 1 to 1.25 million nephrons. Each nephron consists of a glomerulus which has done the filtration and several tubeles which have done the active secretion and reabsorption. Arterial blood is entering into the glomerulus where filtration takes place.

Fig: Formation of urine from blood by nephrons 129


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Water, glucose, amino acid, salts, low molecular weight protein, urea, uric acid and creatinine are filtered out. The process of reabsorption takes place at the entrance of the proximal tube (tubele) where glucose, amino acid, protein, water and salt are chiefly reabsorbed. Under elevated concentration of a particular chemical in the blood, the reabsorption by the tubeles is not complete. For example, in the case of diabetes, the blood sugar level exceeds about 9 mmol/litre, the glucose appears in the urine. Since the urine reflects the composition of the blood plasma, urinalysis is used in the diagnosis of diseases that are accompanied by metabolic disorders. In the case of renal damage, the plasma creatinine (nitrogen containing substances) level in the urine is reduced below 7-14 millimol/day. Similarly urea level in the urine is also decreased in the case of renal failure. In the case of complete renal failure, uremia is developed. During that time, most of the metabolic breakdown products cannot be excreted and they collect in the body itself. Thus the urea and creatinine levels in the blood are increased. By that way the acid-base balance in the body is upset and acidosis is developed. Because of acidosis, the amount of potassium in the extra cellular fluid increases and this increase in potassium may affect the heart function. Within few weeks, the death may occur. The advanced renal failure may be due to inflammation of the kidneys, obstruction of urine by stones or tumors, poisoning by organic and inorganic chemicals. Intermittent treatment with a mechanical device, called artificial kidney will reduce the accumulation of waste products and water in the body. II. VENTILATORS A medical ventilator may be defined as an automatic machine designed to mechanically move breathable air into and out of the lungs, to provide the mechanism of breathing for a patient who is physically unable to breathe, or breathing insufficiently. Ventilators are chiefly used in intensive care medicine, home care, and emergency medicine (as standalone units) and in anesthesia (as a component of an anesthesia machine). As a part of intensive care, the patients often require assistance with breathing. When artificial ventilation is required for a long time, a ventilator is used to provide oxygen enriched, medicated air to a patient at a controlled temperature. Ventilators can operate in different modes: Controlled breathing where breathing is initiated by a timing mechanism and Assisted breathing or patient initiated breathing. Controlled breathing is an automatically timed breathing which is usually provided for patients who cannot breathe on their own. It provides inspirations and expirations at fixed 130


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rates except during the rest period for the patient. In the case of assisted breathing, the patient's own spontaneous attempt to breathe in, causes the ventilator to cycle on during inspiration. Thus it is used for the patient who has difficult breathing due to high air way resistance. There are servo controlled ventilators which can switch automatically to any mode depending upon the condition of the patient. This type of mode is called assist-control mode. By this mode, the patient controls his own breathing as long as he can, but if he should fail to do so, the control mode is able to take over for him. The ventilator treatment gives the following: a) Adequate ventilation by which enough oxygen is supplied and the right amount of carbon dioxide is eliminated. Thus hyperventilation which creates respiratory alkalosis and hypoventilation which creates respiratory acidosis are avoided. b) Elimination of respiratory work c) Increased intrathoracic pressure which prevents atelectasis that is collapse of portions of the lung and counteracts edema of the lung. Every ventilator operates cyclically. During insufflation or inspiration air or some other gaseous mixture is pumped into the lungs. During expiration the pressure ceases. This cycle is regulated by a mechanical, pneumatic or electronic circuit. The regulation is obtained by pressure limited, volume limited and servo-controlled systems. i) Pressure limited ventilators Pressure limited ventilators are based on the principle that the insufflation is terminated when the gaseous mixture pumped into the patient's lungs reaches a preset pressure. Pressure-limited ventilators are driven by the compressed gaseous mixture used for ventilation. These are so simple in design and reliable in operation. Below figure shows the pressure limited ventilator system. ii) Volume limited ventilators Volume limited ventilators are based on the principle that for each breath, a constant volume of air is delivered. During insufflation, the constant volume of air is sent into the lungs by applying pressure to a chamber containing constant volume. The volume limited ventilators do not give the desired ventilation in cases where the pre-set maximum pressure cannot completely empty the chamber. iii) Servo-controlled ventilators This is based on the usage of modern electronic control techniques such that the flow to and from the patient is controlled by feedback circuits. The electronic unit 131


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controls the amplifiers and logic circuits that control the ventilation. It also monitors pressures, activates alarms and computes mechanical lung parameters.

Fig: Block diagram of a ventilator with its accessories III. ANESTHESIA MACHINE The anesthetic machine (or anesthesia machine) is used by anesthesiologists to support the administration of anesthesia. The most common type of anesthetic machine in use in the developed world is the continuous-flow anesthetic machine, which is designed to provide an accurate and continuous supply of medical gases (such as oxygen and nitrous oxide), mixed with an accurate concentration of anesthetic vapour (such as isoflurane), and deliver this to the patient at a safe pressure and flow. Modern machines incorporate a ventilator, suction unit, and patientmonitoring devices. 132


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The original concept was invented by the British anesthetist H.E.G. Boyle in 1917. Prior to this time, anesthetists often carried all their equipment with them, but the development of heavy, bulky cylinder storage and increasingly elaborate airway equipment meant that this was no longer practical for most circumstances. The anesthetic machine is usually mounted on anti-static wheels for convenient transportation.

Fig: Anesthesia Machine The above figure shows the block diagram of an anesthesia machine. It corresponds to the modern partial rebreathing system. The most commonly used anesthetic is nitrous oxide used in combination with fluorocarbons, such as halothene, enflurance, methoxyflurane, etc. and oxygen. These are nonflammable. This mixture is delivered to the patient on the inspiration cycle. The flow rate is correctly maintained by the flow meters in the each gas tubing. Exhalation passes through a one way valve, through a CO2 absorber and is delivered to again to the patient. The anesthetic is constantly monitored and adjusted for the correct mixture by means of controlling circuits using flow meters like turbine flow meter or rotameter. A portion of the anesthetic is exhausted and usually delivered to the outside through vent ducts. During the supply of anesthesia, the respiration and blood circulation should be monitored even though the supplied anesthesia is very small. 133


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DIAGNOSTIC ELECTROMECHANICAL DEVICES (EMD’s) Diagnostic instruments, as the name itself implies finds the application in finding disease conditions. In medicine, diagnosis has two distinct dictionary definitions. The first definition is "the recognition of a disease or condition by its outward signs and symptoms", while the second definition is "the analysis of the underlying physiological/biochemical cause(s) of a disease or condition". Simply put, it is the process of identifying a medical condition or disease by its signs, symptoms, and from the results of various diagnostic procedures. The conclusion reached through this process is called a diagnosis. Usually Pulmonary Function Analysers are used as a Diagnostic EMD in Biomedical engineering. PULMONARY FUNCTION ANALYSERS Pulmonary function analysers are used to evaluate the state of the lungs or the respiratory process. Clinically three basic types of measurements are performed. Ventilation, distribution and diffusion. Ventilation Ventilation deals with the determination of the ability of the body to displace air volume quantitatively and the speed with which it moves the air. Mostly spirometers are used in the ventilation measurements. Distribution Distribution measurements indicate the degree of lung obstructions for the flow of air and also determine the residual volume of air that cannot be removed from the lungs. Pneumotachometers are used to measure the instantaneous rate of volume flow of respired gases. Diffusion Diffusion measurements indicate the lung ability to exchange gas with the circulatory system, or the rate at which gas is exchanged with the blood stream. Gas analysers are used in the diffusion measurements.

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LUNG VOLUMES AND CAPACITIES All the pulmonary function analysers are used to determine the lung volumes and capacities. These parameters depend on the individual’s physical characteristics and the condition of his/her breathing mechanism.

Fig: Lung volumes and capacities Figure shows the lung volumes and capacities. The lung capacities are indicated by milliliters and the volumes are indicated by percentages. i.

The total lung capacity (TLC) is the amount of gas contained in the lungs at the end of a maximal inspiration. As in figure, it is the sum of the vital capacity (VC) and residual volume (RV).

ii.

During inspiration the lung volume is increased and during expiration, it is decreased. Thus the vital capacity (VC) is the maximum volume of gas that can be expelled from the lungs after a maximal inspiration. The tidal volume (TV) is the volume of gas inspired or expired during each normal, quiet and respiration cycle.

iii.

The residual volume (RV) is the volume of gas remaining in the lungs at the end of a maximal expiration. Inspiratory reserve volume (IRV) is the extra volume of gas that can be inspired with maximal effort after reaching the normal end of inspiratory level. Expiratory reserve volume (ERV) is the extra 135


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volume of gas that can be expired with maximum effort beyond reaching the normal end of expiratory level. iv.

Inspiratory capacity (IC) is the maximum amount of gas that can be inspired after reaching the end expiratory level. Functional residual capacity (FRC) is the volume of gas remaining in the lungs at the end of expiratory level.

v.

There are some forced breathing tests which are used to assess the muscle power associated with breathing and the resistance of the airway like forced vital capacity (FVC), which is the total amount of air that can forcibly be expired as quickly as possible after taking the deepest possible breath and forced expiratory volume (FEV) which is the maximum amount of gas that can be expelled in a given time.

SPIROMETER Already the use of the spirometer is discussed in the Ventilators. Spirometer is mainly used to measure the respiratory volume measurements. Thus with the aid of spirometer, all lung volumes and capacities can be determined by measuring the amount of gas inspired or expired under a given set of conditions or during a given time interval. In the ventilator, the spirometer with cylinder – piston has been discussed.

Fig: Spirometer

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Figure shows an electrical spirometer. It consists of light weight bellows. Due to light weight, there is no airway resistance error. These bellows are mechanically articulated to a biased potentiometer such that the wiper arm voltage is proportional to volume, VOL of the bellows. The maximum volume of the bellows in the spirometer in the spirometer is given by

VOL max = L π r 2 If α is the proportionality constant giving the fractional position of the wiper arm on the potentiometer ‘R’ such that

α =

∴ VOL =

Vout VBB

=

VOL VOL max

Vout VOL max VBB

Thus one can get better linearity in measuring respiratory volumes, provided the indicator (voltmeter) should have better linearity over the desired volume. Normally a mouthpiece is provided with a spirometer along with the connecting tube.

REFERENCES 1) Mechatronics

- W. Bolton

2) Mechatronics

- Ganesh S. Hegde

3) Control Systems and Mechatronics

- J.Srinivas

4) Biomedical Instrumentation

- Dr. M. Arumugam

5) Mechatronics

- Dan S. Necsuleseu

6) Understanding Electro Mechanical Engineering

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Introduction to Control Systems Engineering

MODULE - 3 Introduction to control SYSTEMS engineering CONTROL SYSTEM Control system is a system in which the output quantity is controlled by varying the input quantity. The output quantity is called controlled variable or response and the input quantity is called command signal or excitation.

The primary objective of any control system is to maintain the response of a process at a desired value. For example, we want to maintain the level at a desired value by controlling the inflow rate by adjusting valve opening.

Fig: Liquid level Control System The control system compares the desired level (set point) with the present level (controlled variable). The present level is obtained by a sensor (here Level Sensor). If any difference (error) between set point and controlled variable, the controller takes the necessary action to increase or decrease the valve opening. This was shown below as a block diagram. 138


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This type of control system is called Closed Loop Control System (feed back control system). It is also called Automatic Control System. The sensitivity of the closed loop system may be made small to make the system more stable. Another division of control system is Open Loop Control System. Any system which does not automatically correct the variation in its output is called an open loop system. That is the output has no effect on its input.

In open loop system the output can be varied by varying the input. In open loop systems the changes in output are corrected by changing the input manually.

TYPES OF CONTROL SYSTEMS Broadly control system can be classified as 1. Open Loop System and 2. Closed Loop System OPEN LOOP SYSTEM A system in which the output is dependent on input but input is totally independent of the output or changes in output of the system, is called an open loop system. That is any physical system which does not automatically correct for variation in its output, is called an open loop system. Such a system may be represented by the block diagram of figure. 139


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Reference input, r(t) is applied to the controller which generates the actuating signal (u) required to control the process which is to be controlled. Process is giving out the necessary desired controlled output c(t). Usual case there will be no variation in output for a particular input. We can say for a given input the desired output is obtained. But if disturbances are occurred in between the controller and process, the output varies. Such an open loop system is shown below.

Here the controller output will force the system to give the desired response. Because of the disturbances present in the system, the output may or may not equal to the desired response. It can be described on the basis of an example shown in figure.

Here the driver wants to drive the car at 80 Km/hr. To achieve the desired speed, he applies required pressure on the accelerator pedal and the car starts moving in the desired speed. But after some time due to disturbances like wind velocity and road conditions, the speed of the car deviated from the desired speed. The car does not run at the desired speed even though there is no change in the pressure applied to accelerator pedal. The distinguished characteristic of an open loop system is that it cannot compensate or take corrective action for any disturbances that affect the system performance. 140


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CLOSED LOOP SYSTEM A system in which the controlling action or input is somehow dependent on the output or changes in output is called closed loop system. To have dependence of input on the output, such system uses the feedback property. Feedback is a property of the system by which it permits the output to be compared with the reference input to generate the error signal based on which the appropriate controlling action can be decided. In such system, output or part of the output is feedback to the input for comparison with the reference input applied to it. Closed loop system can be represented as shown in figure.

Here the output response (controlled variable) is measured and compared with the desired value (set point) and the deviation is given to the controller. The controller generates the manipulated variable that minimizes the deviation between the desired response and controlled response. If there is no difference between the desired value and measured value, the error signal becomes zero and the controller does not take any corrective action and the output of the controlled system is maintained at the desired response. Usually the output value changes due to external disturbances. In closed loop systems, the information about the instantaneous state of the output is feedback to the input and is used to modify it in such a manner as to achieve the desired output. The action of a man walking from a starting point to destination point along a prescribed path is an example for closed loop feedback control systems. Here the reference input is prescribed path. The eye performs the function of sensor. Brain compares the actual path of movement with prescribed path and generates an error signal. Then it amplifies the error signal and transmits a control signal to the legs to correct the actual path of movement to the desired path. 141


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Driving a car at the desired speed is another example for closed loop control. Here the driver compares the speed of the car with the desired speed. If he finds any deviation in speed from the desired speed due to some disturbances then he may increase or decrease the speed by increasing or decreasing the pressure on the accelerator pedal so that the deviation becomes zero. In this case the pressure applied on the accelerator pedal is manipulated variable or control variable.

Comparison between Open Loop and Closed Loop Control System

Open Loop Control System

Closed Loop Control System

1

Simple and economical

Complex and Costlier

2

Open loop system are stable

Closed loop system are unstable

3

Inaccurate and unreliable

Accurate and reliable

Open loop systems are affected by Closed loop systems are less affected

5

noise

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AUTOMATIC CONTROL SYSTEM Automatic control systems are a special case of closed loop control systems. Let us investigate the control aspect of the steering mechanism of an automobile (engine vehicle). The error between the actual and desired directions of the automobile is given to the controller (Here steering mechanism). The driver senses this error by tactile means (body movement) and by visually.

Fig: The driver uses the difference between the actual and desired direction of travel to adjust the steering wheel accordingly

Additional information is available to the driver from the feel (sensing) of the steering wheel through his hands, these information’s constitute the feedback signals which are interpreted by driver's brain, who then signals his hand to adjust the steering wheel accordingly. This again is an example of a closed loop system where human visual and tactile measurements constitute the feedback loop. It is shown as a block diagram (given below).

Fig : Automatic Steering Control System 143


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Usually closed loop systems involve continuous manual control by a human operator. So they are also called manually controlled systems. In many complex and fastacting systems, the presence of human element in the control loop is undesirable because the system response may be too rapid for an operator to follow or the demand on operator's skill may be unreasonably high. Furthermore, some of the systems e.g., missiles, are self destructive and in such systems human element must be excluded. Even in situations where manual control could be possible, an economic case can often be made out for reduction of human supervision. Thus in most situations the use of some equipment which performs the same intended function as a continuously employed human operator is preferred. A system incorporating such equipment is known as automatic control system. In fact in most situations an automatic control system could be made to perform intended functions better than a human operator, and could further be made to perform such functions as would be impossible for a human operator. The general block diagram of an automatic control system which is characterized by a feedback loop is shown in figure. An error detector compares a signal obtained through feedback elements, which is a function of the output response, with the reference input. Any difference between these two signals constitutes an error or actuating signal, which actuates the control elements. The control elements in turn alter the conditions in the plant (controlled member) in such a manner as to reduce the original error.

Fig : General block diagram of an Automatic Control System

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SERVO MECHANISMS Servomechanisms are feedback control systems in which the output is mechanical position (or time derivatives of position, example velocity and acceleration). Such a servomechanism is shown in figure.

Fig: Position Control System It is also called position control system. It consists of a servomotor powered by a generator. The load whose position has to be controlled is connected to motor shaft through gear wheels. Potentiometers are used to convert the mechanical motion to electric signals. The desired load position (QR) is set on the input potentiometer and the actual load position (QC) is fed to feedback potentiometer. The difference between the two angular positions generates an error signal, which is amplified and fed to generator field circuit. The induced emf of the generator drives the motor. The rotation of the motor stops when the error signal is zero, i.e. when the desired load position is reached. Few other examples of servomechanism are, 1. 2. 3. 4. 145

Power steering apparatus for an automobile. Machine tool position control. Missile launchers. Roll stabilization of ships. Prepared by Shijin C.S.

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TRANSFER FUNCTION For analysis and design, control systems are usually described by a set of different equations. The inter relationships of the equations can be pictorially shown as a block diagram. Each component of the block is described by transfer function. In actual size, the transfer function is mathematically defined as the ratio of Laplace transform of the output component to the Laplace transform of the input with all initial conditions assumed to be zero. If Laplace transform of input r(t) is represented by R(s), and that of output c(t) is C(s).

Then Transfer function, G(s) = ∴ G(s) =

Laplace Transformof Output Laplace Transformof Input C(s) R(s)

all initial conditions are zero

all initial conditions are zero

Transfer function is a mathematical model and it gives the gain of the system, G(s). A transfer function is defined only for a linear, stationary system. A non-stationary system often called a time-varying system has one or more time-varying parameters and the Laplace transformation may not be utilized. Properties of Transfer Function The properties of the transfer function are given below: 1. The ratio of the Laplace transform of output to input with all initial conditions to be zero is known as transfer function of a system. 2. The transfer function of a system is the Laplace transform of its impulse response under assumption of zero initial conditions.

d in transfer function of a dt system, the differential equation of the system can be obtained.

3. Replacing ’s’ variable with linear operation D ≡

4. The transfer function of a system does not depend on the inputs to the system. 5. The system poles and zeros can be determined from its transfer function. 6. Stability can be found from characteristic equation. 7. Transfer function cannot be defined for non-linear systems. It can be defined for linear systems only. 146


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BLOCK DIAGRAM Block diagram is a pictorial representation of the given system. Each element of a complicated system is represented by a block. Each block is functional block. In block diagram representation, each block represents the transfer function of an element in the system. Unidirectional block which represents the transfer function of the system is known as the block diagram of the system. BASIC ELEMENTS OF BLOCK DIAGRAM 1) Block Diagram: Pictorial representation of the relationship between the input and output of a physical system is known as block diagram.

2) Output: The value of input multiplied by the block gain is known as output. C(s) = G(s) R(s) 3) Summing Point: At summing point, two or more signals can be added or subtracted.

4) Branch Point (Take off Point): A branch point is a point from which the signal from a block goes concurrently to other blocks or summing point.

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or Application of one input source to two or more systems is represented by a take off point as shown at point A in figure.

BLOCK DIAGRAM REDUCTION The block diagram can be reduced to find the overall transfer function of the system. The following rules can be used for block diagram reduction. 1. Combining the Blocks in Cascade

2. Combining Parallel Blocks (or combining feed forward paths)

3. Moving the Branch Point ahead of the Block

4. Moving the Branch Point before the Block

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5. Moving the Summing Point ahead of the Block

6. Moving the Summing Point before the Block

7. Interchanging Summing Point

8. Splitting Summing Point

9. Combining Summing Points

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10. Elimination of feedback loop

Output, C = (R - CH) G C = RG - CHG C + CHG = RG C (1 + HG) = RG ∴

C G = R 1 + HG

REPRESENTATION OF CONTROL COMPONENTS AND SUBSYSTEMS Or

MATHEMATICAL MODELING OF MECHANICAL SYSTEMS To study and examine a control system it is necessary to have some type of equivalent representation of the system. Such a representation can be obtained from the mathematical equations, governing the behaviour of the system. Most of such mathematical equations are different equations whether the system may be electrical, mechanical, thermal, hydraulic etc. The set of mathematical equations, describing the dynamic characteristic of a system is called mathematical model of the system. Most of the control systems contain mechanical or electrical or both types of elements and components. To analyse such systems, it is necessary to convert such systems into mathematical models based on transfer function approach.

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ANALYSIS OF MECHANICAL SYSTEMS In mechanical systems, motion can be of different types, i.e. Translational, Rotational or combination of both. The equations governing such motion in mechanical systems are often directly or indirectly governed by Newton’s laws of motion.

I. MECHANICAL TRANSLATIONAL SYSTEMS Consider a mechanical system in which motion is taking place along a straight line such systems are of translation type. These systems are characterized by displacement, linear velocity and linear acceleration. The model of mechanical translational systems can be obtained by using three basic elements mass, spring and dash-pot. a) Mass The weight of the mechanical system is represented by the element mass and it is assumed to be concentrated at the center of the body. If a force is applied to the mass, displacement takes place and a reaction force is produced which acts in a direction opposite to that of applied force. This acceleration force is proportional to the acceleration.

Let F = Applied force and FM = Opposing force due to mass then

F = FM

and

FM α a

or

FM = Ma

where M is the mass

d2x dt 2 d2x F = FM = M 2 dt FM = M

or

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b) Spring The elastic deformation of the body can be represented by a spring. When we apply a force on the spring, the spring will offer an opposing force which is proportional to displacement of the body.

Let

F = Applied force and FK = Opposing force due to elasticity

then

F = FK

and

FK α X FK = K X

or

where K is the stiffness of spring; N/m

F = FK = K X

When the spring has displacement at both ends as shown in figure, then the opposing force is proportional to differential displacement

∴

FK α (X1 - X 2 ) FK = K (X1 - X 2 )

or F = FK = K (X1 - X 2 ) c) Dash-Pot (Damper) The friction existing in mechanical systems can be represented by the dash-pot. The dash-pot is a piston moving inside a cylinder filled with viscous fluid. The dashpot is shown in figure.

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If a force is applied to the shaft, the piston move and press the fluid, this increase the pressure on side ‘b’ and decreasing the pressure on side ‘a’. As a result, the fluid flow around the piston from side ‘b’ to side ‘a’. An ideal dash-pot with one end fixed is shown in figure.

The dash-pot will offer an opposing force which is proportional to velocity of the body.

Let

F = Applied force and FB = Opposing force due to friction

then F = FB dX dt dX FB = B dt

and FB α

or F = FB = B

where B is the viscous friction coefficient; N-sec/m dX dt

When the dash-pot has displacement at both ends as shown in figure, then the opposing force is proportional to differential velocity.

d (X1 - X 2 ) dt d or FB = B (X1 - X 2 ) dt d or F = FB = B (X1 - X 2 ) dt

∴ FB α

Procedure to determine the transfer function of Mechanical Translational System 1. Draw the free body diagrams of the system. The free body diagram is obtained by drawing each mass separately and then marking all the forces acting on that mass. 2. For each free body diagram write one differential equation by equating the sum of applied forces to the sum of opposing forces. 3. Take Laplace Transform of differential equations. This ratio is the transfer function of the system. 153


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II. MECHANICAL ROTATIONAL SYSTEMS The model of rotational mechanical systems can be obtained by using three elem ents Moment of Inertia (J) of mass, Dash-pot with rotational frictional coefficient (B) and Torsional spring with stiffness (K). a) Moment of Inertia (J) The weight of the rotational mechanical system is represented by the moment of inertia of the mass. The moment of inertia of the system or body is considered to be concentrated at the centre of gravity of the body. When a torque is applied to a rotating body, a reactive torque is produced which acts in an opposite direction to the applied torque. The reactive torque (opposing torque) due to moment of inertia is proportional to the angular acceleration.

Let

T = Applied torque and Tj = Opposing torque due to moment of inertia of the body

then

T = Tj

d 2θ and Tj α 2 where θ is the angular displacement dt d 2θ or Tj = J 2 where J is the moment of inertia dt d 2θ or T = Tj = J 2 dt b) Dash Pot with Rotational Frictional Coefficient (B) The friction existing in rotational mechanical system can be represented by the dash-pot. The dash-pot is a piston rotating inside a cylinder filled with viscous fluid. When a torque is applied to the dash-pot, it will offer an opposing torque which is proportional to the angular velocity of the body.

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Let

T = Applied torque and Tb = Opposing torque due to friction

then

T = Tb

and or or

dθ where θ is the angular displacement dt dθ where B is the rotational frictional coefficient Tb = B dt dθ T = Tb = B dt Tb α B

When the dash-pot h as angular displacement at both ends as shown in figure, the opposing torque is proportional to the differential angular velocity.

d (θ1 - θ 2 ) dt d or Tb = B (θ1 - θ 2 ) dt d or T = Tb = B (θ1 - θ 2 ) dt Tb α

c) Torsional Spring The elastic deformation of the body can be represented by torsional spring. When a torque is applied to a spring, it is twisted by an angle θ. The torsional spring will offer an opposing force which is proportional to angular displacement of the body.

Let

T

= Applied torque

and

TK = Opposing torque due to elasticity then 155

T

= TK


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and

TK α θ

where θ is the angular displacement

or

TK = K θ

where K is the Stiffness of the spring

or T = TK = K θ When the spring has angular displacement at both ends as shown in figure, the opposing torque is proportional to the differential angular displacement.

TK α (θ1 - θ2) or TK = K (θ1 - θ2) ∴ T = TK = K (θ1 - θ2)

III. ELECTRICAL SYSTEMS The models of electrical systems can be obtained by using resistor, capacitor and inductor. For modeling electrical systems the electrical network or equivalent circuit is formed by using R, L and C and voltage or current source. The differential equations governing the electrical systems can be formed by writing Kirchoff’s current law equations by choosing various nodes in the network or Kirchoff’s voltage law equations by choosing various closed path in the network. The transfer function can be obtained by taking Laplace transform of the differential equations and rearranging them as a ratio of output to input. Table.1: Current voltage relation of R, L and C

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Consider a series RLC circuit shown in figure.

The mathematical model of the system is

V(t) = R i + L

di 1 + i d(t) dt C ∫

Taking Laplace Transform

V(s) = R I(s) + L s I(s) +

1 I(s) Cs

1   ∴ V(s) =  R + L s +  I(s) Cs   TRANSFER FUNCTION OF ARMATURE CONTROLLED DC MOTOR The speed of DC motor is directly proportional to armature voltage and inversely proportional to flux in field winding. The desired speed is obtained by varying the armature voltage. Because of the field is excited by a constant voltage, we consider only the armature circuit. The mechanical system consists of the rotating part of the motor and load connected to the shaft of the motor. The armature controlled DC motor speed control system is shown in figure.

Fig: Armature Controlled DC Motor 157


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The equivalent circuit of armature is shown as

where

ia

= Armature current

Va = Armature voltage Ra = Armature resistance La = Armature inductance Eb = Back emf By applying Kirchoff’s Voltage law,

ia R a + La

di a + e b = Va dt

 → (1)

The torque of DC motor is proportional to the product of flux and current. Since flux is constant in this system, the torque is proportional to armature current.

T α ia ∴ Torque, T = K t i a

 → (2)

where Kt is the torque constant. The mechanical system of the motor is shown as

The differential equation governing the mechanical system of motor is given by

d 2θ dθ J 2 +B =T dt dt 158


 → (3)

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The back emf of DC machine is proportional to speed (angular velocity) of shaft.

∴ eb α

dθ dt

Back emf, e b = K b

dθ  → (4) dt

where Kb is the Back emf constant. The differential equations governing the armature controlled DC motor speed control system are

di a + e b = Va dt Torque, T = K t i a

ia R a + La

 → (1)

 → (2)

d 2θ dθ = T J 2 + B dt dt Back emf, e b = K b

 → (3)

dθ  → (4) dt

On taking Laplace transform with zero initial conditions we get,

Ra Ia (s) + Las Ia (s) + Eb (s) = Va (s)

 → (5)

T(s) = Kt Ia (s)

 → (6)

J s2 θ(s) + B s θ(s) = T(s)

 → (7)

Eb (s) = Kb s θ(s)

 → (8)

Equating (6) and (7) we get

K t Ia (s) = ∴ Ia (s) =

(J s (J s

2

2

) + Bs ) θ(s)

+ Bs θ(s)

Kt

 → (9)

Equation (5) can be written as

(R a + Las) Ia (s) + E b (s) = Va (s) substituting E b (s) and Ia (s) from (4) and (9) 159


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( Ra


(J s + L s) a

(

2

+ Bs

Kt

) θ(s) + K

b

s θ(s) = Va (s)

)

 ( R a + La s ) J s 2 + Bs K t K b s    θ(s) = Va (s) Kt   θ(s) will be ∴ Transfer function Va (s)

  Kt θ(s)  =  Va (s)  ( R a + La s ) J s 2 + Bs K t K b s   Kt =  2 3 2  R a J s + R a Bs + La J s + s La B + K t K b

(

)

  s

Kt s J Ra s + R a B + J La s2 + s La B + K t Kb  Kt = s (J s + B)Ra + (J s2 + B s) La + Kt Kb 

=

=

Kt s [ (J s + B)R a + (J s + B) s La + K t Kb ]

=

Kt s [ (J s + B) (R a + s La ) + K t Kb ]

The block diagram of the armature controlled DC motor is shown in figure,

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TRANSFER FUNCTION OF FIELD CONTROLLED DC MOTOR The speed of DC motor is directly proportional to armature voltage and inversely proportional to flux in field winding. In field controlled DC motor the armature voltage is kept constant and the speed is varied by varying the flux of the machine. Since flux is directly proportional to field current, the flux is varied by varying field current. For analysis only field circuit is considered because the armature is excited by a constant voltage. The mechanical system consists of the rotating part of the motor and the load connected to the shaft of the motor. The field controlled DC motor speed control system is shown in figure.

Fig: Field Controlled DC Motor The equivalent circuit of field is shown as

where

if

= Field current

Vf = Field voltage Rf = Field resistance Lf = Field inductance

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By applying Kirchoff’s Voltage law, we can write

di f = Vf dt

R f if + Lf

 → (1)

The torque of DC motor is proportional to the product of flux and armature current. Since armature current is constant in this system, the torque is proportional to flux alone, but flux is proportional to field current.

T α if ∴ Torque, T = K tf if

 →

(2)

where Ktf is the torque constant. The mechanical system of the motor is shown in figure as

The differential equation governing the mechanical system of the motor is given by

d 2θ dθ J 2 + B =T dt dt

 → (3)

The differential equations governing the field controlled DC motor are

di f = Vf dt

R f if + Lf

∴ Torque, T = K tf i f J

d 2θ dθ + B =T dt dt 2

 → (1)  → (2)  → (3)

On taking Laplace transform with zero initial conditions we get,

R f If (s) + Lf s If (s) = Vf (s) T(s) = K tf I f (s)

J s 2θ(s) + B s θ(s) = T(s)

 → (4)  → (5)

 →

(6)

equating (5) and (6) we get

K tf If (s) = J s 2θ(s) + B s θ(s) ∴ 162

I f (s) =


(J s 2 + B s) θ(s) K tf |


Module |3


substituting If (s) in (4)

(R f + Lf s) (J s 2 + B s) θ(s) = Vf (s) K tf Transfer function is

θ(s) K tf = Vf (s) (R f + Lf s) (J s 2 + B s) The block diagram of the field controlled DC motor is shown in figure,

TEMPERATURE CONTROL SYSTEM Thermal systems are those that involve the transfer of heat from one substance to another. The model of thermal systems is obtained by using thermal resistance and capacitance which are the basic elements of the thermal system. The thermal resistance, R for heat transfer between two substances is defined as the ratio of change in temperature and change in heat flow rate.

∴ Thermal resistance, R =

Change in Temperature Change in heat flow rate

Thermal capacitance is defined as the ratio of change in heat stored and change in temperature.

∴ ThermalCapacitance, C =

Change in heat stored Change in temperature

It is also defined as the product of the body’s mass, M and the specific heat of the body, C.

i.e.

Thermal Capacitance, C = M C

Consider a simple thermal system shown in figure. Let us assume that the tank is insulated to eliminate heat loss to the surrounding air.

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The change in output heat flow rate,

q 0 = Liquid flow rate, G X Specific heat of liquid, C X Change in temperature, θ

q0 = G C θ

 → (1)

Χ Specific heat of liquid, c

ThermalCapacitance, C = Mass, M

∴

C = Mc

 → (2)

Thermal resistance, R =

Change in temperature, θ Change in heat flow rate, q 0

θ q0

 → (3)

θ 1 = G Cθ GC

 → (4)

i.e. R = Substitute (1) in (3)

∴

R =

The rate of change of temperature is directly proportional to change in heat input rate

∴

dθ α qi - qo dt

The constant of proportionality in the capacitance C of the system

∴ C

dθ dt

(3) ⇒ R =

θ qo

164

= q i - qo


or

 → (5)

qo =

θ R

 → (6)

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Substitute (6) in (5)

dθ θ = qi dt R dθ q R -θ = i C dt R dθ = R qi - θ RC dt dθ + θ = R qi RC dt C

Taking Laplace transform

R C s θ(s) + θ(s) = R Q i (s) θ(s) [R C s + 1] = R Q i (s)

θ(s) R = Q i (s) s R C +1

REFERENCES 1) Control Systems

- Nagoorkani A.

2) Control Systems Engineering

- Ramesh Babu

3) Linear Control Systems

- B.S. Mange

4) Control System Engineering

- Nagrath & Gopal

5) Control Systems Theory & Applications - Smarajit Ghosh 6) Problems & Solutions in Control System Engineering

- Sivanandam & Deepa

7) Modern Control Engineering

- Katsuhiko Ogata

8) Control Systems

- U.A. Bakshi & V.U. Bakshi


- Norman S. Nise

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System Response

MODULE - 4 SYSTEM RESPONSE TIME RESPONSE The time response of the system is the output of the closed loop system as a function of time. It is denoted by C(t).

The output in s domain, C(s) is given by the product of the transfer function and the input R(s).

C(s) = R(s)

G(s) 1 + G(s) H(s)

On taking the inverse Laplace transform of this product the time domain response, C(t) can be obtained.

Closed loop transfer function,

C(s) G(s) = R(s) 1 + G(s) H(s)

Response in s-domain, C(s) = R(s)

G(s) 1 + G(s) H(s)

  G(s) Response in time domain, C(t) = L-1[C(s)] = L-1  R(s) 1 + G(s) H(s)   The time response of a control system consists of two parts. 1) The transient response 2) The steady state response

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System Response

The transient response shows the response of the system when the input changes from one state to another or it is the response before the output reaching the steady state value. The steady state response shows the response as time, t approaches infinity. Therefore the total time response is

TEST SIGNALS To predict the response of the system, knowledge of input signal is required. The commonly used test input signals are impulse, step, ramp and parabolic signals. a) Impulse Signal A signal which is available for very short duration is called impulse signal. Impulse signal is a signal having zero values at all times except at t=0. At t=0, the magnitude becomes infinite. It is denoted by δ(t).

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System Response

It is expressed as

= 0 for t ≠ 0

δ(t)

+ t1

and

Lt

t1 → 0

∫ δ(t)

dt = 1

- t1

Laplace transform of the impulse function is unity. The response of the system, with input impulse signal is called weighting function (impulse response) of the system.

  G(s) C(t) = L-1  R(s) 1 + G(s) H(s)     G(s) = L-1  ( Q R(s) = 1 for impulse )  1 + G(s) H(s) 

i.e.

b) Step Signal The step signal is a signal whose value changes from zero to A at t = 0 and remains constant at A for t > 0.

The mathematical representation of the step signal is

r(t) = A u (t)

where or

u(t) = 1;

t≥0

u(t) = 0;

t <0

r(t) = A; for t ≥ 0 r(t) = 0; for t < 0

The Laplace transform of the step signal is

R(s) = L[r(t)] = 168


A s |


Module |4

System Response

For a unit step signal (i.e. A = 1)

∴

R(s) =

1 s

c) Ramp Signal The ramp signal is a signal whose value increases linearly with time from an initial value of zero at t=0. The ramp signal resembles a constant velocity input to the system.

The mathematical representation of the ramp signal is

r(t) = At; for t ≥ 0 r(t) = 0; for t < 0 Laplace transform of the ramp signal is

R(s) = L [r(t)] = L [At] = A L [t] A R(s) = 2 s For a unit ramp signal (i.e. A = 1)

∴

169

R(s) =


1 s2

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System Response

d) Parabolic Signal In parabolic signal, the instantaneous value varies as square of the time from an initial value of zero at t=0. The parabolic signal resembles a constant acceleration input to the system.

The mathematical representation of the parabolic signal is

At 2 r(t) = ; for t ≥ 0 2 r(t) = 0; for t < 0 The Laplace transform of the parabolic signal is given by

R(s) = = = =

 At 2  L [r(t)] = L    2  A L [t 2 ] 2 A 2 2 s3 A s3

For a unit parabolic signal (i.e. A = 1)

∴

170

R(s) =

1 s3


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System Response

ORDER OF A SYSTEM The input and output relationship of a control system can be expressed by a differential equation. The order of the system is given by the order of the differential equation governing the system. The order of the system is given by the maximum power of ‘s’ in the denominator polynomial.

TransferFunction,T(s) = K

P(s) Q(s)

Order of the system is denoted by ‘n’

If n = 0; If n = 1; If n = 2;

K ; then the system is Zero Order System 2 K T(s) = ; then the system is First Order System 2s + 1 K (s + 2) T(s) = ; then the system is Second Order System 2s 2 + s + 1 T(s) =

The value of n gives the number of poles in the transfer function.

RESPONSE OF FIRST ORDER SYSTEM FOR UNIT IMPULSE INPUT Let the transfer function of a first order system is

C(s) K = R(s) Ts + 1 where K is the gain constant and T is the time constant of the system. Time constant indicates how fast the system reaches the final value. The input is unit impulse, then

r(t) = δ(t) and R(s) = 1 The response in s domain,

∴

171

C(s) = R(s)

C(s) =

K Ts + 1

=

K


K Ts + 1

1  Ts +  T  |


Module |4

System Response

The response in time domain is given by     K  C(t) = L-1   T s + 1      T  

=

K - t/T e T

When t = 0,

C(t) =

When t = 1 T,

C(t) =

When t = 2 T,

C(t) =

When t = 3 T,

C(t) =

When t = 4 T,

C(t) =

When t = 5 T,

C(t) =

When t = ∞,

C(t) =

K T K -1 e T K -2 e T K -3 e T K -4 e T K -5 e T K -∞ e T

 1  Q L-1  = e -at  s + a 

= 0.3679 = 0.1353 = 0.0498 = 0.0183 = 0.0067

K T K T K T K T K T

= 0

It can be plotted as

The output starts at K/T at t = 0 and decreases exponentially and reaches to zero at t = ∞.

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System Response

RESPONSE OF FIRST ORDER SYSTEM FOR UNIT STEP INPUT Let the transfer function of a first order system is

C(s) R(s)

1  → (1) Ts + 1

=

If the input is unit step, then

r(t) = 1 and R(s) =

1 s

The response in s domain,

1 Ts + 1 1 1 = s Ts + 1 1 = 1  sT  s +  T  1 T = 1  s s +  T 

C(s) = R(s)

By partial fraction expansion C(s) can be expressed as

C(s) =

1 T

1  s s +  T 

=

B A  → (2) + 1 s  s +  T 

Multiplying (2) by s 1 T

1  s +  T 

= A +

Bs 1  s +  T 

Put s = 0 ∴ 1= A

173


i.e. A = 1

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Module |4

System Response

1  Multiplying (2) by  s +   T 1 T s

Put s =

 1 A s +  T + B =  s

-1 T 1 ∴ T = 0 + B -1 T i.e. B = - 1

∴ C(s) =

1 1 1 s  s +  T 

The response in time domain is given by

C(t) = L-1 [ C (s) ]

  1  1  = L-1  s s + 1       T  

∴ C(t) = 1 - e -t/T When t = 0,

C(t) = 1 - e 0

= 0

When t = 1 T,

C(t) = 1 - e -1

= 0.632

When t = 2 T,

C(t) = 1 - e -2

= 0.865

When t = 3 T,

C(t) = 1 - e -3

= 0.95

When t = 4 T,

C(t) = 1 - e -4

= 0.9817

When t = 5 T,

C(t) = 1 - e -5

= 0.993

When t = ∞,

C(t) = 1 - e -∞

=1

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Module |4

System Response

It is plotted as

RESPONSE OF FIRST ORDER SYSTEM FOR UNIT RAMP INPUT Let the transfer function of a first order system is

C(s) R(s)

=

1  → (1) Ts + 1

If the input is unit ramp, then

r(t) = t

and R(s) =

1 s2

The response in s domain,

1 Ts + 1 1 1 = 2 s Ts + 1 1 1 = 2 1  s T s +  T  1 T = 1  s2 s +  T 

C(s) = R(s)

175


|


Module |4

System Response

By partial fraction expansion C(s) can be expressed as

1 T

C(s) =

1  s2  s +  T 

=

C B A  → (2) + 2 + 1 s s  s +  T 

Multiplying (2) by s2

1 T

Cs 2 = As + B + 1 1   s +  s +  T  T 

Put s = 0 1 T = B 1 T

∴

i.e. B = 1

1  Multiplying (2) by  s +   T

 1  1 A s +  B s +  T  T + C =  + s s2

1 T s2 Put s =

-1 T 1 T = C 1 T2

∴

i.e. C = T

Substitute s = 1 in (2)

1 T

1  1 +   T

= A + B +

C 1  1 +   T

Substitute the value of B & C 1 T = A +1+ T T +1 T +1 T T 176


|


Module |4

System Response

1 T2 = A +1+ T +1 T +1 ∴ A =

1 T2 -1T +1 T +1

1 - (T + 1) - T 2 - T - T2 - T (1 + T ) = = -T = = T +1 T +1 T +1 So C(s) =

∴ C(s) =

1 -T + 2 + s s

∴ A = -T

T s+

1 T

1 T T + 2 1 s s s+ T

The response in time domain is given by

C(t) = L-1 [ C (s) ]

    1 T T = L-1  2 + 1 s s s+   T

∴ C(t) = t - T + Te -t/T When t = 0,

C(t) = - T + Te 0

= 0

When t = 1 T,

C(t) = T - T + Te -1

= 0.36797

When t = 2 T,

C(t) = 2T - T + Te -2 = T + 0.1353 T

When t = ∞,

C(t) = ∞ - T + Te -∞

= ∞

It is plotted as

177


|


Module |4

System Response

SECOND ORDER SYSTEMS The standard form of closed loop transfer function of second order system is given by

C(s) ω2n = 2 R(s) s + 2 ζ ωn s + ω2n where wn = natural frequency, ζ = Damping ratio The characteristic equation of the second order system is

s2 + 2 ζ ωn s + ωn2 = 0 It is a quadratic equation and the roots of this equation is given by

s1 , s 2 = =

4 ζ 2 ωn2 - 4 ωn2

- 2 ζ ωn ±

2 - 2 ζ ωn ± 2 ζ 2 ωn2 - ωn2 2

= - ζ ωn ±

(ζ

= - ζ ωn ± ωn

2

)

- 1 ω2n

(ζ

2

)

-1

The response C(t) of second order system depends on the value of damping ratio. Depending on the value of ζ, the system can be classified into the following four cases, When ζ = 0,

Undamped System,

When 0 < ζ < 1,

Under damped System,

When ζ = 1,

Critically damped System,

When ζ > 1,

Over damped System.

Note: Most of the physical systems are of under damped system.

178


|


Module |4

System Response

RESPONSE OF UNDAMPED SECOND ORDER SYSTEM FOR UNIT STEP INPUT The standard form of a closed loop transfer function of second order system is given by

C(s) ω2n = 2 R(s) s + 2 ζ ωn s + ωn2 For Undamped system, ζ = 0

∴

C(s) ω2n = 2 R(s) s + ωn2

When the input is unit step,

r(t) = 1 and R(s) =

1 s

Therefore The response in s-domain will be

ω2n C(s) = R(s) 2 s + ωn2 1 ω2n C(s) = s s 2 + ωn2 By partial fraction expansion

ω2n C(s) = s s 2 + ωn2

(

Note :- Normal case

)

A B + 2 s s + ω2n

=

A Bs + C + 2 s s + ωn2

But here the roots are lie on the imaginary axis. So the value of B = 0.

ω2n C(s) = s s 2 + ω2n

(

179


)

=

A B + 2 s s + ω2n

|

 → (1)


Module |4

System Response

Multiplying (1) by s

ω2n B = A + s s 2 + ωn2 s2 + ωn2 Put s = 0 ω2n = A ω2n

(

∴ A = 1 2

2

Multiplying (1) by s + ω n

ω 2n A = s s

(s

2

Put s 2 = - ω n2 ∴

ω2n =B jωn

∴

B=

)

+ ω n2

)

or

s = -jω n

+ B

ωn = -jω n = -s j

∴ B = -s

∴

C(s) =

1 s - 2 s s + ω 2n

The time response C(t) is

C(t) = L-1 [ C(s) ] 1  s = L-1  - 2  s + ωn2  s i.e.

180

C(t) = 1 - Cos ωn t


L-1 Cos ω n t =

Q

|

s

2

s + a2


Module |4

System Response

The response of undamped second order system for unit step input is shown in figure.

The response of undamped second order system for unit step input is completely oscillatory. Every practical system has some amount of damping. Hence undamped system does not exist in practice.

RESPONSE OF UNDER DAMPED SECOND ORDER SYSTEM FOR UNIT STEP INPUT The standard form of closed loop transfer function of second order system is given by

C(s) ω2n = 2 R(s) s + 2 ζ ωn s + ωn2 For Under damped system, 0 < ζ < 1 and roots of the denominator (characteristic equation) are

s1 , s2 = - ζ ωn ± ωn

(ζ

2

)

-1

But ζ < 1 So s1 , s 2 = - ζ ωn ± ωn

(

- 1 - ζ2

= - ζ ωn ± jωn

)

1 - ζ2

The roots are complex conjugate The response in s-domain,

C(s) = R(s)

181


ω2n s 2 + 2 ζ ωn s + ωn2 |


Module |4

System Response

∴

1 ω2n C(s) = s s2 + 2 ζ ωn s + ωn2

By partial fraction expansion,

ω2n s s2 + 2 ζ ωn s + ω2n

C(s) =

(

)

=

A Bs + C + 2 s s + 2 ζ ωn s + ω2n

 → (1)

Multiplying (1) by s

(s

ω2n 2

+ 2 ζ ωn s + ω2n

)

( Bs

= A +

+ C) s

s + 2 ζ ωn s + ω2n 2

Put s = 0

ω2n ω2n

= A

∴ A = 1

on cross multiplication in (1)

(

)

ω 2n = A s 2 + 2 ζ ω n s + w 2n + ( Bs + C ) s

ω 2n = s 2 + 2 ζ ω n s + ω 2n + Bs 2 + Cs Equating coefficients of s2

1+ B = 0

∴ B = -1

Equating coefficients of s

2 ζ ωn + C = 0

∴

C(s) =

∴ C = -2 ζ ω n

s + 2 ζ ωn 1 - 2 s s + 2 ζ ω n s + ω 2n

Note:- To take the Laplace transform we want the denominator term (s + a)2 + b2

∴

C(s) = =

182


1 s + 2 ζ ωn - 2 s s + 2 ζ ω n s + ωn2 + ζ 2 ωn2 - ζ 2 ωn2 1 s

s + 2 ζ ωn

( s + ζ ωn ) |

2

+ ω n2 - ζ 2 ω n2


Module |4

System Response

1 s

=

Substitute

(s + ζ ωn )

2

(

+ ω 2n 1 - ζ 2

)

(1 - ζ )

ωd = ωn

2

1 s

=

−1

s + 2 ζ ωn

s + 2 ζ ωn

( s + ζ ωn )

2

+ ωd2



 s+a = e -at Cos bt 2 2  (s + a ) + b 

We know L 

−1



=

1 s

s + ζ ωn + ζ ωn

=

1 s + ζ ωn s ( s + ζ ω n ) 2 + ωd2

( s + ζ ωn )

2

+ ω 2d +

ζ ωn

( s + ζ ωn )

2

+ ωd2

 = e-at Sin bt 2 2  (s + a ) + b 

We know L 

b

=

1 s + ζ ωn s ( s + ζ ωn )2 + ω2d

+

ζ ω n ωd 2 ωd ( s + ζ ωn ) + ωd2   

On taking inverse Laplace transform

C(t) = 1 - e -ζ ωn t Cos ωd t = 1-e

-ζ ωn t

Cos ωd t -

ζ ωn -ζ ωn t e Sin ωd t ωd ζ ωn ωn 1 - ζ

 = 1 - e -ζ ωn t Cos ωd t + 

2

e

-ζ ωn t

Sin ω d t

 Sin ωd t   1 - ζ2 ζ

e -ζ ωn t  1 - ζ 2 Cos ωd t + ζ Sin ωd t  = 12   1-ζ 183


|


Module |4

System Response

On constructing a right angle triangle with ζ and 1 - ζ 2 , we get

The time response C(t) is

C(t) = 1 -

∴ C(t) = 1 -

e

-ζ ωn t

1 - ζ2

e -ζ ωn t 1 - ζ2

[Sinθ Cos ωd t

+ Cosθ Sin ωd t ]

Sin ( ωd t + θ )

Where θ = tan

-1

1 - ζ2 ζ

The response of under damped second order system oscillates before settling to a final value. The oscillations depend on the value of damping ratio. The following figure shows the response of under damped second order system for unit step input.

Fig : The response of Under damped Second order system for unit step input

184


|


Module |4

System Response

RESPONSE OF CRITICALLY DAMPED SECOND ORDER SYSTEM FOR UNIT STEP INPUT The standard form of closed loop transfer function of second order system is given by

ω2n C(s) = 2 R(s) s + 2 ζ ωn s + ω2n For Critical damping ζ = 1

ω2n C(s) = 2 R(s) s + 2 ωn s + ωn2

∴

ω2n

=

( s + ωn )

2

When input is unit step, then

r(t) = 1

R(s) =

and

1 s

The response in s-domain will be,

C(s) = R(s)

C(s) =

ω2n

(s + ωn )

2

ω2n

s ( s + ωn )

2

By partial fraction expansion, we can write

C(s) =

ω2n

s ( s + ωn )

2

=

A B C + +  → (a) 2 s s + ωn ( s + ωn )

Multiplying (a) by s

ω2n

( s + ωn ) 185

2

= A +


Bs + s + ωn

Cs

( s + ωn ) |

2


Module |4

System Response

Put s = 0

ω2n = A ω2n ∴

A = 1

Multiplying (a) by

( s + ωn )

2

A ( s + ωn ) ω2n = s s

2

+ B ( s + ωn ) + C

Put s = - ωn ω2n = C ωn ∴

C = - ωn

Equation (a) can be written as

ω 2n = A ( s + ω n ) + B s ( s + ω n ) + Cs 2

Put s = 1 ω 2n = A (1 + ω n ) + B (1 + ω n ) + C 2

(1 + ω n )

ω 2n =

2

+ B (1 + ω n ) - ω n

(

)

ω2n - 1 + 2ωn + ωn2 + ωn = B (1 + ωn ) -1 - 2ωn + ωn = B (1 + ω n )

∴

B =

− (1 + ωn )

(1 + ωn )

i.e. B = -1

∴ C(s) =

186

1 1 ωn s s + ωn ( s + ωn )2


|


Module |4

System Response

The response in time domain is expressed as

C(t) = L−1 [ C(s) ]

1 1 ωn  = L−1   2 + s s ω  ( s + ωn )  n = 1 - e -ω n t - ω n t e -ω n t

∴

C(t) = 1 - e-ωn t (1 - ωn t )

The response of critically damped second order system has no oscillations. The following figure shows the response of critically damped second order system for unit step input.

Fig : The response of Critically damped Second order system for unit step input.

187


|


Module |4

System Response

TIME DOMAIN SPECIFICATIONS The desired performance characteristics of a system of any order may be specified in terms of the transient response to a unit step input signal. The response of a second order system for unit step input with various values of damping ratio is shown in figure.

The transient response of a system to a unit step input depends on the initial conditions. The transient response of a practical control system often exhibits damped oscillation before reaching steady state.

Fig : Damped Oscillatory response of Second Order System

188


|


Module |4

System Response

The transient response characteristics of a control system to a unit step input is specified in terms of the following time domain specifications 1.

Delay time, td

2.

Rise time, tr

3.

Peak time, tp

4.

Maximum overshoot, Mp

5.

Settling time, ts

EXPRESSIONS FOR TIME DOMAIN SPECIFICATIONS 1. Delay time (td) It is the time taken for response to reach 50% of the final value, for the very first time. Expression Response of second order system for under damped case is given by

C(t) = 1 -

e -ζ ωn t 1-ζ

2

→ (1) Sin ( ωd t + θ ) 

The time required to reach 50% of output is known as delay time

∴ C(t) =

1 2

t = td

at

From equation (1)

1 e -ζ ωn t d = 1Sin ( ωd t d + θ ) 2 2 1-ζ

1 2

=

e

-ζ ωn t d

1-ζ

2

Sin ( ωd t d + θ )

The result of this equation is

td =

189

1 + 0.7 ζ ωn


|


Module |4

System Response

2. Rise time (tr) It is the time taken for response to rise from 0 to 100% of the final value, for the very first time.

Expression Response of second order system for under damped case is given by

C(t) = 1 -

e -ζ ωn t

Sin ( ωd t + θ )  → (1)

1 - ζ2

At t = t r , C(t) = C(t r ) = 1

∴ C(t r ) = 1 -

i.e. -

e

-ζ ωn t r

1 - ζ2 e -ζ ωn t r 1-ζ

2

( Q Input is Step)

Sin ( ωd t r + θ ) = 1 Sin ( ωd t r + θ ) = 0

Since -e-ζ ωn t r ≠ 0, If -e -ζ ωn t r = 0, t r = ∞ It's not possible The term, Sin ( ωd t r + θ ) = 0 Note:-

SinΦ = 0 When Φ = 0, π, 2π, 3π,...........

∴

ω d t r + θ = nπ ωd t r + θ = π - θ

∴ Rise time, t r = 190


Here n = 1

π-θ ωd |


Module |4

System Response

Where θ = tan

-1

1 - ζ2 and ω d = ω n 1 - ζ 2 ζ π - tan

or Rise time, t r =

-1

1 - ζ2 ζ

ωn 1 - ζ

2

in secs

3. Peak time (tp) It is the time taken for the response to reach the peak value for the very first time.

Expression To find the expression for peak time, tP, differentiate C(t) with respect to ‘t’ and equate to ‘0’.

i.e.,

d C(t) dt

=0 t = tP

For a function f(t) to be maximum when

f (t) = 0

The unit step response of second order system is given by

C(t) = 1 -

191


e

-ζ ωn t

1 - ζ2

Sin ( ωd t + θ )

|


Module |4

System Response

Differentiating C(t) with respect to t

 e -ζ ωn t  d e -ζ ωn t C(t) = 0 -  ζωn ) Sin ( ωd t + θ ) + Cos ( ωd t + θ ) ωd  ( dt  1 - ζ 2  1 - ζ2

d C(t) = 0 dt

⇒

-e

-ζ ω n t

1 - ζ2

( - ζω n ) Sin ( ω d t + θ ) + Cos ( ω d t + θ ) ω d  = 0

Cos ( ωd t + θ ) ωn 1 - ζ 2 - ζωn Sin ( ωd t + θ ) = 0 Cos ( ωd t + θ )

1 - ζ 2 - ζ Sin ( ωd t + θ ) = 0

On constructing a right angle triangle with ζ and 1 - ζ 2 ,

We get

Cos ( ω d t + θ ) Sinθ - Cosθ Sin ( ω d t + θ ) = 0

Sin ( ω d t + θ − θ ) = 0 Sin ( ωd t ) = 0 Note:-

SinΦ = 0 When Φ = 0, π, 2π, 3π,...........

∴

ω dtp = nπ

∴ Peak time, t p = or t p =

192


π ωd

π ωn 1 - ζ 2

|


Module |4

System Response

4. Maximum Overshoot or Peak Overshoot (Mp) Maximum overshoot is a measure of how much the response exceeds the final value following a step change. Let final value

= C(∞)

Maximum value

= C(tP)

Maximum Overshoot, M P = % Maximum Overshoot, % M P = where

C(t P ) - C(∞) C(∞) C(t P ) - C(∞) X 100 % C(∞)

C(tP) = Peak response at t=tP C(∞) = Final steady state value

Expression The unit step response of second order system is given by

C(t) = 1 -

e

-ζ ωn t

1-ζ

2

Sin ( ωd t + θ )

At t = ∞,

C(t) = C(∞ ) = 1 -

e

-∞

1 - ζ2

Sin ( ω d × ∞ + θ )

= 1-0

= 1 At t = t p ,

C(t) = C(t p ) = 1 Put t p =

∴

193

- ζ ωn t p

e

1 - ζ2

Sin ( ωd t p + θ )

π wd

C(t p ) = 1 -


e

- ζ ωn

π ωd

1 - ζ2

  π Sin  ωd +θ  ωd  |


Module |4

System Response

= 1-

e

Sin ( π + θ )

1 - ζ2 - ζ ωn

= 1-

π ωd

- ζ ωn

e

π ωn 1 - ζ 2

1-ζ

2

( -Sinθ )

-ζπ 1 - ζ2

e

= 1 +

1 - ζ2

Sin θ

On constructing a right angle triangle with ζ and 1 - ζ 2 , we get

-ζπ

∴ C(t p ) = 1 +

1 - ζ2

e

1 - ζ2

1 - ζ2

-ζπ 1 - ζ2

= 1 + e ∴ % MP =

C(t P ) - C( ∞ ) X 100 C( ∞ ) -ζπ

=

1 - ζ2

1 + e

-1

1

X 100

-ζπ

% MP = e

194


1 - ζ2

X 100

|


Module |4

System Response

5. Settling time (ts) It is defined as the time taken by the response to reach and stay with in a specified tolerance band of its final value. The tolerance band is usually 2% or 5% of the final value. Expression The unit step response of second order system is given by

C(t) = 1 -

e

-ζ ω n t

1 - ζ2

Sin ( ω d t + θ )

The response of second order system has two components. They are,

e 1.

Decaying exponential component,

2.

Sinusoidal component, Sin ( ω d t + θ )

-ζ ωn t

1 - ζ2

The decaying exponential term damped (or reduces) the oscillations produced by sinusoidal component. Hence the settling time is decided by the exponential component. Allowable tolerance is 2% or 5%.

∴ The settling time for 2% tolerance is at t = t s , e

-ζ ω n t s

1-ζ 195

2


= 0.02

|


Module |4

System Response

For least values of ζ

∴

e -ζ ωn ts = 0.02

On taking natural logarithm we get,

− ζ ω n t s = ln ( 0.02 )

−ζ ωn t s = - 4

∴ Settling time, If T =

ts =

4 ζ ωn

1 = Time constant of the system ζ ωn

t s = 4T;

for 2 % error

The settling time for 5% error tolerance is at t = t s , -ζ ω n t s

e

1-ζ

2

= 0.05

For least values of ζ

∴

e

-ζ ωn t s

= 0.05

On taking natural logarithm we get,

− ζ ω n t s = ln ( 0.05 )

−ζ ω n t s = - 3

∴ Settling time, t s = If T =

3 ζ ωn

1 = Time constant of the system ζ ωn

t s = 3T;

196


for 5 % error

|


Module |4

System Response

STEADY STATE ERROR The Steady state error ess is the difference between the input (or desired value) and the output of a closed loop system when t tends to infinity. As the steady state error is an index of accuracy of a control system, therefore, the steady state error should be minimum as far as possible.

The steady state error is the value of error signal e(t), when ‘t’ tends to infinity. Consider a closed loop system shown in figure,

The error signal,

E(s) = R(s) − C(s) H(s)  → (1)

The output signal,

C(s) = E(s) G(s)  → (2)

Substitute (2) in (1)

(1) ⇒ E(s) = R(s) − [E(s) G(s)] H(s) ∴ E(s) + E(s) G(s) H(s) = R(s)

E(s) [1 + G(s) H(s)] = R(s) 197


|


Module |4

System Response

∴ The error signal

E(s) =

R(s) 1 + G(s) H(s)

But the steady state error is defined as the value of error signal when t tends to infinity.

∴ Steady state error,

ess = lim e(t) t→∞

lim f (t) = lim s F (s)

From final value theorem,

∴

i.e.,

t→∞

s →0

e ss = lim s E (s) s→0

ess = lim s→0

s R(s) 1 + G(s) H(s)

STEADY STATE ERROR WHEN THE INPUT IS UNIT STEP SIGNAL The input is unit step signal, R(s) =

1 s

s R(s) 1 + G(s) H(s)

The steady state error, ess = slim →0

1 s ∴ e ss = lim s → 0 1 + G(s) H(s) s.

= lim s→0

=

1 1 + G(s) H(s)

1 1 + lim G(s) H(s) s →0

∴ ess =

1 1 + KP

Where K P = lim G(s) H(s) s→0

The constant KP is called Positional error constant. 198


|


Module |4

System Response

STEADY STATE ERROR WHEN THE INPUT IS UNIT RAMP SIGNAL The input is unit step signal, R(s) =

The steady state error,

ess = lim s→0

1 s2

s R(s) 1 + G(s) H(s)

1 2 s ∴ e ss = lim s → 0 1 + G(s) H(s) s.

1 s = lim s → 0 1 + G(s) H(s)

= lim s→0

=

1 s + s G(s) H(s)

1 lim s G(s) H(s)

s →0

∴ ess =

1 KV

Where K V = lim s G(s) H(s) s →0

The constant KV is called Velocity error constant.

STEADY STATE ERROR WHEN THE INPUT IS UNIT PARABOLIC SIGNAL The input is unit step signal, R(s) =

The steady state error,

199

ess = lim


s→0

1 s3

s R(s) 1 + G(s) H(s) |


Module |4

System Response

1 s3 ∴ e ss = lim s → 0 1 + G(s) H(s) s.

1 s2 = lim s → 0 1 + G(s) H(s)

= lim s→0

=

1 s 2 + s 2 G(s) H(s)

1 lim s G(s) H(s) 2

s →0

∴

ess =

1 Ka

Where Ka = lim s2 G(s) H(s) s→0

The constant Ka is called Acceleration error constant.

The error constants are tabulated as

The Positional Error Constant

K P = lim G(s) H(s)

The Velocity Error Constant

K V = lim s G(s) H(s)

The Acceleration Error Constant

K a = lim s 2 G(s) H(s)

200


s→0

s→0

s→0

|


Module |4

System Response

STABILITY OF SYSTEMS The closed loop transfer function can be expressed as a ratio of two polynomials in s. The denominator polynomial of closed loop transfer function is called characteristic equation. The roots of characteristic equation are called poles. The roots of numerator polynomial are called zeros.

For e.g.

M(s) =

s 2 + 3s + 2 (s + 4) (s 2 + 5s + 6)

M(s) =

(s + 1) (s + 2) (s + 4) (s + 2) (s + 3)

The poles are s = -4, s= -2, s= -3 The zeros are s= -1, s= -2 The poles and zeros are plotted on the s-plane. The poles are represented by the symbol 'X' and the zeros are represented as 'o'. The x axis of 's' plane is "Real axis" plots the real part of the complex variable. The y axis is "Imaginary axis" and plots the imaginary part of the complex number.

The complex variable s = σ ± jw is represented in this’s’ plane. The’s’ plane have two half’s "Left Half" and "Right Half".

When the poles of the transfer function lie in the left half of s-plane, then the system is said to be stable. or If all the roots of characteristic equation have negative real parts then the system is said to be a stable system. 201


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Module |4

System Response

ROUTH HURWITZ CRITERION The closed loop transfer function of a system is a ratio of two polynomials in s. The denominator polynomial of closed loop transfer function is called the characteristic equation of the system. The roots of the characteristic equation of a stable system should lie on the left of s plane. Hence the roots should have negative real parts. The Routh-Hurwitz stability criterion is an analytical procedure for determining whether all the roots of a polynomial have negative real parts or not.

ANALYSIS OF STABILITY Step 1:- Examine the characteristic equation. The necessary condition for stability is that all the coefficients of the polynomial be positive. If some of the coefficients are zero or negative it can be concluded that the system is unstable. Step 2:- Construct a Routh array. Let the characteristic polynomial be

a 0 s n + a 1 s n - 1 + a 2 s n - 2 + a 3 s n - 3 + .......... ... + a n - 1 s 1 + a n s 0 The coefficients of the polynomial are arranged in two rows as shown below

sn

: a0

a2

a4

a 6 .......... .........

sn

: a1

a3

a5

a 7 .......... .........

Step 3:- Construction of third row in Routh array. Third row is constructed from the first two rows.

s n-2 :

a1 × a 2 - a 0 × a 3 a1

a1 × a 4 - a 0 × a 5 a1

Note:- By the construction of Routh array the missing terms are considered as zeros. Step 4:- Form rows up to s0

CHECKING STABILITY i.

The necessary condition for stability is that all of the elements in the first column of the Routh array be positive.

ii.

The number of sign changes in the elements of the first column of the Routh array corresponds to the number of roots of the characteristic equation in the right half of the s-plane. 202


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System Response

Note:- If the order of first column element is +, +, -, +. Then + to – is considered as one sign change and – to + is another sign change. If there is no sign change in the first column of Routh array then all the roots are lying on left half of s-palne and the system is stable.

ADVANTAGES AND LIMITATIONS OF ROUTH’S CRITERION Advantages Advantages of Routh’s Array methods are: i)

Stability of the system can be judged without actually solving the characteristic equation.

ii)

No evaluation of determinants, which saves calculation time.

iii)

For unstable system it gives number of roots of characteristic equation having positive real part.

iv)

Relative stability of the system can be easily judged.

v)

By using this criterion, critical value of system gain can be determined hence frequency of sustained oscillations can be determined.

vi)

It helps in finding out range of values of K for stability.

vii) It helps in finding out intersection points of root locus with imaginary axis. Limitations Limitations of Routh’s Array methods are: i)

It is valid only for real coefficients of the characteristic equation.

ii)

It does not provide exact locations of the closed loop poles in left or right half of s – plane.

iii)

It does not suggest methods of stabilizing an unstable system.

iv)

Applicable only to linear systems.

203


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Module |4

System Response

SPECIAL CASES Case I : A Row of all zeros A row with all zeros indicates the possibility of roots on imaginary axis. Solution Method 1. Determine the auxiliary polynomial A(s). 2. Differentiate the auxiliary polynomial with respect to s, to get

d A(s) . ds

d A(s) . ds 4. Continue the construction of the array in the usual manner.

3. The row of zeros is replaced with coefficients of

If there are sign changes in the first column of routh array then the system is unstable. The number of roots on imaginary axis can be estimated from the roots of auxiliary polynomial. If there is no sign changes in the first column of routh array then the all zeros row indicate the existence of purely imaginary roots and so the system is immediately or marginally stable.

Case II : First element of a Row is zero If a zero is encountered as first element of a row in the Routh array then all the elements of the next row will be infinite. To over come this problem substitute ∈ for 0 → 0 and and complete the construction of array in the usual way. Finally let ∈  determine the values of the elements of the array which are functions of ∈ .

Checking for Stability If there is no sign change in first column of Routh array, then the system is stable. If sign change occurs, then the system is unstable. If there is a row of all zeros after letting ∈ → 0, then there is a possibility of roots on imaginary axis (then do like case I). 204


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Module |4

System Response


- Nagoorkani A.


- Ramesh Babu


- B.S. Mange

4) Control System Engineering

- Nagrath & Gopal

5) Control Systems Theory & Applications - Smarajit Ghosh 6) Problems & Solutions in Control System Engineering


7) Modern Control Engineering

- Katsuhiko Ogata

8) Control Systems



- Norman S. Nise

205


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Module | 5

Frequency Response Analysis

MODULE - 5 FREQUENCY RESPONSE ANALYSIS The frequency response is the steady state response (output) of a system when the input to the system is a sinusoidal signal. Consider a linear time invariant (LTI) system, H. Let x(t) be an input sinusoidal signal. The response or output y(t) is also a sinusoidal signal of same frequency but with different magnitude and phase angle.

The magnitude and phase relationship between the sinusoidal input and the steady state output of a system is termed the frequency response. The frequency response of a system is normally obtained by varying the frequency of the input signal by keeping the magnitude of the input signal at a constant value. In the system transfer function T(s), if s is replaced by jω then the resulting transfer function T(jω) is called sinusoidal transfer function. The frequency response of the system can be directly obtained from the sinusoidal transfer function T(jω) of the system. The frequency response can be evaluated for both open loop system and closed loop system.

G(jω) = G(jω) ∠G(jω)

Open Loop Transfer Function, Loop Transfer Function is,

G(jω) H(jω) = G(jω) H(jω) ∠G(jω) H(jω)

Closed Loop Transfer Function is,

206


C(jω) = M(jω) = M(jω) ∠M(jω) R(jω)

|


Module | 5


FREQUENCY DOMAIN SPECIFICATIONS The performance and characteristics of a system in frequency domain are measured in terms of frequency domain specifications. The requirements of a system to be designed are usually specified in terms of these specifications. The frequency domain specifications are 1.

Resonant Peak, Mr

2.

Resonant Frequency, ω r

3.

Bandwidth

4.

Cut-off rate

5.

Gain Margin

6.

Phase Margin

GAIN MARGIN, Kg The gain margin, Kg is defined as the reciprocal of the magnitude of Open Loop Transfer Function at Phase Cross Over Frequency. The frequency at which the phase of Open Loop Transfer Function is 1800 is called the phase cross-over frequency, ω pc .

Gain Margin, K g =

1 G(jω pc )

The gain margin in db can be expressed as,

K g in db = 20 log K g = 20 log

1 G(jω pc )

= -20 log G(jω pc ) Note:- G(jωpc ) is the magnitude of G(jω) at ω = ωpc The Gain Margin indicates the amount by which the gain of the system can be increased without affecting the stability of the system.

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PHASE MARGIN ( γ ) The Phase Margin γ is that amount of additional phase lag at the Gain Cross over frequency required to bring the system to the verge of instability. The Gain Cross over frequency ω gc is the frequency at which the magnitude of the Open Loop transfer function is unity. The Phase Margin γ is obtained by adding 1800 to the phase angle Φ of the open loop transfer function at the Gain Cross over frequency

Phase Margin, γ = 1800 + Φ gc

where Φ gc = ∠ G(jωgc ) and ∠ G(jω gc ) is the Phase angle of G(jω) at ω = ωgc

FREQUENCY RESPONSE PLOTS Frequency Response analysis of control systems can be carried either analytically or graphically. The various graphical techniques available for frequency response analysis are 1. Bode Plot 2. Polar Plot (or Nyquist Plot) 3. Nichols Plot 4. M and N Circles 5. Nichols Chart The frequency response plots are used to determine the frequency domain specifications, to study the stability of the systems and to adjust the gain of the system to satisfy the desired specifications. Bode plot, Polar plot and Nichols plot are usually drawn for Open loop systems. From the Open loop response plot the performance and stability of closed loop systems are estimated. M and N circles and Nichols chart are used to graphically determine the frequency response of unity feedback closed loop system from the knowledge of open loop response. 208


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Module | 5


BODE PLOTS Bode plot is drawn for open loop systems. Sometimes it can be drawn for closed loop systems also. Bode plot consists of two graphs. One is a plot of the magnitude of a sinusoidal transfer function versus log ω. The other is a plot of the phase angle of a sinusoidal transfer function versus log ω. The standard representation of the logarithmic magnitude of open loop transfer function of

G(jω) is 20 log G(jω) . The unit used in this representation of the magnitude is the decibel (db). The curves are drawn on semilog paper, using the log scale for frequency and the linear scale for either magnitude (in decibels) or phase angle (in degrees). Advantages of Bode Plot •

The main advantage of the bode plot is that multiplication of magnitudes can be converted in to addition.

•

A simple method for sketching an approximate log-magnitude curve is available.

Consider the Open loop transfer function,

G(s) =

K(1 + sT1 ) s(1 + sT2 ) (1 + sT3 )

put s = jω ∴ G(jω) = =

q

K ∠ 0 1 + ω2T12 ∠ tan -1ωT1 ω ∠ 90 1 + ω2 T22 ∠ tan -1ωT2

1 + ω 2T32 ∠ tan -1ωT3

The Magnitude of G(jω)

G(jω) =

q

K(1 + jωT1 ) jω(1 + jωT2 ) (1 + jωT3 )

K 1 + ω 2 T12 ω 1 + ω2 T22

1 + ω2 T32

The Phase angle of G(jω)

∠ G(jω) = tan -1ωT1 - 90 - tan -1ωT2 - tan -1ωT3 209


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Module | 5


The magnitude can be expressed in decibels as

G(jω) in db = 20 log G(jω)  K 1 + ω2T12 = 20 log   ω 1 + ω2 T22 1 + ω2T32

  

K  1 1 2 2  X = 20 log  X 1 + ω T1 X  ω 1 + ω2T22 1 + ω2T32  1 K + 20 log = 20 log + 20 log 1 + ω2T12 + 20 log ω 1 + ω2T22 = 20 log

1 1 + ω2T32

K + 20 log 1 + ω2T12 − 20 log 1 + ω2T22 − 20 log 1 + ω2T32 ω

So it is clear that, when the magnitude is expressed in db, the multiplication is converted to addition. To sketch the magnitude plot, knowledge of the magnitude variations of individual factor is essential. BASIC FACTORS OF G(jω) The basic factors that very frequently occur in a typical transfer function G(jω) are, 1. Constant Gain, K Let G(s) = K ∴

G(jω) = K and K < 0

Magnitude, A = G(jω) in db = 20 log K Phase, Φ = ∠ G(jω) = 0 Therefore the Magnitude Plot for a Constant Gain K is a horizontal straight line at the magnitude of 20 log K db. The Phase Plot is straight line at 00.

210


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Module | 5


K   jω 

2. Integral Factor, 

K s K K ∴ G(jω) = = ∠ -90 0 jω jω

Let G(s) =

Magnitude, A =

G(jω) in db = 20 log

K ω

Phase, Φ = ∠ G(jω) = -90 0 1 = 20 db 0.1 When ω = K, ∴ A = 20 log 1 = 0 db 1 When ω = 10K, ∴ A = 20 log = −20 db 10 When ω = 0.1K, ∴ A = 20 log

§

From the above analysis it is evident that the magnitude plot of the factor is a straight line with a slope of –20 db/dec and passing through zero db, when ω = K.

§

Since the ∠ G(jω) is a constant and independent of ω the phase plot is a straight line at –900.

2.b Integral Factor has multiplicity of n,

K

( jω )

n

K sn K K ∴ G(jω) = = n ∠ -90n 0 n (jω) ω

Let G(s) =

211


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Module | 5


Magnitude, A = G(jω) in db = 20 log  1n K = 20 log   ω   Phase, Φ = ∠ G(jω) =

n

K ωn

  = 20 n log    -90 n 0

 1n K  ω  

    

Now the magnitude plot of the integral factor is a straight line with a slope of –20 n db/dec and passing through zero db when ω = K1/n. For example let G = K/s2, then the slope is –40 db/dec. The phase plot is a straight line at –90 n0. 3. Derivative Factor, K(jω)

Let G(s) = Ks ∴ G(jω) = K ( jω )

=

( Kω )

∠ 90 0

Magnitude, A = G(jω) in db = 20 log ( Kω ) Phase, Φ = ∠ G(jω) = + 90 0 0.1 , K 1 When ω = , K 10 When ω = , K When ω =

§

∴ A = 20log 0.1 = − 20 db ∴ A = 20log 1

= 0 db

∴ A = 20log 10 = + 20 db

From the above analysis it is evident that the magnitude plot of the derivative factor is a straight line with a slope of +20 db/dec and passing through zero db, when ω = 1/K. Since the ∠ G(jω) is a constant and independent of ω, the phase plot is a

§

straight line at +900.

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Module | 5


n 3.b Derivative Factor with a multiplicity of n, [ K(jω) ]

Let G(s) = Ks n ∴ G(jω) = K(jω) n = Kω n ∠ 90 n 0

(

Magnitude, A = G(jω) in db = 20 log Kω n

)

1 n

= 20 n log (K ω) Phase, Φ = ∠ G(jω) = 90 n 0 Now the magnitude plot of the integral factor is a straight line with a slope of +20 n db/dec and passing through zero db when ω = 1/K1/n. For example let G = Ks2, then the slope is +40 db/dec. The phase plot is a straight line at +90 n0.

4. First Order Factor in denominator

1 1 + sT 1 ∴ G (jω ) = 1 + jω T

1 1 + jωT

Let G (s) =

M agnitu de, A =

1

=

1+ ω T 2

∠ -tan -1ω T

2

1

G (jω ) in db = 2 0 lo g

= -20 log

1 + ω 2T 2

1 1 + ω2T 2

At very low frequencies ωT = 1 ∴ A = -20 log 1 + ω 2 T 2 ≈ -20 log 1 = 0 At very high frequencies ωT ? 1 ∴ A = -20 log 1 + ω 2 T 2 ≈ -20 log 1 , T 10 at ω = , T at ω =

213

ω 2 T 2 = -20 log ωT

A = -20 log 1

= 0

A = -20 log 10 = -20 db


|


Module | 5


The above analysis shows that the magnitude plot of the factor

can be

approximated by two straight lines, one is a straight line at 0db for the frequency range 0 < ω < range (

and the other is a straight line with slope –20 db/dec for the frequency

< ω < ∞). The two straight lines are asymptotes of the exact curve. The

frequency at which the two asymptotes meet is called the corner frequency or break the frequency ω =

frequency. For the factor

is the corner frequency, ωc. It

divides the frequency response curve into two regions, a curve for low frequency region and a curve for high frequency region. The Phase Plot is obtained by calculating the phase angle of G(jω) for various values of ω.

∴ Phase angle, Φ = ∠ G(jω) = -tan -1ωT 1 At the corner frequency, ω = ω c = T 1  & Phase angle, Φ = -tan -1  X T  = -tan -1 1 = -45 0 T  -1 As ω   → 0 Φ = -tan 0 = 0 As ω   → ∞

Φ = -tan -1∞

The Phase angle of the factor

= -90 0

varies from 00 to –900 as ω is varied from zero

to infinity. The Phase Plot is a curve passing through –450 at ωc.

Bode Plot of the factor 214


|

1 1 + jωT


Module | 5


4.b. First Order Factor in the denominator has a multiplicity of m; Let G (s) = & G (jω ) = =

M agnitude, A =

1

(1

+ jωT )

m

1

(1 + sT )

m

1

(1 +

(

jω T )

m

1 + ω 2T 2

)

1 m

∠ m tan -1 ω T

G (jω ) in db

= 20 log

1

(

1 + ω 2T 2

= -20 m log

)

m

1 + ω 2T 2

Phase, Φ = ∠ G (jω ) = -m tan -1 ω T Now the magnitude plot can be approximated by two straight lines, one is a straight line at zero db for the frequency range 0 ∠ w ∠

∠ w ∠ ∞.

slope –20 m db/dec for the frequency range The corner frequency ωc =

and the other is a straight line with

. The phase angle of the factor

(

ω )

varies

from 00 to –90 m0 as ω is varied from zero to infinity. The phase plot is a curve passing through –45 m0 at ωc.

5. First Order Factor in the numerator, (1 + jωT)

Let G (s) = 1 + sT & G (jω) = 1 + jωT ∴

G (jω) =

M agnitude, A =

1 + ω 2 T 2 ∠ tan -1 ωT

G (jω) in db

= 20 log

Phase,

1 + ω 2T 2

Φ = ∠ G(jω) = tan -1 ω T

215


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Module | 5


By an analysis similar to that of previous section it can be shown that the magnitude plot of the factor (1+jωT) can be approximated by two straight lines, one is a straight line at zero db for the frequency range 0 ∠ ω ∠

∠ ω ∠ ∞.

slope +20 db/dec for the frequency range The corner frequency ωc =

and the other is a straight line with

. The phase angle of the factor (1+jωT) varies from

00 to +900 as ω is varied from zero to infinity. The phase plot is a curve passing through +450 at ωc.

Bode Plot of the factor (1 + jωT ) 5. b. First Order Factor in the numerator has a multiplicity of m, (1 + jωT)m

(1 + sT ) m = (1 + jωT )

Let G(s) = & G(jω)

∴ G(jω) =

m

(

1 + ω2T 2

)

m

∠ m tan -1ωT

Magnitude, A = G(jω) in db = 20 log

Ph ase,

(

1 + ω2T 2

)

m

= 20 m log 1 + ω 2 T 2 Φ = ∠ G(jω) = m tan -1 ωT

Now the magnitude plot of the factor (1+jωT)m can be approximated by two straight lines, one is a straight line at zero db for the frequency range 0 ∠ ω ∠ is a straight line with a slope of +20 m db/dec for the frequency range 216


|

and the other ∠ ω ∠ ∞.


Module | 5


The corner frequency ωc =

. The phase angle of the factor (1+jωT)m varies from

00 to +90 m0 as ω is varied from zero to infinity. The phase plot is a curve passing through +45 m0 at ωc.

1 6. Quadratic Factor in the denominator,

Let G(s) =

G(jω) =

=

 jω 1 + 2ς   ωn

  jω  +    ωn 

2

1  s   s  1 + 2ς  +   ωn   ωn  1  jω 1 + 2ς   ωn  ω  1−    ωn 

2

  jω  +    ωn  1

2

2

 ω  + j2 ς    ωn 

ω ωn 1 ∠ -tan -1 2 ω2 2    ω2  ω 1− 2 2  1 − 2  + 4ς  2  ωn ωn    ωn  2ς

=

Magnitude, A = G(jω) in db = 20 log

217

1  ω2  1 − 2  ωn  

2

 ω2  + 4ς  2   ωn  2

2

= -20 log

 ω2  1 − 2  ωn  

= -20 log

2 ω4 ω2 2 ω 1 + 4 -2 2 + 4 ς ωn ωn ω 2n

= -20 log

ω2 1− 2 ωn


 ω2  + 4ς  2   ωn  2

( 2 - 4ς ) 2

|

ω4 + 4 ωn


Module | 5


At very low frequencies when ω = ω n , ω2 The terms 2 ωn

( 2 - 4ς ) 2

ω4 & 4 approches to zero ωn

∴ The magnitude is, A = -20 log 1 = 0

At very high frequencies when ω ? ω n , Then 1 -

ω2 2 - 4ς 2 2 ωn

(

when compared to

)

≈

ω2 2 - 4ς 2 2 ωn

(

(

)

)

ω 4 ω2 , 2 2 - 4ς 2 is negligible 4 ωn ωn

∴ The magnitude is, A = -20 log

ω4 ω 4n

ω2 = -20 log 2 ωn 2

 ω  = -20 log    ωn   ω  = -20 X 2 log    ωn 

 ω  ∴ A = -40 log    ωn  At ω = ω n ,

A = -40 log 1

At ω = 10 ω n , A = -40 log 10

= 0 db = -40 db

From the above analysis it is evident that the magnitude plot of the quadratic factor in the denominator can be approximated by two straight lines, one is a straight line at zero db for the frequency range 0 ∠ ω ∠ ωn and the other is a straight line with a slope of -40 db/dec for the frequency range ωn ∠ ω ∠ ∞. The two straight lines are asymptotes of the exact curve. The frequency at which the two asymptotes meet is called the corner frequency. For the quadratic factor, the frequency ωn is the corner frequency, ωc. 218


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Module | 5


The Phase Plot is obtained by calculating the phase angle of G(jω) for various values of ω.

 ω  2ς ωn ∴ Φ = ∠ G(jω) = -tan -1   ω2  1 − ω2 n  -1  2 ς 

At ω = ω n

→0 At ω  →∞ At ω 

Φ = -tan    0  Φ = -tan -1 0

∞ Φ = -tan -1   ∞

      = -tan -1 ∞ = -90 0 = 00 = -180 0

[Here the angle contribution obtained must be considered by subtracting 180 from the positive φ. This happens because behavior of tan-1 function for the complex quantities with real part negative or imaginary part negative, cannot be identified on calculator by using above formula.] 2   jω   jω   7. Quadratic Factor in the Numerator, 1 + 2 ς  +     ω n   ω n  

 s Let G(s) = 1 + 2ς   ωn

  s  +    ωn 

2

 jω   jω  G(jw) = 1 + 2ς  +  ω  n   ωn 

2

ω 1 ωn ∠ tan -1 2 2 ω 2 2  ω  1− 2 2 ω   1 − 2  + 4ς  2  ωn  ωn   ωn  2ς

=

The magnitude plot of the quadratic factor in the numerator can be approximated by two straight lines, one is a straight line at zero db for the frequency range 0 ∠ ω ∠ ωn and the other is a straight line with a slope of +40 db/dec for the frequency range ωn ∠ ω ∠ ∞. The two straight lines are asymptotes of the exact curve. The frequency at which the two asymptotes meet is called the corner frequency. The corner frequency is ωc. The phase angle varies from 00 to +1800, as ω is varied from zero to infinity. At the corner frequency the phase angle is +900. 219


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Module | 5


The basic factors of G(jw) in the magnitude and phase plot are tabulated as No.

Basic Factors of G(jw)

1.

K

2.

K jω K

3.

( jω )

Magnitude Plot Amplitude, A = 20 log K No Slope A = 20 log

Angle 00

Angle -900

Slope is –20 db A = 20 log

K eg., 2 s

n

Phase Plot

Slope is –20 n db

Angle –90 n0 eg., -1800

eg., -40 db A = 20 log (Kω)

K(jω)

4.

Slope is +20 n db A = 20 log (Kωn)

5.

K(jω)

n

eg., Ks

2

Slope is +20 n db eg., +40 db

1 1 + jωT

6.

7.

1

(1 + jωT )

m

1

(1 + 0.2s )

(1 + jωT )

m

eg., (1 + 0.2s )

2

11.

220

 jω   jω  1 + 2ς  +   ωn   ωn 

2

 jω   jω  1 + 2ς  +   ωn   ωn 


eg., +1800 Angle –tan-1 ωT

Slope is –20 n db

Angle –m tan-1 ωT

e.g., -40 db

e.g., –2 tan-1 0.2ω

Slope is +20 db

Angle tan-1 ωT

Slope is +20 m db

Angle m tan-1 ωT

e.g., +40 db

e.g., 2 tan-1 0.2ω

Slope is –40 db

 ω  2ς ωn Angle -tan -1   ω2  1- ω2 n 

     

Slope is +40 db

 ω  2ς ωn Angle tan -1   ω2  1- ω2  n

     

1

10.

Angle +90 n0

Slope is –20 db

2

(1 + jωT )

8. 9.

eg.,

Angle +900

2

|


Module | 5


PROCEDURE FOR MAGNITUDE PLOT OF BODE PLOT Step. 1:- Convert the transfer function into Bode form or time constant form. The Bode form of the transfer function is

G(s) =

∴ G(s) =

K(1 + sT1 )  s2 s  s (1 + sT2 )  1 + 2 + 2 ς  ωn ωn   K(1 + jωT1 )  ω2 ω  jω (1 + jωT2 )  1 − 2 + j2 ς  ωn ωn  

Step. 2:- Find the corner frequencies of each factor in transfer function and list them in increasing order of Corner frequency. If the sinusoidal transfer function has a term like K,

(

)

or K(jω)

then enter that factor as first term in the table.

Find the slop contributed by each factor and net slope from the corner frequency. Prepare a table as shown below.

Term

Corner Frequency

Slope

Change in Slope

rad/sec

db/dec

db/dec

Step. 3:- Choose an arbitrary frequency ωl which is lesser than the lowest corner frequency. Calculate the db magnitude of K,

(

)

or K(jω)

at ωl and at

the lowest corner frequency.

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Step. 4:- Then calculate the gain (db magnitude) at every corner frequency one by one by using the formula, Gain at ωy = Change in gain from ωx to ωy + Gain at ωx

ωy  =  Slope from ωx to ωy X log ωx 

  + Gain at ωx 

Step. 5:- Choose an arbitrary frequency ωh which is greater than the highest corner frequency. Calculate the gain at ωh by using the formula in Step 4. Step. 6:- In a Semi log graph sheet mark the required range of frequency on X – axis (log scale) and the range of db magnitude on Y – axis (Ordinary scale) after choosing proper scale. Step. 7:- Mark all the points obtained in steps 3, 4 and 5 on the graph and join the points by straight lines. Mark the slope at every part of the graph.

PROCEDURE FOR PHASE PLOT OF BODE PLOT The Phase Plot is an exact plot and no approximations are made while drawing the phase plot. Hence the exact phase angles of G(jω) are computed for various values of ω and tabulated. The choices of frequencies are preferably the frequencies chosen for magnitude plot. Usually the magnitude plot and phase plot are drawn in a single semi log sheet on a common frequency scale. Take another Y-axis in the graph where the magnitude plot is drawn and in this Y- axis mark the desired range of phase angles after choosing proper scale. From the tabulated values of w and phase angles, mark all the points on the graph. Join the points by a smooth curve.

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Determination of Gain Margin and Phase Margin from Bode Plot The Gain Margin in db is given by the negative of db magnitude of G(jω) at the Phase Cross-over frequency, ωpc. The ωpc is the frequency at which phase of G(jω) is –1800. If the db magnitude of G(jω) at ωpc is negative then gain margin is positive and vice versa. Let φgc be the phase angle of G(jω) at gain cross over frequency ωgc. The ωgc is the frequency at which the db magnitude of G(jω) is zero. Now the phase margin, γ is given by,

γ = 180 + φgc If φgc is less negative than –1800 then phase margin is positive and vice versa. The positive and negative gain margins are illustrated in figure.

Fig:- Bode Plot showing Phase Margin (γ) and Gain Margin (Kg)

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POLAR PLOT The Polar Plot of a sinusoidal transfer function G(jω) is a plot of the magnitude of G(jω) versus the phase angle of G(jω) on polar coordinates as w is varied from zero to infinity. Thus the Polar Plot is the locus of vectors G(jω) ∠ G(jω) as ω is varied from zero to infinity. The polar plot is also called Nyquist Plot. The Polar plot is usually plotted on a polar graph sheet. The polar graph sheet has concentric circles and radial lines. The circles represent the magnitude and the radial lines represent the phase angles. Each point on the polar graph has a magnitude and phase angle. The magnitude of a point is given by the value of the circle passing through that point and the phase angle is given by the radial line passing through that point. In polar graph sheet a positive phase angle is measured in anticlockwise from the reference axis (00) and a negative angle is measured clockwise from the reference axis (00).

If G(jω) can be expressed in rectangular coordinates as G (jω) = GR (jω) + GI (jω) where GR (jω) = Real part of G (jω) and GI (jω) = Imaginary part of G (jω) Then the polar plot can be plotted in ordinary graph sheet between GR (jω) and GI (jω) as ‘ω’ is varied from 0 to ∞. 224


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To plot the polar plot, first compute the magnitude and phase of G (jω) for various values of w and tabulate them. Usually the choices of frequencies are corner frequencies and frequencies around corner frequencies. Choose proper scale for the magnitude circles. Fix all the points on polar graph sheet and join the points by smooth curve. Write the frequency corresponding to each point on the plot. To plot the polar plot on ordinary graph sheet, compute the magnitude and phase for various values of w. Then convert the polar coordinates to rectangular coordinates using

conversion (Polar to rectangular conversion) in the

calculator. Sketch the polar plot using rectangular coordinates. For minimum phase transfer function with only poles, the type number of the system determines at what quadrant the polar plot starts and the order of the system determines at what quadrant the polar plot ends.

Note:- Type determines the power of ‘s’ term and order is the maximum power of ‘s’ terms of the characteristic equation.

TYPICAL SKETCHES OF POLAR PLOT

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DETERMINATION OF GAIN MARGIN & PHASE MARGIN FROM POLAR PLOT The gain margin is defined as the inverse of the magnitude of G(jω) at phase crossover frequency. The phase crossover frequency is the frequency at which the phase of G(jω) is 1800. Let the polar plot cut the 1800 axis at point B and the magnitude circle passing through the point B is

. Now the Gain Margin,

. If the point B lies within

unity circle then the Gain Margin is positive otherwise negative. The phase margin is defined as, phase margin,

where

is

the phase angle of G(jω) at gain crossover frequency. The gain crossover frequency is the frequency at which the magnitude of G(jω) is unity. Let the polar plot cut the unity circle at point A as shown in figure. Now the phase margin, γ is given by ∠ AOP, i.e., if ∠ AOP is below -1800 axis then the phase margin is positive and if it is above -1800 axis then the phase margin is negative.

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NYQUIST STABILITY CRITERION Consider the closed loop transfer function

C(s) G(s) =  → (1) R(s) 1 + G(s) H(s) The characteristic equation of the system is given by the condition

1 + G(s) H(s) = 0 Let F(s) = 1 + G(s) H(s)  → (2)

or F(s) =

(s - Z1 ) (s - Z2 ) ......... (s - Zm )  → (3) (s - P1 ) (s - P2 ) ......... (s - Pn )

The roots of numerator polynomial are zeros and the roots of denominator polynomial are poles. Let s be a complex variable represented by s = σ + jω on the complex s-plane. The function F(s) is also complex and may be defined as F(s) = u + jv and represented on the complex F(s)-plane with coordinates u and v. The equation (3) indicates that for every point s in the s-plane at which F(s) is analytic, there exists a corresponding point F(s) in the F(s) plane. Hence it can be concluded that the function F(s) maps the points in the s-plane into the F(s)-plane.

Fig: An arbitrary contour in s-plane and its corresponding contour in F(s) plane

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PROCEDURE FOR INVESTIGATING THE STABILITY USING NYQUIST CRITERION The following steps can be followed to investigate the stability of closed loop system from the knowledge of open loop system, using Nyquist Stability Criterion. Step.1:- Choose a Nyquist contour as shown in fig (a), which encloses the entire right half s-plane except the singular points. The Nyquist contour encloses all the right half s-plane poles and zeros of G(s) H(s) [The poles on imaginary axis are singular points and so they are avoided by taking a detour around it as shown in fig (b) and (c)].

Step.2:- The Nyquist contour should be mapped in the G(s) H(s) plane using the function G(s) H(s) to determine the encirclement -1 + j0 point in the G(s) H(s) plane. The Nyquist contour of fig. b can be divided into four sections C1, C2, C3 and C4. The mapping of the four sections in the G(s) H(s) plane can be carried section wise and then combined together to get entire G(s) H(s) contour. Step.3:- In section C1 the value of ω varies from 0 to +∞. The mapping of section C1 is obtained by letting s = jω in G(s) H(s) and varying ω from 0 to +∞,

i.e., G(s) H(s) 229


s = jω ω = 0 to ∞

= G(jω) H(jω) |

ω = 0 to ∞


Module | 5


The locus of G(jω) H(jω) as ω is varied from 0 to +∞ will be the G(s) H(s) contour in G(s) H(s) plane corresponding to section C1 in s-plane. This locus is the polar plot of G(jω) H(jω). To map this section of G(s) H(s) contour separate the real and imaginary part of G(jω) H(jω). Equate the imaginary part to zero, to find the frequency at which the G(jω) H(jω) locus crosses real axis (to find phase crossover frequency). Substitute this frequency on real part and find the crossing point of the locus on real axis. Sketch the approximate locus of G(jω) H(jω) from the knowledge of type number and order of the system or from the value of G(jω) H(jω) at ω = 0 and ω = ∞. Step.4:- In section C2 of Nyquist contour has a semicircle of infinite radius. Therefore, every point on section C2 has infinite magnitude but the argument varies from +

π π to − . Hence the mapping of section C2 from s-plane to G(s) H(s) plane 2 2

can be obtained by letting s = Lt Re jθ in G(s) H(s) and varying θ from R →∞

+

π π to − . 2 2

On letting, s = Lt Re jθ we get R →∞

G(s) H(s) s = Lt

R →∞

Re jθ

K1

=

( Re )

jθ n-m

Lt

R →∞ π -j (n-m) π When θ = , G(s) H(s) = 0 e 2 2

π + j (n-m) π 2 = = θ , G(s) H(s) 0 e When 2

From the above two equations we can conclude that the section C2 of Nyquist contour in s-plane is mapped as circles/circular arc around origin with radius tending to zero in the G(s) H(s) plane. Step.5:- In section C3 the value of ω varies from -∞ to 0. The mapping of section C3 is obtained by letting s = +jω in G(s) H(s) and varying ω from -∞ to 0,

i.e., G(s) H(s) 230


s = + jω ω = -∞ to 0

= G(jω) H(jω) |

ω = -∞ to 0


Module | 5


The locus of G(jω) H(jω) as ω is varied from -∞ to 0 will be the G(s) H(s) contour in G(s) H(s) plane corresponding to section C3 in s-plane. This locus is the inverse polar plot of G(jω) H(jω). The inverse polar plot is given by the mirror image of polar plot with respect to real axis. Step.6:- In section C4 of Nyquist contour has a semicircle of zero radius. Therefore every point on semicircle has zero magnitude but the argument varies from −

π π to + . Hence the mapping of section C4 from s-plane to G(s) H(s) plane 2 2

can be obtained by letting s = Lt Re-jθ in G(s) H(s) and varying θ from R →0

−

π π to + . 2 2

On letting, s = Lt Re -jθ we get R →0

G(s) H(s) s = Lt

R →0

Re jθ

K

=

( Re )

jθ y

Lt

R →0

= ∞ e -jθy π When θ = − , 2 When θ =

π , 2

G(s) H(s) = ∞ e G(s) H(s) = ∞ e

π j y 2

π -j y 2

From the above two equations we can conclude that the section C4 of Nyquist contour in s-plane is mapped as circles/circular arc in G(s) H(s) plane with origin as centre and infinite radius. Note:1. If there are no poles on the origin then the section C4 of Nyquist contour will be absent. 2. If there are poles (for e.g. 8 poles) on imaginary axis then the Nyquist contour is divided into 8 sections and the mapping is performed section wise.

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ROOT LOCUS The Root Locus technique is a powerful tool for adjusting the location of closed loop poles to achieve the desired system performance by varying one or more system parameters. Consider the open loop transfer function of the system,

G(s) =

K s (s + p1 ) (s + p 2 )

The characteristic equation of the system is

s (s + p1 ) (s + p 2 ) + K = 0 The roots of characteristic equation is a function of open loop gain K. When the gain K is varied from 0 to ∞, the roots of characteristic equation will take different values. When K=0, the roots are given by open loop poles. When K=∞, the roots will take the value of open loop zeros. The path taken by the roots of characteristic equation when open loop gain K is varied from 0 to ∞ are called root loci.

PROCEDURE FOR THE CONSTRUCTION OF ROOT LOCUS Step.1:- Locate the poles and zeros of G(s) H(s) on the s-plane. The root locus branch start from open loop poles and terminate at zeros. The poles are marked by cross ‘X’ and zeros are marked by small circle ‘O’. The number of root locus branches is equal to number of poles of open loop transfer function. If n = number of poles and m = number of finite zeros, then ‘m’ root locus branches ends at finite zeros. The remaining (n - m) root locus branches will end at zeros at infinity. Step.2:- Determine the root locus on real axis. Take a test point (left most point) on real axis. Count the total number of poles and zeros up to right most. If the total number of poles and zeros on the real axis to the right of this test point is odd number then the test point lies on the root locus. If it is even then the test point does not lie on the root locus. 232


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Step.3:- Determine the asymptotes of root locus branches and meeting point of asymptotes with real axis. [Asymptote is the line which continually approaches a given curve, but does not meet it with in a finite distance]. If n = number of poles and m = number of zeros, then (n – m) root locus branches will terminate at zeros at infinity. These root locus branches will go along an asymptotic path and meets the asymptotes at infinity. Hence number of asymptotes is equal to number of root locus branches going to infinity. The angle of asymptotes =

±180 ( 2q + 1) n -m

where q = 0, 1, 2, 3 ............. (n - m) Centroid =

Sum of poles -Sum of zeros n-m

Centroid is the meeting point of asymptote with real axis Step.4:- Find the break away and break in points. These points lie on real axis or exist as complex conjugate pairs. If there is a root locus on real axis between 2 poles then there exists a break away point. If there is a root locus on real axis between 2 zeros then there exists a break in point. If there is a root locus on real axis between a pole and zero then there may be or may not be break away or break in point. Let the characteristic equation be in the form

B(s) + K A(s) = 0 ∴ K=

- B(s) A(s)

The break away and break in point is given by roots of the equation

dK =0 ds

Find the value of s Substitute the value of s in K =

- B(s) A(s)

If the value of K is positive and real then only the break in and break away point s are real otherwise there will not be any break in and break away point. 233


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Step.5:- Angle of Departure and Angle of Arrival. If there is a complex pole then determine the angle of departure from the complex pole. If there is a complex zero then determine the angle of arrival at the complex zero. Angle of departure from a complex pole A

Sum of angles of vectors  = 180 -  to the complex pole A  from all other poles

 Sum of angles of vectors  +  to the complex pole A     from all other zeros

   

 Sum of angles of vectors  +  to the complex zero A     from all other poles

   

Angle of arrival at a complex zero A

Sum of angles of vectors  = 180 -  to the complex zero A  from all other zeros For example

From the following figure, Angle of departure = 180 − [θ1 + θ 2 + θ 3 ] + [θ 4 + θ 5 ]

From the following figure, Angle of arrival = 180 − [θ1 + θ 2 ] + [θ 3 + θ 4 + θ 5 ]

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Step.6:- Point of intersection of root locus with imaginary axis. To find the points where the root loci may cross the imaginary axis is by putting s = jω in the characteristic equation. Separate the real part and imaginary part. Two equations are obtained (One by equating real part to zero and the other by equating imaginary part to zero). Solve the two equations; give ‘ω’ and ‘K’. The value of ‘ω’ gives the point where the root locus crosses imaginary axis. The value of ‘K’ gives the value of gain K at this crossing point. Also this value of K is the limiting value of K for stability of the system. Advantages of Root Locus Method The root locus technique is more advantageous as it gives us following information: i)

The absolute stability of the system can be predicted from the locations of the roots in the s-plane.

ii)

Limiting range of the values of the system gain ‘K’ can be decided for absolute stability of the system.

iii)

Marginal value of the system gain ‘K’ which makes the system marginally stable can be determined and the corresponding value of the frequency of oscillations can be determined from intersection of root locus with imaginary axis.

iv)

Using root locus, value of system gain ‘K’ for any point on the root locus can be determined, by using magnitude condition.

v)

For particular damping ratio of the system, gain ‘K’ can be determined which helps to design system more correctly.

vi)

Root locus analysis also helps in deciding the stability of the control systems with time-delay.

vii) Gain margin of the system can be determined from root locus. viii) Phase margin of the system can be determined from root locus. ix)

Relative stability about a particular value of 's = −σ ' can be determined.

x)

Information about settling time of the system also can be determined from the root locus.

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- Nagoorkani A.


- Ramesh Babu

3) Control Systems



- B.S. Mange

5) Problems & Solutions in Control System Engineering 6) Control System Engineering


- Nagrath & Gopal

7) Control Systems Theory & Applications - Smarajit Ghosh

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Mechatronics

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