Basic Control System.pdf

MALAYSIA POLYTECHNICS MINISTRY OF EDUCATION

MO D U L E E 3 1 4 5 BASIC CONTROL SYSTEM

SALMAH THUKIMAN (PJB) NOOR FADZILLAH ABDULLAH (PJB)

E3145 BASIC CONTROL SYSTEM

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BIODATA OF MODULE WRITERS E3145 BASIC CONTROL SYSTEM

Name Address

: :

Salmah bt. Thukiman Electrical Engineering Department Politeknik Johor Bahru KM 10, Jalan Kong Kong

Telephone No. : E-mail : Qualifications :

Position

:

Name Address

: :

Telephone No. : E-mail : Qualifications : Position

:

81700 Pasir Gudang Johor Darul Takzim. 07- 2612488 ext.8010 [email protected] BSc Elec. Eng (Instrumentation & Control) (UTM) Dip. Ed (MPT) Dip. In Elec. Eng (Power)(UTM) Cert. In Elec. Eng. (Power) (POLIMAS) Polytechnic Lecturer

Noor Fadzillah bt Abdullah Electrical Engineering Department Politeknik Johor Bahru KM 10, Jalan Kong Kong 81700 Pasir Gudang Johor Darul Takzim. 07-2612488 ext.8010 [email protected] BSc Elec. Eng (Instrumentation & Control) (UTM) Dip. Ed (MPT) Polytechnic Lecturer


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How much do you agree with the following statements? A. FORMAT 1 The pages are organized in an interesting manner. The font size makes it easy for me to read the module. The size and types of pictures and charts used are suitable for the input. The pictures and charts are easy to read and understand. The tables used are well-organised and easy to understand. The arrangement of the Input makes it easy for me to follow. All the instructions are displayed clearly. B. CONTENTS 1 I understand all the objectives clearly. I understand the ideas conveyed. The ideas are presented in an interesting manner. All the instructions are easy to understand. I can carry out the instructions in this module. I can answer the questions in the activities easily. I can answer the questions in the self-assessment. The feedback section can help me identify my mistakes. The language used is easy to understand. The way the module is written makes it interesting to read. I can follow this module easily. Each unit helps me understand the topic better. I have become more interested in the subject after using this module.

SCALE 2

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CURRICULUM GRID The curriculum grid of this module is based on the curriculum used by Malaysian polytechnics. No.

TOPIC

1

Introduction to Control System

1

2 Hours

2

Principles of Controllers

2

3 Hours

3

Piping and Instrumentation Drawing (PNID)

3

3 Hours

4

Introduction to Relay and

4

4 Hours

5

3 Hours

6

2 Hours

5

6

Contactor Introduction to PLC Transfer Functions

UNIT

Total Hours


UNIT 1 1.0 1.1 1.2 1.3

INTRODUCTION TO CONTROL SYSTEM The Basic Concept of Control System Identifying the Definition and Terminology related to Control System Explanation of Control System Types Examples of Application Systems (1.2) on Electrical Equipments

UNIT 2 2.0 2.1 2.2 2.3

PRINCIPLES OF CONTROLLERS Explanation of Principles of Basic Controllers Explanation of Basic Controllers Components Design of Schematic Circuit for Controller Action Types Explanation of Circuits Operations

UNIT 3 3.0 3.1

PIPING AND INSTRUMENTATION DRAWING (PNID) Explanation of PNID Identifying Instruments Symbols

UNIT 4.0 4 4.1 4.2 4.3 4.4

INTRODUCTION TO and RELAY AND CONTACTOR Explanation of Relay Contactor Relay Using of Relay in Traffic Light System Examples Contactor Comparison between Relay and Contactor

UNIT 5 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7

INTRODUCTION TO PLC Explanation of PLC PLC Terminology PLC Historical Background Functions of PLC Advantages of PLC PLC Block Diagram PLC Basic Instructions Design and Write Programmed Ladder based on (6.6)

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UNIT 6 6.0 6.1 6.2 6.3

THE TRANSFER FUNCTION Explanation of the Transfer Function Definition of Transfer Function Derivation of Transfer Function from a simple Electric Circuit Derivation of Transfer Function from Block Diagram Systems

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MODULE GUIDELINES To achieve maximum benefits in using this module, students must follow the instructions carefully and complete all the activities. 1. 2.

This module is divided into 6 units. Each page is numbered according to the subject code, unit and page number. E3145 / UNIT 1 / 5

Subject Unit 1 Page Number 5 3. 4.

The general and specific objectives are given at the beginning of each unit. The activities in each unit are arranged in a sequential order and the following symbols are given:

OBJECTIVES The general and specific objectives for each learning topic are stated in this section.

INPUT This section introduces the subject matter that you are going to learn.

ACTIVITIES The activities in this section test your understanding of the subject matter. You have to complete this section by following the instructions carefully.


FEEDBACK Answers to the questions in the activity section are given here

SELF-ASSESSMENT Self-assessment evaluates your understanding of each unit.

FEEDBACK OF SELF-ASSESSMENT This section contains answers to the activities in the selfassessment.

5. 6.

You have to follow the units in sequence. You may proceed to the next unit after successfully completing the unit and you are confident of your achievement.

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GENERAL AIMS This module is prepared for students in the third semester who are following the Diploma programme in Malaysian Polytechnics. It aims to expose students to the control system concept in each unit and to lead them towards self-directed learning or with guidance from their lecturers.

PREREQUISITE SKILLS AND KNOWLEDGE The prerequisite for this module is at least a pass in Electrical and Electronic Studies at the SPM level and a successful completion of module E1001 and E2001.

GENERAL OBJECTIVES

At the end of this module, students should be able to: 1. 2. 3. 4.

state the basic control system concept find the principles of controllers simplify the PNID know about relays

5. understand about contactors 6. determine the PLC 7. understand the transfer functions

TEACHING AIDS AND RESOURCES NEEDED 1. 2.

Calculator Training Kit (OMRON)


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REFERENCES 1. Katsuhiko Ogata (1990). Modern Control Engineering . New Jersey : Prentice Hall 2. S.P Eugene Xarier & Joseph Cyril Babu.J (1999).Principles of Control System. New Delhi : S.Chand & Company LTD 3. Mansor Bin Laman(1996). Amalan Bengkel Peralatan. Kuching : Unit Teknologi Petroleum 4. Zainol Anuar (1989). Asas Kejuruteraan Kawalan. Kuala Lumpur : UTM 5. W.Bolton (2000). Programmable Logic Controllers Second Edition. Britain : Newues 6 Roger M.Bertrand (1995). Programmable Controller Circuits. New York : Delmer Publishers 7. Manual OMRON (1999).Beginner Guide To PLC. Omron Asia Pacific Pte. Ltd. 8. Manual SMC International Training (1999). Introduction To PLC Controller. SMC Pneumatic (SEA) Pte. Ltd. 9. Jubaidi Bin Razali. Pneumatik & Hidraulik. Politeknik Ungku Omar, Ipoh, Perak. 10. Manual FESTO DIDACTIC. Electro-hydraulics – Learning System for Automation & Communication. FESTO DIDACTIC.


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E3145/1/1 INTRODUCTION TO CONTROL SYSTEM

UNIT1

INTRODUCTION TO CONTROL SYSTEM

OBJECTIVES

General Objective

: To know and to apply the concept of control system.

Specific Ob jectives

: At the end of the unit you will be able to : 

Explain the basic of control system with general block diagram of concept control system.



State the definition and terminology of control system elements.



Classify and differentiate the two categories of control system : open-loop and closed-loop systems.



Draw the block diagram of electrical equipments based on control system types.



List the advantages and disadvantages of open-loop and closed-loop control systems.


INPUT

Control system is a characteristic which influences our lifes today. We use this system in many fields. For example, in industries, domestic, medical, robotics, generation of electrical energy and so on.

1.0

THE BASIC CONCEPT OF CONTROL SYSTEM

Automatic control has played a vital role in the advance of engineering and science. In addition to its extreme importance in space-vehicle system, missile-guidance systems, air-craft-autopiloting systems, robotic systems and the likes, automatic control has become an important and integral part of modern manufacturing and industrial processes. For example, automatic control is essential in the numerical of machine tools in the manufacturing industries. The controlled variable is the quantity or condition that is measured and controlled. The manipulated variable is the quantity or condition that is varied by the controller so as to affect the value of the controlled variable. Normally, the controlled variable is the output of the system. Control means measuring the value of the controlled variable of the system and applying the manipulated variable to thevalue. system to correct or limit deviation of the measured value from a desired In studying control engineering, we first need to define additional terms that are necessary to describe control systems, such as plants,


disturbances, processes, feedback control systems and etc. Then a description of closed-loop and open-loop control systems and their advantages and disadvantages will be given in the following sections.

1.1

IDENTIFYING THE DEFINITION AND TERMINOLOGY RELATED TO CONTROL SYSTEM

The various definitions of the system variables and components are as mentioned below: 1.1.1 Pneumatic Control Systems The working medium in a pneumatic control systems uses a compressible fluid, such as air because it may be exhausted to the atmosphere at the end of the device’s work cycle, thus eliminating the need for return lines. 1.1.2 Hydraulic Control Systems Hydraulic control systems is the study of incompressible liquids, and hydraulic devices use an incompressible fluid, such as oil, for their working medium. Liquid level systems consisting of storage tanks and connecting pipes are a class of hydraulic systems whose driving force is due to relative difference in the liquid heights in the tanks. 1.1.3 Reference Input It is the actual signal input to the control system. 1.1.4 Process Any operation to be controlled. For example, chemical, economic, and biological processes.


1.1.5 Feedback Element It is the unit which provides the means for feeding back to the output quantity in order to compare it with the reference input.

1.1.6 Disturbances A disturbance is a signal that tends to adversely affect the value of the output of a system. If the disturbance is generated within the system, it is called internal, while an external disturbance is generated outside the system and is an input.


Activity 1A

TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…!

1.1

Define the elements given below : a) Controlled variable b) Manipulated variable c) Control

1.2

Define the elements given below : a) b) c) d) e) f)

Reference input Feedback element Disturbances Process Hydraulic Control System Pneumatic Control System


Feedback To Activity 1A

1.1

a)

variable is the quantity or condition that is Controlled measured and controlled. Controlled variable is the output of the system.

b)

Manipulated variable is the quantity or condition there is varied by the controller so as to affect the value of the controlled variable.

c)

Control

means measuring the value of the controlled variable of the system and applying the manipulated variable to the system to value. correct or limit deviation of the measured value from a desired

1.2

a)

Reference Input It is the actual signal input to the control system.

b)

Feedback Element It is the unit which provides the means for feeding back to the output quantity in order to compare it with the reference input.

c)

Disturbances A disturbance is a signal that tends to adversely affect the value of the output of a system. If the disturbance is generated within the system, it is called internal , while an external disturbance is generated outside the system and is an input.


d)

Process Any operation to be controlled. For example, chemical, economic, and biological processes.

e)

Hydraulic Control Systems Hydraulic control systems is the studied of incompressible liquids, and hydraulic device use an incompressible fluid, such as oil, for their working medium. Liquid level systems consisting of storage tanks and connecting pipes are a class of hydraulic systems whose driving force is due to relative difference in the liquid heights in the tanks.

f)

Pneumatic Control Systems The working medium in a pneumatic control systems using a compressible fluid, such as air because it may be exhausted to the atmosphere at the end of the device’s work cycle, thus eliminating the need for return lines.


INPUT

1.2

EXPLANATION OF CONTROL SYSTEM TYPES

Two types of control systems: a) open-loop system b) closed-loop system

A control system may consists of a number of components. In order to show the functions performed by each component, in control engineering, we commonly use a diagram called theblock diagram. A block diagram of a system is a pictorial representation of the functions performed by each component and of the flow of signals. In ablock diagram all system variables are linked to each other through functional blocks. The functional block or simply block is a symbol for the mathematical operation on the input signal to the block that produces the output. Figure 1.1 shows an element of the block diagram. Such arrows are referred to as signals. Transfer Function G(S)

Figure 1.1

Element of a block diagram

(Source : Katsuhiko Ogata (1990), Modern Control Engineering)


The advantages of the block diagram representation of a system lies in the fact that it is easy to form the overall block diagram for the entire system by merely connecting the blocks of the components according to the signal flow and that it is possible to evaluate the contribution of each component to the overall performance of the system. Summing Point Referring to Figure 1.2, a circle with a cross is the symbol that indicates a summing operation. The plus or minus sign at each arrowhead indicates whether that signal is to be added or subtracted.

Figure 1.2

Summing point


Branch point A branch point is a point from which the signal from a block goes concurrently to other blocks or summing points.

Control systems are classified into two general categories: ☺ open-loop system ☺ closed-loop system The distinction is determined by the control action, which is that quantity responsible for activating the system to produce the output.


1.2.1 Open-loop Control System An open-loop control system is one in which the control action is independent of the output. Figure 1.3 shows the block diagram of an open-loop control system (basic system) and Figure 1.4 shows the block diagram of an open-loop control system (automobile driving system). Input

Output

Reference

Variable Controller

Figure 1.3

Process

An open-loop control systems (basic system)

(Source : S.P. Eugene Xarier & Joseph Cyril Babu.J (1999), Principles of Control System)

Output (controlled)

Input (command) Signal

Variable Accelarator pedal, links and carburettor

Engine Vehicle Speed

Force

Figure 1.4

An open-loop control systems (Automobile driving system)

(Source : S.P. Eugene Xarier & Joseph Cyril Babu.J (1999), Principles of Control System)


1.2.2 Closed-loop Control System Closed-loop control systems are more commonly called feedback control systems. Feedback is the characteristic of closed-loop control systems which distinguishes them from open-loop systems. It is the property of closed-loop control systems which permits the output to be compared with the input of the system so that the appropriate control action may be formed as a function of the output and input. In general, feedback is said to exist in a system when closed sequence of cause-and-effect relation exists between system variables.

Error detector

Controlled

Reference Controller Input

Process Output

Controller Feedback path elements

Figure 1.5

General block diagram of an automatic control system



1.2.3 Comparison between open-loop and closed-loop control systems Open-loop Control System The important features of open-loop control systems are : i. Their ability to perform accurately is determined by their calibration, which simply implies, to establish the input-output relation to obtain a desired system accuracy. ii. They are not generally troubled with problems of instability. Closed-loop Control System The important features of feedback are : i. Reduced effects of nonlinearities and distortion ii. Increased accuracy iii. Increased bandwidth iv. Reduced sensitivity of the ratio of the output to input to variations in system characteristics. v.

Tendency towards oscillation or instability.


1.3

EXAMPLES OF APPLICATION CONTROL SYSTEMS TYPES ON ELECTRICAL EQUIPMENTS

Examples of application of control system on electrical equipments : washing machine, toaster, coffeemaker, refrigerator, room lamp and etc.

1.3.1 Open-loop control system 1.

Washing machine Soaking, washing, and rinsing in the washer operate on a time basis. The machine does not measure the output signal, that is, the cleanliness of the clothes.

2.

Electric coffeemaker One possible input for automatic electric coffeemaker is the amount of coffee used. Most coffeemakers have a dial which can be set for weak, medium or strong coffee. This setting usually regulates a timing mechanism. The brewing-time is therefore another possible input. The output of any coffeemaker can be chosen as coffee strength.


1.3.2 Closed-loop System 1.

Automatic toaster Assume that each heating element supplies the same amount of heat to both sides of the bread, and toast quality can be determined by its colour. The toaster is initially calibrated for a desired toast quality by means of the colour adjustment knob. This setting never needs readjustment unless the toast quality criterion changes. When the switch is closed, the bread is toasted until the colour detector sees the desired colour. Then the switch is automatically opened by means of the feedback linkage, which may be electrical or mechanical.

2.

Automatic Refrigerator The input is the reference temperature and the output is the actual refrigerator temperature.


Activity 1B


1.3

Many closed-loop and open-loop control system may be found in homes. Identify the electrical equipment below and describe them of the system is open-loop or closed-loop control systems. a. Electrical oven b. Blender c. Electric automatic kettle d. Iron e. Lamp

1.4

State the differences between open-loop and closed-loop control systems.

1.5

Give the two general categories of control system.


Feedback To Activity 1B

1.3

a. b. c. d. e.

Closed-loop control system Open-loop control system Closed-loop control system Closed-loop control system Open-loop control system

1.4 Open-loop control system i.

Closed-loop control system

Their ability to perform i. accurately is determined by their calibration, which simply

implies, to establish the input-output relation to obtain ii. a desired system accuracy. iii. ii. They are not generally troubled with problems of iv. instability.

v.

1.5 a) Open-loop system b) Closed-loop system

Reduced effects of nonlinearities and distortion Increased accuracy Increased bandwidth Reduced sensitivity of the ratio of the output to input to variations in system characteristics. Tendency towards oscillation or instability.


KEY FACTS 1.

Control system are classified into two gener al categories : open-loop and clos ed-loop s ystems.

2. In control engineering, to show the function performed by each component, we commonly use a diagram called theblock di agra m .


SELF-ASSESSMENT

You are approaching success.Try all the questions in this self-assessment section and check your answers with those given in the Feedback on SelfAssessment given on the next page. If you face any problems, discuss it with your lecturer. Good luck.

Q1-1 Name the major parts of a closed-loop control system. Q1-2 (a) Draw the block diagram of open-loop and closed-loop control systems. (b) List the advantages of the block diagram. (c ) Draw the general block diagram of an automatic control system.


Feedback To Self-Assessment

Have you tried the questions????? If “YES”, check your answers now.

Q1-1 i. Reference input ii. Controller iii. Process iv. Output v. Feedback element

Q1-2 (a)

i. Open-loop control system

Input

Output

Reference

Variable Controller

Process


ii. Closed loop control system

Error detector

Controlled


Process Output


(b) The advantages of the block diagram representation of a system lies in the fact that it is easy to form the overall block diagram for the entire system by merely connecting the blocks of the components according to the signal flow and that it is possible to evaluate the contribution of each component to the overall performance of the system.


(c)

General block diagram of an automatic control system

Error detector

Controlled


Process Output


E3145/2/1 PRINCIPLES OF CONTROLLERS

UNIT2

PRINCIPLES OF CONTROLLERS

OBJECTIVES

General Objective

: To apply the concept of principles of controllers.



Explain the basic concept of principles of controllers.



State the definition of basic controller components.



Draw the schematic circuits for controller action types.



Explain the circuits operations.


INPUT

2.0

EXPLANATION OF PRINCIPLES OF BASIC CONTROLLERS

The main component of controller are : a) Comparator mechanism b) Controller c) Feedback mechanism

Controller is a device which receives input from two points : (i) a value which is sent by transmitter (ii) a value which is set by set point The output from the controller is send to the valve controller. Sensor Output Comparator mechanism

Feedback mechanism

SP Supply

Relay

Figure 2.0 : Block Diagram of controller (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)


Figure 2.0 shows the input controller is a signal which is sent by transmitter. This signal is known as a transmitter signal (MV) and set point. If the output depends on the two inputs functions well and the process is in a stable condition, then the transmitter signal is similar to the set point. The comparator mechanism functions as comparator of both input signals. An error will exist if the input value is not the same. The detector will detect the error signal and determine if there is imbalance between error signal and feedback signals. If there is a difference, the detector will balance both of these signals. The feedback mechanism is a mechanism which balances the system. The feedback signal is always similar to the output signal. The main components of controller are : (i) Comparator mechanism. It consists of two bellows which is for transmitter signal and set point signal. Its function is to differentiate both the input signals. (ii) The controller consists of a flapper and nozzle. Its function is to detect the error signal from the different output and the feedback signal. (iii) The feedback mechanism consists of the feedback bellows. Its function is to balances and stable the system. It also has an effect towards multiple output of a controller.

2.1

EXPLANATION OF BASIC CONTROLLERS COMPONENTS

2.1.1 Bellows The structure of a bellow is shown in Figure 2.1. It consists of a thin metal which is formed into a wave cylinder shape. Air pressure will depress a bellow. When air pressure is increased, bellow will extend and displacement exists. This displacement is linked to the convenient ‘lever’ for give the pressure increase reading. This displacement force include in mechanical force categories.


Unknown pressure

Bellows movement

Figure 2.1 : Bellows (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)

2.1.2 Flapper Nozzle Flapper nozzle is a displacement transducer which the displacement into a differential pressure parameter. Figure 2.2 shows a structure of flapper nozzle. Basically air isisused asfor work liquid. Airofwilldisplacement give a constant time about 0.1s. Flapper nozzle used measuring between load cell. This displacement is very small.


Variable Resistance

Fixed Resistance

x

Ρs Ρ0

Flapper Plat

Measured element

Figure 2.2 : Flapper Nozzle (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)

2.1.3 Restrictor Accuracy of an instrument is guaranteed by manufacturers only for a certain limit. Normally it is stated in the form of a full scale percent of that particular instrument. Deflection from the specification is called restrictor error.


Activity 2A


2.1

2.2

Explain the basic controllers components below: (i) Bellows (ii) Flapper nozzle Draw the diagram of bellow and flapper nozzle.



2.1.

(i) Bellows consists of a thin metal which is formed into a wave cylinder shape. Air pressure will depress a bellow. When air pressure is increased, bellows will extend and displacement exists. This displacement is linked to convenient ‘ lever ’ for give the pressure increase reading. This displacement force include in mechanical force categories. (ii) Flapper nozzle is a displacement transducer which the displacement into a differential pressure parameter. Basically air is used as work liquid. Air will give a constant time about 0.1s. Flapper nozzle is used for measuring of displacement between load cell. This displacement is very small.

2.2

(i)

Bellows

Unknown pressure

Bellows movement


(ii) Flapper nozzle Variable Resistance

Fixed Resistance

Ρs Ρ0

Flapper Plat

Measured element


INPUT

2.2

DESIGN OF SCHEMATIC CIRCUIT FOR CONTROLLER ACTION TYPES

There are three types of controller : a) Proportional controller b) Integral controller c) Derivative controller

2.2.1 Types of Controller There are a few types of controller used to control a process either in a form of Proportional output to the error, Proportional and Integral to the error or Proportional and Derivative output to the first error. Controller can be used in the form of single mode of Proportional, Integral, or Derivative, two mode of Proportional and Integral (P+I) and Proportional and Derivative (P+D), and three mode of Proportional, Integral and Derivative (P+I+D). The figures below show the design of schematic circuit for controller action types.


(i)

Proportional Controller (P) (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)


(iii)

Integral Controller (I) (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)

(iv)

Derivative Controller (D) (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)


(iv) Proportional + Integral Controller (P+I) (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)

(v)

Proportional + Integral + Derivative Controller (P+I+D) (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)


Activity 2B


2.3

List the form of controllers used to control a process.

2.4

Design the schematic circuit for controller action types below. (i) Proportional controller (P) (ii) Integral controller (I) (iii) Derivative controller (D)



2.3

2.4

Controller can be used in the form of (a) Single mode of Proportional, Integral, or Derivative (b) Two mode of Proportional and Integral (P+I) and Proportional Derivative (P+D) (c) Three mode of Proportional, Integral and Derivative (P+I+D).

(i)


(ii)

(iii)


INPUT

2.3

EXPLANATION OF CIRCUITS OPERATION

2.3.1 Proportional Controller (P) This controller can be found in Proportional controller where the output is always proportional to the error ( e ) signal. If the error signal is small, the control action will also be small and if the error signal is high, the control action will also be high. Once the controller detects an error, it will start to act. Output depends on controller gain, kc i.e. controller output = controller gain x error Figure 2.4 (see INPUT 2.2) shows, when measured signal equals to the set point, the system is stable. In other words, if the input process is equal to the output process, a stable system is obtained. If the Proportional controller is used there will be an offset where the measured signal will not reach the set point. Therefore if the control valve has to be 50% opened, we need to open the control valve more than 50% to achieve stability.

2.3.2 Integral Controller (I) Integral controller responses to the integration of error signal to time. So, output is proportional to the area below the curve with time, Controller output

∫t e dt

In Figure 2.6 (see INPUT 2.2), bellows and spring are in the reverse position compared to Proportional controller in Figure 2.5.


2.3.3 Derivative Controller (D) Derivative controller reacts to the rate of change but not to the change of magnitude. Output is proportional to the derivation error signal (e) to time, Controller output

de dt

If error is not changing or fixed there will be no output. Derivative controller is shown in Figure 2.7 (see INPUT 2.2). Derivative controller has one limit which is known as Derivative Limit. This limit distinguishes Proportional Controller and Derivative Controller. In a stable condition the derivative controller does not affect the output and it is always used in the process where temperature is involved. As a conclusion, if we want a fast controller, then the Proportional controller is better but offset will occur. However, if we want to reduce offset, the Derivative controller can be used and we want to eliminate it, then the Integral controller should used. 2.3.4 Two Mode Control System (Proportional and Integral Controller) The Figure 2.8 (see INPUT 2.2) shows a basic concept of a two mode control system. The comparator mechanism (which consists of two bellows) is place on one end of lever while on the other end there are two feedback bellows. A sensor is placed between the feedback mechanism and comparator. The operation of a two mode control system is different from a single mode control system because it combines the action of either both Proportional controller or Integral controller only. Based on Figure 2.8, two things are added to the controller i.e. Integral/ Reset bellows and Integral limit (adjustable). When measured signal is increased, force impedance will come closer to the nozzle and thus will increase output. Increased will make proportional change the position force impedance pressure hence stabilize output pressure.bellow Pressure will drop when it ofpasses through integration unit. This pressure will pass integration bellow and push force impedance closer to the nozzle. So, output pressure can be increased further.


A stable system will be achieved when measured signal is equal to the set point and output pressure will be stable. Thus, offset can be eliminated. If a stable system cannot be achieved, the integration limit can be adjusted. If the integration limit is fully opened, the controller will act as an ON/OFF Controller. If integration limit is fully closed, thecontroller will act as a Proportional controller only. 2.3.5 Three Mode Controller System (P+I+D) Figure 2.9 (see INPUT 2.2), shows three mode controller system. The operation is similar to P+I Controller but with the addition of a derivative limit. For this system, all controllers (Proportional, Integral and Derivative) will affect the responses. So, we need to adjust every controller to suit the process. Adjustments need to be done individually to stabilize process and eliminate offset. To achieve that, integral limit and derivative limit must be adjusted correctly. 2.3.6 Advantages and Disadvantages Controllers have advantages and disadvantages. Table 2.1 below shows the advantages and disadvantages of a single and two mode controller.

CONTROLLER Proportional

ADVANTAGES

DISADVANTAGES

Integral

Faster response load is changing Eliminate offset

Derivative

Reduce offset

Proportional + Derivative

Reduce recovery time and Offset still occurs offset Can eliminate offset Longer recovery time

Proportional + Integral

when Offset exist Longer recovery time No output when no error

Table 2.1 (Source : Mansor Bin Laman (1996), Amalan Bengkel Peralatan)


Activity 2C


2.5

Draw a suitable figure and explain a basic concept of a two mode control system (Proportional and Integral controller)

2.6

Give the advantages and disadvantages of Proportional, Integral, Derivative, Proportional + Derivative and Proportional + Integral.


Feedback To Activity 2c

2.5

Based on Figure 2.12, two things are added to the controller i.e. Integral/ Reset bellows and Integral limit (adjustable). When measured signal is increased, force impedance will come closer to the nozzle and thus will increase output. Increased pressure will make proportional bellow change the position of force impedance hence stabilize output pressure. Pressure will drop when passes integrationcloser unit. to This willoutput pass integration bellowit and pushthrough force impedance the pressure nozzle. So, pressure can be increased further.


A stable system will be achieved when measured signal is equal to the set point and output pressure will be stable. Thus, offset can be eliminated. If a stable system cannot be achieved, the integration limit can be adjusted. If the integration limit is fully opened, the controller will act as an ON/OFF Controller. If integration limit is fully closed, the controller will act as a Proportional controller only.

2.6

Advantages and Disadvantages

CONTROLLER Proportional

ADVANTAGES

Integral

Faster response load is changing Eliminate offset

Derivative

Reduce offset

Proportional Derivative Proportional Integral

DISADVANTAGES when Offset exist Longer recovery time No output when no error

+ Reduce recovery time and Offset still occurs offset + Can eliminate offset Longer recovery time


KEY FACTS 1.

2.

Controller can be used in the form of single mode of Proportional, Integral, or Derivative, two mode of Proportional and Integral (P+I) and Proportional and Derivative (P+D), and three mode of Proportional, Integral and Derivative (P+I+D).

Proportional controller (P) Output depends on controller gain, kc i.e. Controller output = controller gain x error

3.

Integral controller (I) Output is proportional to the area below the curve with time, Controller output

4.

t

∫ e dt

Derivative controller (D) Output is proportional to the derivation error signal (e) to time, Controller output

de dt


SELF-ASSESSMENT


Q2-1 State the definition of restrictor. Q2-2 Design the schematic circuit for controller action types below. (i) P+I (II) P+I+D

Q2-3 (a) State the difference between two mode control system and single mode system. (b) Explain the operation of three mode controller system(P+I+D)



Have you tried the questions????? If “YES”, check your answers now. Q2-1

Accuracy of an instrument is guaranteed by manufacturers only for a certain limit. Normally it is stated in the form of a full scale percent of that particular instrument. Deflection from the specification is called restrictor error.

Q2-2

(i) P+I


(ii) P+I+D

Q2-3 (a)

The operation of two mode control system is different to single mode control system because it combine the action of either both Proportional controller or Integral controller only.

(b)

The operation of P+I+D controller is similar to P+I Controller but with the addition of derivative limit. For this system, all controllers (Proportional, Integral and Derivative) will affect the response. So, we need to adjust every controller to suit the process. Adjustment need to be done individually to stabilize process and eliminate offset. To achieve that, integral limit and derivative limit must be adjusted correctly.


E3145/3/1 PIPING AND INSTRUMENTATION DRAWING (PNID)

UNIT3

PIPING AND INSTRUMENTATION DRAWING (PNID)

OBJECTIVES

General Objective

: To understand and to apply the concept of piping and instrumentation drawing (PNID).


: At the end of the unit you will be able to :  

State the definition of PNID. Discuss the comparison between pneumatic control system and hydraulic control system.



Draw the instruments symbols.



Name the symbols of pneumatic system components and hydraulic system components.


INPUT

3.0

Explanation of PNID

Piping and instrumentation drawing (PNID) includes the components of pneumatic control system and hydraulic control system.

Piping and instrumentation drawing (PNID) includes the components of pneumatic control system and hydraulic control system. Pneumatic control system uses compressible fluid meanwhile the hydraulic control system uses incompressible fluid. The basic components of pneumatic system are : compressor , air tank, air dryer, regulator, directional control valve and actuator. For hydraulic system the components are : pump, motor or cylinder, oil tank and valve. Basically, pneumatic system is widely used in the electronic, food, and automotive industry. Below are the uses of pneumatic system : Transferring of materials Drilling system Material handling (clamping, shifting, positioning, orienting) • • • •

Stamping Packaging Automation Meanwhile, hydraulic system is normally used to operate : • •


• • • • •

Back hoe Bull dozer CNC machine Load loader Die casting machine

The advantages of using pneumatic system and hydraulic system are shown in Table 3.1 : Pneumatic System 1. Air – easy to get (unlimited).

Hydraulic System 1. Flexible – In power transmission , hydraulic power is more flexible compared to pneumatic power.

2. Transmission – air is easy to transfer for a long distance through pipe line.

2. Force gain – a small force can be used to control the large force.

3. Storage – compressed air can be stored in air storage tank and can be released if not needed.

3. Component – Does not need a lot of moving mechanism.

4. Temperature – compressed air is not sensitive to temperature

4. Compact – hydraulic motor size is smaller compared to electric

reactions that can cause burning. 5. Clean – air leakage does not cause environmental pollution.

motor. 5. Economy – hydraulic system is better and more profit.

6. Component – pneumatic system is easier to maintain and cheaper. 7. Speed – it can work faster than hydraulic system. 8. It responses very fast to the start and stop commands from the controller. 9. Air does not need a back flow. Table 3.1 : Advantages between pneumatic system and hydraulic system (Source : Jubaidi Bin Razali, Pneumatik & Hidraulik)


3.1 IDENTIFYING INSTRUMENTS SYMBOLS

3.1.1 Symbols of pneumatic component The symbols of pneumatic components found in a pneumatic system are shown below :

(Source : Jubaidi Bin Razali, Pneumatik & Hidraulik)










3.1.2 Symbols of hydraulic component The symbols of hydraulic components found in a hydraulic system are shown below :













Activity 3

TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…! 3.1

Explain what is meant by Piping and Instrumentation Drawing (PNID)

3.2

State the basic components of pneumatic system and hydraulic system.

3.3

State 5 components of pneumatic system and hydraulic system.

3.4

Give 3 industries that use pneumatic system.


Feedback To Activity 3

3.1

Piping and instrumentation drawing (PNID) includes the components of pneumatic control system and hydraulic control system. Pneumatic control system uses a compressible fluid while the hydraulic control system uses incompressible fluid.

3.2

The basic components of pneumatic system are : compressor , air tank, air dryer, regulator, directional control valve and actuator. The basic components of hydraulic system are : tank, filter, pump, valve, motor and cylinder.

3.3

Pneumatic system components a. Pneumatic compressor b. Pneumatic cylinder (single acting) c. Pneumatic cylinder (double acting) d. Valve 2/2 e. Flow controller valve Hydraulic system components a. Fixed displacement hydraulic pump b. Double acting cylinder c. Differential cylinder d. Pneumatic motor e. Direction controller valve 2/2 type

3.4

a. b. c.

Food industry Automotive industry Electronic industry


KEY FACTS

1.

Piping and instrumentation drawing (PNID) includes : components of pneumatic control system components of hydraulic control system

• •

2.

The basic components of p neumatic system are : compressor air tank air dryer • • • • • •

3.

regulator control valve directional actuator

The basic components of hydraulic system are : pump motor or cylinder oil tank valve. • • • •


SELF-ASSESSMENT


Q3-1 Define the word ‘PNEUMATIC’ and explain how this system functions. Q3-2 State the advantages between pneumatic system and hydraulic system. Q3-3 State 5 advantages of pneumatic system. Q3-4 Draw the symbols of the pneumatic components given below in the space provided.

COMPONENT

DESCRIPTION

Pneumatic compressor

Fixed displacement

Pneumatic cylinder (single acting)

Non-return spring Spring return

SYMBOLS


One rod Pneumatic cylinder (double acting) Two rod

Closed loop double port 2/2 valve Open loop double port




Q3-1

The word ‘Pneu’ is from Greece which means wind, ‘matic’ refers to power. Therefore pneumatic system means a system which is operated by wind. The pneumatic system uses compressed air as a power transfer medium. The compressed air is obtained from the environment. Then it is compressed using electric motor.

Q3-2 Pneumatic System 1. Air – easy to get (unlimited).

Hydraulic System 1. Flexible – In power transmission , hydraulic power is more flexible compared to pneumatic power.

2. Transmission – air is easy to transfer for a long distance through pipe line.

2. Force gain – a small force can be used to control the large force.

3. stored Storagein–aircompressed air and cancan be storage tank be released if not needed.

3. Component – Does not need a lot of moving mechanism.


4. Temperature – compressed air is not sensitive to temperature reactions that can cause burning.

4. Compact – hydraulic motor size is smaller compared to electric motor.

5. Clean – air leakage does not cause environmental pollution.

5. Economy – hydraulic system is better and more profit.

6. Component – pneumatic system is easier to maintain and cheaper. 7. hydraulic Speed – system. it can work faster than 8. It responses very fast to the start and stop commands from the controller. 9. Air does not need a back flow.

Q3-3

(Any five answers from this list are accepted) 1. Air – easy to get unlimited. 2. line. Transmission – air is easy to transfer for a long distance through pipe 3. Storage – compressed air can be stored in air storage tank and can be released if not needed. 4. Temperature – compressed air reactions that can cause burning.

is not sensitive to temperature

5. Clean – air leakage does not cause environmental pollution. 6. Component – pneumatic system is easier to maintain and cheaper. 7. Speed – it can work faster than hydraulic system 8. It responses very fast to the start and stop commands from the controller. 9. Air does not need a back flow.


Q3-4


E3145/4/1 INTRODUCTION TO RELAY AND CONTACTOR

UNIT4

INTRODUCTION TO RELAY AND CONTACTOR

OBJECTIVES

General Objective

: To know and to apply the concept of relay and contactor.



State the definition of relay.



Draw the symbol and diagram of relay .



Explain the type of relays.



State the definition of contactor.



Draw the symbol and diagram of contactor .



Compare between relay and contactor.


INPUT

4.0

EXPLANATION OF RELAY AND CONTACTOR The representation of relays and contactor in the electrical circuit diagram is identical, as is their operating principle.

4.1

i.

Relays are used to switch relatively small output and currents;

ii.

Contactors to switch relatively large output and currents.

DEFINITION OF RELAY

A relay is an electromagnetic switch. A small current flowing through a coil in the relay creates a magnetic field that pulls one switch contact against or away from another.

Relays are electromagnetically actuated switches. They consist of a housing with electromagnet and movable contacts. An


electromagnetic field is created when a voltage is applied to the coil of the electromagnet. This results in attraction of the movable armature

to the coil core. The armature actuates the contact assembly. The contact assembly can open or close a specific number of contacts by mechanical means. If the flow of current through the coil is interrupted, a spring returns the armature to its srcinal position. Relay can be used for various regulating, control and monitoring functions: i. as interfaces between control circuits and load circuits, ii. for signal multiplication, iii. for separation of direct current and alternating current circuits, iv. for delaying, generating and converting signals and v. for linking information.

4.2

THE SYMBOL AND DIAGRAM OF RELAY

A2

coil

A1

2 1 4

Figure 4.1: Symbol of Relay (Type SPDT-Single Pole Double Throw) (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


A2

A1

coil

2 1

4 6

5 8

Figure 4.2: Symbol of Relay (Type DPDT-Double Pole Double Throw) (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


Functions of Relays Numbers

Number of Relays

Description

1

2

Normally closed contact

3

4

Normally open contact

5

6

Normally closed contact, time delay

7

8

Normally open contact, time delay

1

2

4

5

6

8

A1

A2

Changeover contact Changeover contact, time delay The coil terminals (common)

Table 4.1 : Functions of Relays Numbers (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


Figure 4.3 : Diagram of relay (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)

4.3 TYPES OF RELAYS Relay contacts are either normally open (NO) or normally closed (NC), The term “normally” refers to the state in which the coil is not energized. Relays can have many independent contacts, some NO and others NC, and each contact can be used in a different circuit for a different task. When the coil is energized, all NO contacts belonging to that relay close, whereas all NC contacts open. In most relays with multiple contacts, these are arranged in the double-throw (also called the “changeover” or “transfer”) configuration, as


shown in figure 4.1 and 4.2 above, where an NO and NC contact have a common pole. Such relays are designated as:

i.

SPDT (Single Pole Double Throw) refer to symbol figure 4.1

ii.

DPDT (Double Pole Double Throw) refer to symbol figure 4.2 The word pole refers to the number of sets of contacts and the word throw refers to the number of positions or combinations ( open or close ) the contacts can have. Refer to the two types of relays above (Figure 4.1), single pole (SP) is a single contact (common) where a normally open (NO) and normally closed (NC) relay have a common pole. While a double pole (DP) means that each set of contacts has a common terminal ( 1 and 5 ) connected to both an open and a closed set of contacts (Figure 4.2). When the coil is energized, the circuit between common and NO is closed, and when the coil is deenergized the circuit between common and NC is closed.


Activity 4A


4.1

Explain the definition of relay.

4.2

Draw the symbol of relay.



4.1

A relay is an electromagnetic switch. A small current flowing through a coil in the relay creates a magnetic field that pulls one switch contact against or away from another.

4.2 A2

coil

A1

2 1 4

Symbol of Relay (Type SPDT-Single Pole Double Throw)


A2

A1

coil

2 1

4 6

5 8

Symbol of Relay (Type DPDT-Double Pole Double Throw)


INPUT

4.4

EXPLANATION OF CONTACTOR Contactors work on the same basic principle as relays. The typical features of contactor are: i. double- break ( 2 break points per contact), ii. positive-action contacts and iii. closed arcing chambers (spark arresting chambers). A contactor possesses several contact elements, normally between 4 and 10. There are also different types of contactors with various combinations of normally closed contacts, normally open contacts, changeover contacts, delayed normally closed contacts etc. The contacts are divided into main contact elements and auxiliary contacts (control contacts) i. Outputs of 4 – 30kW are switched via main contact elements. ii. The auxiliary contacts can be used to simultaneously switch further control functions or logic operations. iii. Contactors which only switch auxiliary contacts (control contacts) are called contactor relays (control contactors). iv. For the purpose of classification, contactors with main contact elements for power switching are called power contactors (main contactors).


4.5

THE SYMBOL AND DIAGRAM OF CONTACTOR

14

13

Figure 4.4 : Symbol of Contactor. (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


Figure 4.5 : Diagram of Contactor (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


4.6

COMPARISON BETWEEN RELAY AND CONTACTOR

Relay

Contactor

Relays possess a clapper-type Contactors possess a lifting armature and are armature and are characterized characterized by single contact by double contact separation. separation Relays are used to switch Contactor are used to switch relatively small outputs and relatively large outputs and currents. currents. Table 4.2 : Comparison between Relay and Contactor (Source : FESTO DIDACTIC, Electro-hydraulics – Learning System for Automation & Communication)


Activity 4B


4.3

Draw the symbol of contactor.

4.4

State the typical features of contactor.



4.3

14

13

Figure : Symbol of Contactor

4.4

The typical features of contactor are: i. double- break ( 2 break points per contact), ii. positive-action contacts and iii. closed arcing chambers (spark arresting chambers).


KEY FACTS 1. (i) Relays possess a clapper-type armature and are characterized by single contact separation. (ii)

Relays are used to switch relatively small outputs and currents.

2. (i) Contactors possess a lifting armature and are characterized by double contact separation. (ii) Contactors are used to switch relatively large outputs and currents


SELF-ASSESSMENT


Q4-1

Q4-2

(a)

Identify the application of relay.

(b)

Draw the diagram of relay.

(c)

Explain the function of normally open (NO) and normally closed (NC) relay contacts.

(d)

State the strengths and weaknesses of relay.

(a)

Give the definition of coil in contactor.

(b)

Identify the comparison between relay and contactor.



Have you tried the questions????? If “YES”, check your answers now. Q4-1

(a) Relay can be used for various regulating, control and monitoring functions: i. as interfaces between control circuits and load circuits, ii. for signal multiplication, iii. for separation of direct current and alternating current circuits, iv. for delaying, generating andconverting signals and for linking information. (b)


Diagram of relay

Q4-3

Relay contacts are either normally open (NO) or normally closed (NC), The term “normally” refers to the state in which the coil is not energized. Relays can have many independent contacts, NOcircuit and others NC, and eachWhen contact used in a some different for a different task. the can coil isbe energized, all NO contacts belonging to that relay close, whereas all NC contacts open.

Q4-4

Strengths Easy to change out Durable

Easy to test Available with plug-in base Miniature relays available

Weaknesses Contact wear Moving parts (springs) limit live expectancy from 1-3 million cycles Require more power


Immune to noise The strengths and weaknesses of Relay

Q4-5

The coil is manufactured in a rectangular shape with two square holes in it. This holes provide a space for the magnet yoke to pro-armature move to the closed position.

Q4-6

Relay

Contactor

Relays possess a clapper-type Contactors possess a lifting armature and are armature and are characterized characterized by single contact by double contact separation. separation Relays are used to switch Contactors are used to switch relatively small outputs and relatively large outputs and currents. currents. Comparison between Relay and Contactor





.






E3145/5/1 INTRODUCTION TO PLC

UNIT5

INTRODUCTION TO PLC

OBJECTIVES

General Objective

: To apply and integrate the concept of PLC



Identify the PLC terminology



Explain the PLC historical background



Describe the functions of PLC



Explain the advantages of PLC



Draw the PLC block diagram including processor unit, memory, the power supply unit, input and output interface and the programming device





Explain draw the TIM, logicCNT function LD, OR, AND, AND NOT, LDand NOT, OUT, Design and develop ladder program


INPUT

5.0

EXPLANATION OF PLC

Do you have a motorcycle? If the answer is yes, explain to your students of the PLC system which is used in the traffic light.

In today’s fast-moving, highly competitive industrial world, a company must be flexible, cost-effective and efficient if it wishes to survive. In the process and manufacturing industries, this has resulted in a great demand for industrial control systems in order to streamline operations in terms of speed, reliability and product output. Control systems such as hard-wire relay, logic and computer systems, can and do provide effective control of industrial processes and plant. However, each of this systems has limitations or disadvantages that may often be overcome through the use of a Programmable Logic Controller (PLC). What is a Programmable Logic Controller? A PLC is a digital electronics system which uses a programmable memory for implementing specific functions such as logic, sequencing, timing, counting andvarious arithmetic analog or digital input/output modules, typestoof control machinesthrough or processes.


5.1

PLC TERMINOLOGY In general, a control systems is a collection of electronic devices and equipment which are in place to ensure the stability, accuracy and smooth transition of a process or a manufacturing activity. It takes any form and varies in scale of implementation, from a power plant to a semiconductor machine. As a result of rapid advancement of technology, complicated control tasks accomplished with a highly automated control system, which may be in the form of Programmable Controller (PLC) and possibly a host computer , etc. Besides signal interfacing to the field device (such as operator panel, motors, sensors, switches, solenoid valves and etc.), capabilities in network communication enable a big scale implementation and process coordination besides providing greater flexibility in realizing distributed control system. Every single component in a control system plays an important role regardless of size. For instance, as shown in Figure 5.1 the PLC would not know the happenings around it without any sensing devices. It is also unable to activate any moving mechanism if there is no motor installed. And if necessary, an area host computer has to be in place to coordinate the activities in a specific area at the shop floor.

(Source : Manual OMRON (1999), Beginner Guide To PLC)

Figure 5.1 : It could also be an application as small as single PLC controlling a single or some output service


5.2

PLC HISTORICAL BACKGROUND PLCs highly desireable in a wide variety of industrialplant and process-control application.

PLCs were used mainly in the motor industries in the early 1970s where they replaced large relay panels. Not only do PLCs take up much lesser space than the relay system, they are also more reliable in operation over longer periods. One important point to take note is that PLCs are very flexible in terms of modifying or changing the control sequences. It is now possible to change or modify the control system without having to connect or disconnect a single wire. It is simply done by changing the program (software), using a program console or graphic programming panel attached to the programmer logic controller. Industry demands on PLCs are increasing rapidly and this has encouraged manufacturers to develop whole families of microprocessorsbased systems having various level of performance. Available PLCs now range from small self-contained units to sophisticated modular systems with a range of add-on function modules for tasks such as analog input/output and communications. This modular system allows the expansion or upgrading of a control system with minimum costs and interruption. In 1968, a group of engineers from General Motors developed the concept of PLC with an initial specification. The PLC must be : 1) Easy to program and reprogram 2) Easy to maintain and repair 3) More reliable in an industrial environment 4) Smaller in size than its relay equivalent 5) Cost-competitive


5.2.1 Developments of PLC

YEARS 1968 1969

1974

1976 1977 1980 1983 1985 onwards Table 5.1

DESCRIPTION The concept of PLC was developed A hardware CPU controller was used with logic instructions. It comes with 1K of memory and 128 I/O points Using several processors within a PLC with add-on timers and counters functions. Arithmetic operations are also included. This PLC has 12K of memory and 1024 I/O points Remote I/O systems were introduced. Microprocessor-based PLC was introduced Intelligent I/O modules were developed Small low-cost PLCs were introduced With networking capabilities PLC historical background

(Source : Manual SMC International Training (1999), Introduction to PLC Controller)


Activity 5A

TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…! PART 1 Questions 1 to 5 have four options: A, B, C or D. Choose the correct answer from the options given. 5.1 The term PLC stands for : A Personal Logic Computer B Programmable Local Computer C Personal Logic Controller D Programmable Logic Controller 5.2 Which of the following is most likely to be the voltage level used internally in a PLC, excluding the voltage levels that might occur during conditioning in output/input channels: A 5V B 24V C 110V D 240V 5.3 The cycle time of a PLC is the time it takes to: A Read an input signal B Read all the input signals C Check all the input signals against the program D Read all the inputs, run the program and update all outputs


PART 2 5.4

What is a Programmable Logic Controller (PLC)



PART 1 5.1 5.2 5.3

D A D

PART 2 5.4

A PLC is a digital electronics system which uses a programmable memory for implementing specific functions such as logic, sequencing, timing, counting and arithmetic to control through analog or digital input/output modules, various types of machines or processes.


INPUT

5.3

FUNCTIONS OF PLC PLCs are made to operate for long periods of time in adverse industrial environment. For example, temperature, humidity etc.

PLCs are used in many “real world” applications. If there are industries present, chance are good that there is a PLC present. If you are involved in machining, packaging, material handling, automated assembly or countless other industries you are probably already using them. If you are not, you are wasting money and time. Almost any application that needs some type of electrical control has a need for a PLC. For example, let’s assume that when a switch turns on we want to turn a solenoid on for 5 seconds and then turn it off regardless of how long the switch is on for. We can do this with a simple external timer. But what if the process included 10 switches and solenoids? We would need 10 external timers. What if the process also needed to count how many times the switches individually turned on? Thus we need a lot of external counters.


As you can see the more bigger process you need, we have a PLC. We can simply program the PLC to count its inputs and turn the solenoids for the specified time. There are so many applications where PLCs are used in the various industries. Below is the list of applications : i. conveyor system ii. swimming pool iii. traffic light system iv. lift control system v. food processing vi. pick and place robot control vii. packaging machine viii. security control system ix. car manufacturing plant x. printing industries xi. air condition control xii. cement manufacturing

5.4

ADVANTAGES OF PLC

The following are the major advantages that can be distinguishably realized : i. ii. iii. iv.

The wiring of the system usually reduces by 80% compared to conventional relay control system. The power consumption is greatly reduced as PLC consumes much less power The PLC self diagnostic functions enable easy and fast trouble shooting of the sequence system or application can easily be Modification of control done by programming through the console or computer


v. vi.

vii.

viii. ix.

software without changing of I/O wiring, if no additional Input or Output devices are required. In PLC system spare parts for relay and hardware timers are greatly reduced as compared to conventional control panel. The machine cycle time is improved tremendously due to the speed of PLC operation is a matter of milliseconds. Thus, productivity increases. It cost much less compared to conventional system in situations when the number of I/Os is very large and control functions are complex. The reliability of the PLC is higher than the mechanical relays and timers. An immediate print out of the PLC program can be done in minutes. Therefore, hardcopy of documentation can be easily maintained.


Activity 5B


5.5

State five (5) applications of PLC.

5.6

State the five (5) advantages of PLC.



5.5

a) b) c) d) e)

Conveyor system Swimming pool Traffic light system Lift control system Food processing

5.6 (i)

The wiring of the system usually reduces by 80% compared to conventional relay control system. (ii) The power consumption is greatly reduced as PLC consumes much less power (iii) The PLC self diagnostic functions enable easy and fast trouble shooting of the system (iv) Modification of control sequence or application can easily be done by programming through the console or computer software without changing of I/O wiring, if no additional Input or Output devices are required. (v) In PLC system spare parts for relay and hardware timers are greatly reduced as compared to conventional control panel. (vi) The machine cycle time is improved tremendously due to the speed of PLC operation is a matter of milliseconds. Thus, productivity increases. (vii) It cost much less compared to conventional system in situations when the number of I/Os is very large and control functions are complex. (viii) The reliability of the PLC is higher than the mechanical relays and timers.


INPUT

5.5

PLC BLOCK DIAGRAM Typically a PLC system has five basic components. These are the processor unit, memory, the power supply unit, input/output interface section and the programming device. Figure 5.2 shows the basic arrangement.

Figure 5.2

Block Diagram of PLC

(Source : Manual OMRON (1999), Beginner Guide To PLC)


1.

The processor unit or Centr al Process ing Unit (CPU) is the unit containing the microprocessor. This unit interprets the input signals and carries out the control actions, according to the program stored in its memory and communicating the decisions

2.

as signals to the Theaction power supply unitoutputs. is needed to convert the mains a.c voltage to the low d.c voltage (5V) necessary for the processor and the circuits in the input and output interface modules. The programming device is used to enter the required program into the memory of the processor. The program is developed in the device and then transferred to the memory unit of the PLC. The memory unit is where the program is stored, that is to be used for the control actions to be exercised by the microprocessor. Ladder program, Timer and Counter Values are stored in the user memory. Depending on user’s need, various types of memory are available for choice : Read-Only Memory (ROM), Random Access Memory (RAM), Erasable Programmable Read Only Memory (EPROM) and Electrically Erasable Programmable Read-Only Memory (EEPROM). The input and output sections are where the processor receives information from external devices and communicates information to external devices

3.

4.

5.

In addition, PLCs consists of three functional areas : processing, memory and input/output.


PLC BASIC INSTRUCTIONS The most important from any PLC programming language is that it is easily understood and used in a control system.

A very commonly used method of programming PLCs is based on the use of the ladder diagrams. Writing a program is then equivalent 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. In drawing a ladder diagram, certain conventions are adopted: 1. The vertical lines of the diagram represent the powerrails between which circuits are connected. 2. Each rung on the ladder defines one operation in the control process. 3. A ladder diagram is read from left to right and from top to bottom, Figure 5.3 shows the scanning motion employed by the PLC. The top rung is read from left to right. Then the second rung down is read from left to right and so on. When the PLC is in its run mode, it goes through the entire ladder program to the end, the end rung of program being clearly denoted, and then promptly resumes at the start. This procedure of going through all the rungs of the program is termed a cycle .


Figure 5.3

The rung ladder


4. Each rung must start with an input or inputs and must end with at least one output. The term input is used for a control action, such as closing the contacts of a switch, used as an input to the PLC. The term output is for a devices device connected thetheir output of a PLC, e.g. a motor. 5. used Electrical are shownto in normal condition. Thus a switch which is normally open until some object closes it, is shown as open on the ladder diagram. A switch that is normally closed is shown closed. 6. A particular device can appear in more than one rung of a ladder. For example, we might have a relay which switches on one or more devices. The same letters and/or numbers are used to label the device in each situation. 7. The inputs and outputs are all identified by their addresses, the notation used depending on the PLC manufacturer. This is the address of the input or output in the memory of the PLC. The OMRON series of PLCs precedes input elements by an 00 and output elements by an 01 and uses the following numbers : Inputs 00000 - 00011 (12 possible inputs) Outputs 01000 - 01007 ( 8 possible outputs) Meanwhile 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 , 500 - 507, 510 - 513 (24 possible inputs)

Outputs

Y430 - 437, 530 - 537 (16 possible outputs)

Ladder Diagrams’ Explanation Ladder diagram uses standard symbols to represent the circuit components and functions found in a control system. Ladder symbols

Input, normally-open contact

Input, normally-closed contact

Inputs in series connections

Inputs in parallel connections


Outputs device

Figure 5.4 : Ladder Symbols (Source : Manual SMC International Training (1999), Introduction to PLC Controller)

Logic Instructions (Mnemonic) The instruction set consists of logic instructions also known as mnemonics that represent the actions to be performed within a given PLC. Each program instruction consists of two parts : a mnemonic operation component also known as opcode and an address or data component that identifies a particular element (e.g output) within the PLC. Table 5.2 below is an example of a mnemonic code. Address 00000 00001 00002

Instructions LD OUT END(01) Table 5.2

Data 00000 01000

Mnemonic Code


Here the instruction refers to output (01) number 0.


Input/Output (I/O) Assignment These instructions are used to program logic circuits in ladder diagram form, by assigning all physical inputs and outputs with an operand (address) suitable to the PLC being used. The I/O assignment used differ between manufacturers but certain common terms exist. Logic Instructions and Graphic Programming Logic instructions are used as the basic programming language for PLCs. Although logic instructions are easy to earn and use, it can be very time – consuming to check and relate a large coded program to the actual circuit function. Furthermore, logic instruction tends to vary between different types of PLC. A factory or plant may use a range of different PLCs, in which confusion can result over differences in the instruction sets.

Name/Mnemonic

Symbol

Description Creates a normally open

AND (AND)

condition as the first condition off the bus bar. All instruction lines begin with either LOAD or LOAD NOT. Creates a normally closed condition as the first condition off the bus bar. All instruction lines begin with either LOAD or LOAD NOT. Combines a normally open condition in series with a previous condition.

AND NOT (AND NOT)

Combines a innormally closed condition series with a previous condition.

LOAD (LD)

LOAD NOT (LD NOT)


OR (OR)

Combines a normally open condition in parallel with a previous condition.

OR NOT (OR NOT)

Combines a normally closed condition in parallel with a previous condition.

AND LOAD (AND LOAD)

Combines two group of conditions in series. These groups are called blocks.

OR LOAD (OR LOAD)

Combines two parallel groups of conditions. These group are called block.

Specifies an output bit that is to be turned ON for an ON execution condition and OFF for an OFF condition.

OUTPUT (OUT)

OUTPUT NOT (OUT NOT)

Specifies an output bit that is to be turned OFF for an ON execution and ON for an OFF condition.

TIMER

Creates a 0-1 s decrementing timer that starts from the set value

(TIM)

TIM

(SV) whenturns the execution condition ON.


COUNTER (CNT)

CP

CNT R

NO OPERATION (NOP)

None

Table 5.3

Counts down the number of times the input conditions turns ON. Each time the input condition turns ON, the present value (PV) is reduced by 1 and when the count reaches 0, the Completion Flag (accessed through the counter number) turns ON. Does nothing. Can be inserted into a program when modification are made that would otherwise change program address.

Basic Instructions


5.7

DESIGN AND WRITE PROGRAM LADDER

Examples of Logic Function (Source : Manual SMC International Training (1999), Introduction to PLC Controller)

1.

00000

AND function

00001 00002 01000

ADDRESS

00000 00001 00002 00003

INSTRUCTIONS

LD AND AND OUT

DATA

00000 00001 00002 01000


2.

OR function ADDRESS

00001 01001 00002

00000 00001 00002 00003

INSTRUCTIONS

LD OR OR OUT

DATA

00001 00002 00003 01001

00003

3.

LOAD and LOAD NOT function

ADDRESS

00000 01000

00001 01001

4.

DATA

LD OUT

00000 01000

00002 00003

LD NOT OUT

00001 01001

AND and AND NOT function ADDRESS

00000

INSTRUCTIONS

00000 00001

00001

00002 01002

00000 00001 00002 00003

INSTRUCTIONS

LD AND NOT AND OUT

DATA

00000 00001 00002 01002


5.

OR and OR NOT function

ADDRESS

00000 01003

00001

00000 00001 00002 00003

INSTRUCTIONS

LD NOT OR NOT OR OUT

DATA

00000 00001 00002 01003

00002

6. 00000

AND and OR function 00001

00003

01004 00002

7.

ADDRESS

00000 00001 00002 00003 00004

INSTRUCTIONS

LD AND OR AND OUT

DATA

00000 00001 00002 00003 01004

END function

00000

ADDRESS

00001 01005

END

INSTRUCTIONS

DATA

00000

LD

00000

00001 00002 00003

AND NOT OUT END (01)

00001 01005


Activity 5C

TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT INPUT…! PART 1 5.7

Decide whether each of these statements is True (T) or False (F). Figure shows a ladder diagram rung for which: (i) The input contacts are normally open (ii) There is an output when there is an input to the contacts A B C D

(i) T (ii) T (i) T (ii) F (i) F (ii) T (i) F (ii) T

PART 2 5.8

Draw a block diagram showing in very general terms the main units in a PLC.

5.9

State five (5) advantages of PLC.

5.10

What is the address of the input or output in the memory of the PLC manufacturer below : (i) OMRON series (ii) MITSUBISHI F series


5.11 Draw the ladder symbols to represent the circuit components and function in a control system such as : (i) (ii) (iii) (iv) (v)

Input, normally -open contact Input, normally – closed contact Inputs in series connections Inputs in parallel connections Output devices


Feedback To Activity 5C

PART 1 5.7

A

PART 2 5.8

Block diagram of PLC


5.9

i. ii. iii. iv.

v.

5.10

(i)

The wiring of the system usually reduces by 80% compared to conventional relay control system. The power consumption is greatly reduced as PLC consume much less power The PLC self diagnostic functions enable easy and fast trouble shooting of the system Modification of control sequence or application can easily be done by programming through the console or computer software without changing of I/O wiring, if no additional Input or Output devices are required. In PLC system spare parts for relay and hardware timers are greatly reduced as compared to conventional control panel.

OMRON series Inputs Outputs

00000 - 00011 (12 possible inputs) 01000 - 01007 ( 8 possible outputs)

(ii) MITSUBISHI F series Inputs X400 - 407 , 410 - 413 , 500 - 507, 510 - 513 (24 possible inputs) Outputs Y430 - 437, 530 - 537 (16 possible outputs)


5.11

Ladder symbols

a) Input, normally-open contact

b) Input, normally-closed contact

c) Inputs in series connections

d) Inputs in parallel connections

e) Outputs device


KEY FACTS 1.

PLC stands for PROGRAMMABLE LOGIC CONTROL.

2.

PLC system has five basic components

: processor unit, memory, the power supply unit, input/output interface section and the programming device.


SELF-ASSESSMENT

You are approaching success.Try all the questions in this self-assessment section and check your answers with those given in the Feedback on SelfAssessment given on the next page. If you face any problems, discuss it with your lecturer. Good luck. Q5-1

What is the characteristic of a PLC ?

Q5-2

Why do we need a PLC ?

Q5-3 (a) Draw the logic instructions below: (i) AND NOT (ii) TIM (iii) (iv) (v) (vi)

OUTPUT OR OR NOT LOAD NOT

(b) Draw the ladder rungs to represent: Two switches which are normally open and both have to be closed for a motor to operate. (c) Convert the ladder diagrams given below to its equivalent mnemonic codes. 00000

00001

00002

00003 01000

00004

00005


Feedback To S elf-Assessment


Q5-1

The PLC must be : a) Easy to program and reprogram b) Easy to maintain and repair c) More reliable in an industrial environment d) Smaller in size than its relay equivalent e) Cost-competitive

Q5-2

PLC are used in bigger processes because we can simply program the PLC to count its inputs and turn the solenoids for the specified time.

Q5-3 (a)

i.

ii.

iii.

TIM


iv.

v.

vi.

vii.

(b)


(c) Address 00000 00001 00002 00003 00004 00005 00006 00007 00008

Instruction LD AND NOT LD AND OR OR AND LD OUT END(01)

Data 01000 01001 00002 00003 00004 00005 --01000

E3145/6/1 THE TRANSFER FUNCTION

UNIT6

THE TRANSFER FUNCTION

OBJECTIVES

General Objective

: To understand and interpret the concept of transfer function.


: At the end of the unit you will be able to :  

State the definition of transfer function. Identify the transfer function from a simple electric circuit.



Solve the transfer function from block diagram of openloop control system and closed-loop control system.



Reduce a block diagram of multiple subsystem to a single block representing the transfer function from input to output.



Rewrite the reduction method of block diagram.


INPUT

6.0

EXPLANATION OF THE TRANSFER FUNCTION

In this unit we discuss how to find a mathematical model, called a Transfer Function, for linear, time-invariant electrical, mechanical and electromechanical systems. The transfer functions is define as G(s) = C(s)/R(s), or the ratio of the Laplace transform of the output to the Laplace Transform of the input. This relationship is algebraic and also adapts itself to modeling interconnected subsystems. We realize that the physical world consists of more systems than what we have illustrated in this unit. For example, we could apply transfer function modeling to electrical systems. Of course, we must assume these systems to be linear, or make linear approximations, in order to use this modeling technique.

6.1

DEFINITION OF TRANSFER FUNCTION

The “transfer function” of a system is : The ratio of Laplace Transform of the output variable to the Lap lace Transform of the input variable with all the initial conditions zero.


Whenever a system is perturbed by some input signal all, of the dependent variables in the system vary as a result.The “transfer function” of a system is the ratio of Laplace Transform of the output variable to the Laplace Transform of the input variable with all the initial conditions zero. When a physical system is analysed, a mathematical model is developed by writing differential equations with the help of various physical laws governing the system. The steps involved in obtaining the transfer function are as follows : (i) Write the differential equations governing the system. (ii) Laplace Transform the equations i.e, to replace the terms involving d/dt by s and ∫ dt by 1/s . (iii) Obtain the ratio of Transformed output to input variables.

6.2

DERIVATION OF TRANSFER FUNCTION FROM THE EASIER ELECTRIC CIRCUIT

There are assumptions made while deriving Transfer Function of electrical systems. (i) When a device is a part of a larger system, it should not load the source which provides it input signal, i.e., ideally the source should have zero (or low) internal impedance. (ii) The output of the device should not be loaded by the component that receives its output signal. The systems is approximated by linear lumped parameters model with suitable assumptions The loading effects occur with electrical, mechanical, electromechanical and fluid devices and should be taken into account while deriving transfer functions.


Let us now implement the procedure of the deriving the transfer functions through various examples to follow :

Example 6.1 : Obtain the transfer function of the circuit shown in Figure 6.1

R

L

vi(t)

C

vo(t)

Figure 6.1 : An RLC electrical circuit (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Assume the current response i (t) due to a change in applied voltagev (t) is required. Application of Kirchhoff’s voltage law around the circuit gives vi(t )

=

vo(t ) =

Ri (t ) + L

1 C

di dt

+

1 C

∫ idt

(6.2.1)

∫ idt

(6.2.2)

Laplace Transforming equations (6.2.1) and (6.2.2) we have, 1 Vi( s )

=

RI ( s ) + LsI ( s ) +

Cs

I ( s)

(6.2.3)

E3145/6/5 THE TRANSFER FUNCTION 1

=

Vo( s )

Cs

(6.2.4)

I ( s)

Hence we have from equations (6.2.3) and (6.2.4), Vo( s ) Vi ( s )

=

1 2

Cs L + CsR + 1

Example 6.2 : Derive the transfer function of the circuit shown in Figure 6.2

R

vi(t)

C

vo(t)

Figure 6.2 : An RC electrical circuit (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Writing the differential equations with the help of Kirchhoff’s voltage law vi(t )

=

vo(t )

=

Ri (t ) +

1 C

1 C

∫ idt

∫ idt

(6.2.5)

(6.2.6)

Laplace Transforming equations (6.2.5) and (6.2.6) we have, Vi( s )

=

RI ( s ) +

1 I ( s)

Cs

(6.2.7)

E3145/6/6 THE TRANSFER FUNCTION Vo( s )

=

1 Cs

I ( s)

Hence we have from equations (6.2.7) and (6.2.8), Vo( s ) Vi ( s )

=

1 1 + sRC

(6.2.8)


Activity 6A


6.1

Define the transfer function.

6.2

For the network given, what is the transfer function? C

R vi(t)

vo(t)



6.1

6.2

The “transfer function” of a system is theratio of Laplace Transform of the output variable to the Laplace Transform of the input variable with all the initial conditions zero.

Writing the differential equations with the help of Kirchhoff’s voltage law vi(t )

=

1 C

∫ idt + Ri(t )

vo(t ) = Ri(t )

(6.2.9) (6.2.10)

Laplace Transforming equations (6.2.9) and (6.2.10) we have, Vi( s )

=

1 Cs

I ( s ) + RI ( s )

Vo( s ) = RI ( s )

Hence we have from equations (6.2.11) and (6.2.12),

(6.2.11) (6.2.12)


Vo( s ) Vi ( s )

=

RCs

1 + RCs

INPUT

6.3 DERIVATION OF TRANSFER FUNCTION FROM BLOCK DIAGRAM SYSTEMS We can make a simple transfer function from a complete diagram whether in open-loop control system or closed-loop control system. 6.3.1 Open-loop Control System A system without feedback is called an open-loop system.

R(s)

C(s) G(s)

Input

Output

Figure 6.3 : Block diagram of open-loop system (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

For open loop system,


C(s) = G(s) R(s)

6.3.2 Closed-loop control system All automatic control systems are of the closed-loop type of control system. This is necessitated by the introduction of feedback for comparing the reference input R(s), with the controlled output C(s).

E(s) G(s) R(s)

C(s

_ B(s) H(s)

Figure 6.4 : Block diagram of closed-loop system (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Let us assume that, R(s) C(s) B(s) G(s) E(s)

= = = = =

input (reference) or controlling variable output or controlled variable feedback signal C(s) / E(s) = forward path transfer function Actuating signal


H(s) = B( s) E (s)

feedback transfer function

=

G(s) H(s) = (open) loop transfer function

C s

M(s) =

( )

R( s)

= closed-loop transfer function (controlratio)

From Figure 6.4, we have C(s) =

G(s) E(s)

(6.3.1)

E(s)

R(s) – B(s) R(s) – H(s) C(s)

(6.3.2)

= =

Eliminating E(s) from equation (6.3.1) and (6.3.2), we have C(s) = C ( s) R(s)

G(s) R(s) – G(s) H(s)C(s)

= M(s) =

G ( s)

(6.3.3)

1 + G( s) H ( s)

Hence, the system shown in Figure 6.4 can be reduced to single block shown in Figure 6.5.

R(s)

G(s)

1 + G (s) H (s)

Figure 6.5 : Reduce form of Figure 6.4

C(s)


Equation (6.3.3) is valid for negative feedback system. Hence, for a positive feedback system we have

C (s) R( s)

G( s)

= M(s) =

1 − G( s) H (s )

In general, for a positive/negative feedback systems, the control ratio is given by

C (s) R( s)

= M(s) =

G ( s)

as the case may be.

1 ± G (s) H ( s)

6.3.3 Block Diagram Reduction Rules Rule (1) : Combining blocks in cascade R1G1

R1

G1

R1G1G2 ≡

G1

G2

Figure 6.6 (a) : Blocks in cascade

R1G1G2 G1G2


Rule (2) : Combining blocks in Parallel RG1 ± RG2

R

RG1 ± RG2

R

+

G1

≡

RG1

G1 ± G2

±

G2 RG2

Figure 6.6 (b) : Blocks in Parallel

Rule (3) : Moving a pick-off point after a block RG

R G

R

RG G

≡

R R

1 G

Figure 6.6 (c) : Moving a pick-off point after a block


Rule (4) : Moving a take-off point ahead of a block RG R

RG G

R

≡

G

G RG

RG

Figure 6.6 (d) : Moving a take-off point ahead of a block

Rule (5) : Moving a summing point after a block R1 ± R2

G[R1 ± R2]

+

G R1

R1 ≡

R1G+

G[R1 ± R2]

G

±

±

G R2

R2G

Figure 6.6 (e) : Moving a summing point after a block

R2


Rule (6) : Moving a summing point ahead of a block

R1

R1 ± R2/G

R1G ± R2

R1G+ G

R1G ± R2

+

≡

G

R1

±

± 1/G

R2

R2

Figure 6.6 (f) : Moving a summing point ahead of a block

Rule (7) : Eliminating a feedback loop

R

+

C

C

R

G

G ≡

1 ± GH

± H

Figure 6.6 (g) : Eliminating a feedback loop


Figure 6.6 (a,b,c,d,e,f,g) : Block diagram reduction rules (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

6.3.4 A Block Diagram Reduction The block diagram of a multiple-loop feedback control system is shown in Figure 6.6. Use block diagram reduction to simplify this to a single block relating C(s) to R(s). Note that, for clarity, the dependency upons has been omitted from the transfer functions within the blocks.

R(s)

+

+

C(s)

+

G1(s)

G2(s) _

+

G3(s)

_

H1(s)

H2(s)

H3(s) Figure 6.7 Block Diagram


R(s)

C(s)

G1(s)

G2(s) -

G3(s)

-

H1(s)

+ H2(s)

H3(s) (a)

+

R(s)

C(s)

G1(s)

G2 (s)G3 (s)

H1(s)H2(s)H3(s) (b)


R(s)

G3 ( s )G2 ( s )G1 ( s )

C(s)

1 + G2 ( s)G3 ( s)[H1 ( s) − H 2 ( s) + H 3 ( s )]

(c) Figure 6.8 (a,b,c) : Steps to reduce the block diagram (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Steps to reduce the block diagram : (Figure6.8(a)) collapse summing junctions; (Figure6.8(b)) form equivalent cascaded system in the forward path and equivalent parallel system in the feedback path; (Figure6.8(c)) form equivalent feedback system and multiply by cascaded G1 (s) Finally, the feedback system is reduced and multiplied by G1 (s) to yield the equivalent transfer function shown in Figure 6.7 (c ).

6.3.5 Block Diagram of Two Input System In the present of more than one input to a system, the system may be a single output system called a multiple-input-single-output (MISO) system or


a multiple output system called a multiple-input-multiple-output (MIMO) system. The output of the system are obtained by applying the ‘law of homogeneity’ or ‘Principle of Superposition’.

Let us consider a two-input linear system as shown in Figure 6.9. D(s) C(s)

R(s) G2 ( s )

G1 (s)

_

H(s)

Figure 6.9 : Block diagram of a two-input system (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

The response to the input R(s) is obtained by letting the disturbance signal D(s) = 0. The corresponding block diagram is shown in Figure 6.9, which gives C R (s) =

C ( s)

R s

( )

acting alone with D(s) = 0




G ( s )G

(s)



1 2 C R (s) =   R(s) 1 G ( s ) G + 1 2 ( s) H ( s)  

(6.3.4)

(a)

R(s)

CR(s) G1 (s)

G2 ( s )

-

H(s)

(b) R(s)

CR(s) G1 (s) G2 ( s )

-

H(s)


(c) CR(s)

G1 ( s )G2 ( s )

1 + G1 ( s)G2 ( s) H ( s)

Figure 6.10(a,b,c) : Block Diagram Reduction with R(s) alone. (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Similarly the response to the disturbance signal D(s) is obtained by assuming R(s) = 0. The block diagram for this case is shown in Figure 6.11, which gives C D (s) =

C ( s)



D(s)

acting alone with R(s) = 0

G

( s)



2 C D (s) =   D(s) 1 + G1 ( s)G2 ( s) H ( s) 

(6.3.5)

The actual response of the system when both R(s) and D(s) are acting is obtained by adding the two individual responses CR (s) and C D (s).


(a) D(s)

CD(s) G2 ( s )

-

G1(s)

H(s)

(b)

D(s)

CD(s) G2 ( s )

-

G1(s) H(s)


(c)

CD(s)

D(s)

G2 ( s )

1 + G1 ( s)G2 ( s) H ( s)

Figure 6.11 (a,b,c) : Block Diagram Reduction with D(s) alone. (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

This example shows how superposition may be used to handle system with more than one input : Example 6.3: Determine the output Y(s) in the system shown below. D(s) +

R(s) +

Y(s) 2

K s +3

-

S+1

+

s


Figure 6.12 : Block diagram of a two input system in the Laplace domain (Source : Katsuhiko Ogata (1990), Modern Control Engineering)

Solution : 1. Setting D(s) = 0, gives the transfer function between Y(s) and R(s) as :

Y ( s) R( s)

2.

=

2K s ( s + 3) +

2 K ( s + 1)

Setting R(s) = 0, gives the transfer function between Y(s) and D(s) as :

Y ( s) D( s )

=

2( s + 3) s ( s + 3) +

2 K ( s + 1)

Since a Laplace transfer function is a linear operator, the principle of superposition is used to generate the overall output as the sum of the two input contributions: Y (s) =

2 KR( s) s ( s + 3) +

or

2 K ( s + 1)

+

2( s + 3) D( s) s ( s + 3) +

2 K ( s + 1)


Y (s) =

2 KR( s) + 2( s + 3) D( s ) s ( s + 3) + 2 K ( s + 1)

Activity 6B


6.3

The block diagram of a certain system is shown below. Determine the transfer function Y(s)/U(s). Y(s) G1(s)

G2(s)

-

6.4

The block diagram of a certain system is shown below. Determine the transfer function C(s)/R(s).


C(s)

R(s) G(s) -


6.3

6.4

Y (s) U ( s)

C (s) R( s)

=

=

G1 ( s )G2 ( s )

1 + G1 ( s)G2 ( s) G( s)

1 + G( s)


KEY FACTS 1.

The transfer functions is define as G(s) = C(s)/R(s), or the ratio of the Laplace transform of the output to the Laplace Transform of the input.


SELF-ASSESSMENT

You are approaching success.Try all the questions in this self-assessment section and check answers with those in the Feedback on SelfAssessment given your on the next page. If you given face any problems, discuss it with your lecturer. Good luck. Q6-1 State the steps to obtain the transfer function. Q6-2 (a)

The transfer function E0(s)/E 1 (s) of the RC-network shown is given by: R C

Ei(t)

Eo(t)


(b) R L Ei(t)

Eo(t)

Q6-3 Simplify the block diagram in the figure below and obtain the closed loop in transfer function C(s)/R(s).

R(s)

+

G1

+

+

G2

-

G3 G4

C(s)


Feedback To S elf-Assessment

Have you tried the questions????? If “YES”, check your answers now. Q6-1 (i) The steps involved in obtainingequations the transfer functionthe aresystem. as follows : To write the differential governing (ii) To Laplace Transform the equations i.e, to replace the terms involving d/dt by s and ∫ dt by 1/s . (iii) To obtain the ratio of Transformed output to input variables.

Q6-2 (a)

(b)

E0 ( s ) Ei ( s )

E0 ( s ) Ei ( s )

=

=

1 RCs + 1

Ls R + Ls

Q6-3 R(s)

C(s)


G1 + G2 -

G3 – G4

C ( s) R( s)

=

(G1 + G2 ) 1 + (G1 + G2 )(G3 − G4 )

C(s)

R(s) (G1 + G2 ) 1 + (G1 + G2 )(G3 − G4 )

Basic Control System.pdf

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