1. Process Control

2. Feedback control y sp = set point (target value) y = measured value The process information (y) is fed back to the controller The objective is to reduce the error signal to zero, where the error is defined as: process transmitter controller disturbance comparator manipulated variable controlled variable + – error set-point y sp y

3. The typical control problems  Regulatory control – the task is to counteract the effect of external disturbances in order to maintain the output at its constant set-point (disturbance rejection)  Servo control – the objective is to cause the output to track the changing set-point In both cases, one or more variables are manipulated by the control system

4. Summary for on-off control Advantages simple & easy to design inexpensive easily accepted among operators  Pitfalls not effective for “ good ” set-point control (the controlled variable cycles) produce wear on the final control element (it can be attenuated by a large dead band, at the expense of a loss of performance)

5. Proportional (P) controllers The control variable is manipulated according to: u 0 is the controller bias K C is the controller gain The controller gain can be adjusted ( “ tuned ” ) to make the manipulated variable changes as sensitive as desired to the deviations between set-point and controlled variable The sign of K C can be chosen to make the controller output u increase or decrease as the error increases

6. P-only controllers : at the nominal steady state The bias u 0 is the value of the controller output which, in manual mode, causes the measured process variable to maintain steady state at the design level of operation [e (t )=0] when the process disturbances are at their expected values The bias value is assigned at the controller design level, and remains fixed once the controller is put in automatic

7. Summary for P-only control Advantages conceptually simple easy to tune (a single parameter is needed, K C ; the bias is determined from steady state information)  Pitfalls cannot remove off-set (off-set is enforced by the controlled)

8. PI controllers u 0 is the controller bias K C is the controller gain  I is the integral time (also called reset time) P=Proportional, I=Integral integral action contribution The P controller cannot remove off-set because the only way to change the controller bias during non-nominal operations is to cause e  0 The rationale behind a PI controller is to set the “ actual ” bias different from u 0, thus letting the error be zero The control variable is manipulated according to:

9. PI controllers (cont ’ d) Note that until e  0, the manipulated input keeps on changing because of the presence of the integral term The change in u (t ) will stop only when e = 0 The integral action can eliminate off-set

10. Performance of PI controllers Response to a disturbance step change: effect of K C The offset is eliminated Increasing K C : the process response is speeded up the system may oscillate CAUTION For large values of the controller gain, the closed-loop response may be unstable !

11. Summary for PI control Advantages steady state off-set can be eliminated steady state off-set can be eliminated the process response can be considerably speeded up with respect to open-loop  Pitfalls tuning is harder (two parameters must be specified, K C and  I ) the process response becomes oscillatory; bad tuning may even lead to instability the integral action may “ saturate ”

12. PID controllers  D is called derivative time i) If the error if increasing very rapidly, a large deviation from the setpoint may arise in a short time ii) Sluggish processes tend to cycle P=Proportional, I=Integral, D=Derivative derivative action contribution The rationale behind derivative action is to anticipate the future behavior of the error signal by considering its rate of change The control variable is manipulated according to:

13. Performance of PID controllers Response to a disturbance step change Increasing  D : the oscillations caused by the integral action are dampened the process response is speeded up CAUTION Noisy measurements may disrupt the controller performance !

14. Summary for PID control Advantages oscillations can be dampened with respect to PI control  Pitfalls tuning is harder than PI (three parameters must be specified, K C,  I and  D ) the derivative action may amplify measurement noise  potential wear on the final control element  Use of derivative action avoid using the D action when the controlled variable has a noisy measure or when the process is not sluggish ( )

15. Controller selection recommendations When steady state offsets can be tolerated, use a P-only controller (many liquid level loops are on P control) When offset cannot be tolerated, use a PI controller (a large proportion of feedback loops in a typical plant are under PI control) When it is important to compensate for some natural sluggishness in the system, and the process signal are relatively noise-free, use a PID controller