אוטומציה ובקרה – PID Control
Between the measuring device and the final control element comes the controller. Its function is to receive themeasured output signal Ym (t) and after comparing it with the set point YSP to produce the actuating signal c (t) in such a way as to return the out put to the desired value YSP. Therefore the input to the controller is the error ε(t) = YSP –Ym (t), while its out put is c (t). The various types of continous feedback controllers differ in the way they relate ε (t) and c (t).
The best feed back controller is the proportional – integral- derivative controller.
In the industrial practice it is commonly known as the proportional-plus-reset-plus-rate controller.
The actuating signal of this controller is given by the following mathematical equation.
c (t) = Kc ε (t) + Kc/Ʈ1 ∫0 t ε (t) dt + Kc ƮD dε/dt + Cs
Kc = proportional gain of the controller
Cs = controllers bias signal (i.e. its actuating signal when ε =0)
Ʈ1 = integral time constant OR reset time in minutes
TD = derivative time constant in minutes
Proportional = Kc ε (t)
Here the actuating out put c (t) is proportional to the error ε (t) = YSP –Ym (t),
It is clear that larger the gain Kc, the higher the sensitivity of controllers actuating signal to deviations (ε).
ie: Y SP =100, Ym(t) =96, hence error ε = 4.
If Kc=1, then controllers actuating signal, c = 4% to close/open, for TCV.
If Kc=3, then controllers actuating signal, c= 12% to close/open, for TCV
Integral = Kc/Ʈ1 ∫0 t ε (t) dt
The reset time, Ʈ1 is the time needed by the controller to repeat the initial proportional action change in its out put. Reset time, Ʈ1 is an adjustable parameter and some manufacturers do not calibrate their controllers in terms of Ʈ1, but in terms of its reciprocals, 1/ Ʈ1 (repeats per minute), which is known as the reset rate.
ie:
Reset rate=0.1, it means the reset time is = 1/0.1= 10 scans, Hence every 10 scans the controller will add the proportional action change (Kc ε (t)).
In most of the PID’s time scans is configurable and called “update loop time” if it equals to 1 then every 10 seconds the controller will add the proportional action
Remark:
The integral term of a controller causes its output to continue changing as long as there is a non-zero error. Often the errors cannot be eliminated quickly, and given enough time they produce larger and larger values for the integral term, which in turn keeps increasing the control action until it is saturated ( ie: the valve is completely open or closed) & called as integral wind up.
Derivative = Kc ƮD dε/dt
ƮD is the derivative time constant in minutes, with the presence of the derivative term, (dε/dt), the PID controller anticipates what error will be in the immediate future and applies a control action which is proportional to the current rate of change in the error. Due to this property, the derivative control action is referred to as anticipatory control.
Because of the forecasting action of the derivative parameter, the control valve will never “rest” it will always open and close to maintain the Setpoint therefore – this parameter must be used only for fast PID’s such as compressed air control, Steam control, ETC
,This guide was written by llan shaya, control and automation specialist
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