CE- Lab
2008-Mech-245 2008-Mech-245
Basic Controller; The Basic Controller for an application can be visualized as
The controller consists of
A measuring unit with an appropriate instrument to measure the state of process, a temperature transmitter, pressure transmitter or similar. An input set point device to set the desired value. A comparator for comparing the measured value with the set point, calculating the difference or error between the two. A control unit to calculate the output magnitude and direction to compensate the deviation from the desired value. An output unit converting the output from the controller to physical action, a control valve, a motor or similar.
Controller Principles The Control Units are in general build on the control principles
proportional controller integral controller derivative controller
CE- Lab
2008-Mech-245
Proportional control; A proportional control system is a type of linear control system. Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor. The proportional control system is more complex than an on-off control system like a bi-metallic domestic thermostat. On-off control will work where the overall system has a relatively long response time, but will result in instability if the system being controlled has a rapid response time. Proportional control overcomes this by modulating the output to the controlling device, such as a continuously variable valve One of the most used controllers is the Proportional Controller (P-Controller) who produce an output action that is proportional to the deviation between the set point and the measured process value. OP = -k P Er
(1)
where OP = output proportional controller k P = proportional gain or action factor of the controller Er = error or deviation between the set point value and the measured value
The gain or action factor - k P
influence on the output with a magnitude of k P determines how fast the system responds. If the value is too large the system will be in danger to oscillate and/or become unstable. If the value is too small the system error or deviation from set point will be very large. can be regarded linear only for very small variations.
The gain k P can be expressed as k P = 100 / P
(1b)
where P = proportional band
The proportional band P, express the value necessary for 100% controller output. If P = 0, the gain or action factor k P would beinfinity - the control action would be ON/OFF . Note! A proportional controller will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error.
CE- Lab
2008-Mech-245
Integral Controller (I-Controller); With integral action, the controller output is proportional to the amount of time the error is present. Integral action eliminates offset. O I = - k I Σ(Er dt)
(2)
where O I = output integrating controller k I = integrating gain or action factor of the controller dt = time sample
The integral controller produce an output proportional with the summarized deviation between the set point and measured value and integrating gain or action factor. Integral controllers tend to respond slowly at first, but over a long period of time they tend to eliminate errors. The integral controller eliminates the steady-state error, but may make the transient response worse. The controller may be unstable. The integral regulator may also cause problems during shutdowns and start up as a result of the integral saturation or wind up effect. An integrating regulator with over time deviation (typical during plant shut downs) will summarize the output to +/- 100%. During start up the output is set to 100%m which may be catastrophic.
Derivative Controller (D-Controller); With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the deviation or error with time. O D = - k D dEr / dt
(3)
where O D = output derivative controller k D = derivative gain or action factor of the controller dEr = deviation change over time sample dt dt = time sample
The derivative or differential controller is never used alone. With sudden changes in the system the derivative controller will compensate the output fast. The long term effects the controller allows huge steady state errors.
CE- Lab
2008-Mech-245
A derivative controller will in general have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.
Proportional Integral Derivative Controller (PID-Controller); The functions of the individual proportional, integral and derivative controllers complement each other. If they are combined it’s possible to make a system that responds quickly to changes (derivative), tracks required positions (proportional), and reduces steady state errors (integral). Note that these correlations may not be exactly accurate, because P, I and D are dependent of each other. Changing one of these variables can change the effect of the other two.
Controller Response
Rise Time
Overshoot
Settling Time
Steady State Error
P
Decrease
Increase
Small Change
Decrease
I
Decrease
Increase
Increase
Eliminate
D
Small Change
Decrease
Decrease
Small Change
A block diagram of a PID controller
A proportional – integral – derivative controller (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems – a PID is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable and a desired set point. The controller attempts to minimize the error by adjusting the process control inputs.
CE- Lab
2008-Mech-245
The PID controller calculation (algorithm) involves three separate constant parameters, and is accordingly sometimes called three-term control: the proportional, the integral and derivative values, denoted P, I, and D. Heuristically, these values can be interpreted in terms of time: P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve, or the power supplied to a heating element. In the absence of knowledge of the underlying process, a PID controller has historically been considered to be the best controller. By tuning the three parameters in the PID controller algorithm, the controller can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the set point and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability. Some applications may require using only one or two actions to provide the appropriate system control. This is achieved by setting the other parameters to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are fairly common, since derivative action is sensitive to measurement noise, whereas the absence of an integral term may prevent the system from reaching its target value due to the control action.
