Chapter 12

1. Controller Design (todetermine controller settings for P, PI or PID controllers) Based on Transient Response Criteria Chapter 12

2. Desirable Controller Features • The closed-loop system must be stable. • The effects of disturbances are minimized, i.e., good disturbance rejection. • Quick and smooth responses to the set-point changes are guaranteed, i.e., good set-point tracking. • Off-set is eliminated. • Excessive controller action is avoided. • The control system is robust, i.e., it is insensitive to changes in operating conditions and to inaccuracies in process model and/or measurements. Chapter 12

3. Chapter 12

4. Simplified Block Diagram

5. Simplified Block Diagram D(s) B(s) P(s)

6. Example

7. Chapter 12

8. Example 12.1

9. Chapter 12

10. Chapter 12

11. Alternatives for Controller Design • Direct synthesis (DS) method • Internal model control (IMC) method • Controller tuning relations • Frequency response techniques • Computer simulation • On-line tuning after the control system is installed. Chapter 12

12. Direct Synthesis

13. Direct Synthesis Steps • Specify desired closed-loop response (transfer function) • Assume process model • Solve for controller transfer function

14. Direct Synthesis to Achieve Perfect Control

15. Direct Synthesis to Achieve Finite Settling Time

16. Example

17. Example

18. Direct Synthesis for Time-Delayed Systems

19. Taylor Series Approximation

20. Example 1

21. Example 2

22. Pade Approximation

23. Example

24. Example 12.1 Use the DS design method to calculate PID controller settings for the process: Chapter 12

25. Consider three values of the desired closed-loop time constant: . Evaluate the controllers for unit step changes in both the set point and the disturbance, assuming that Gd = G. Repeat the evaluation for two cases: • The process model is perfect ( = G). • The model gain is = 0.9, instead of the actual value, K = 2. Thus, Chapter 12 The controller settings for this example are:

26. Chapter 12 Figure 12.3 Simulation results for Example 12.1 (a): correct model gain.

27. Simulation results for Example 21.1(b): incorrect model gain.

28. Chapter 12

29. PID vs. IMC

30. PID Controller Design Procedure Based on IMC Method –Step 1: factor process model

31. PID Controller Design Procedure Based on IMC Method –Step 2: derive IMC transfer function

32. PID Controller Design Procedure Based on IMC Method –Step 3: derive PID transfer function

33. Chapter 12

34. Example

36. Controller Synthesis Criteria in Time Domain Time-domain techniques can be classified into two groups: (a) Criteria based on a few points in the response (b) Criteria based on the entire response, or integral criteria

37. Approach (a) Based on settling time, % overshoot, rise time, decay ratio (Fig. 5.10 can be viewed as closed-loop response). Several methods based on 1/4 decay ratio have been proposed, e.g., Cohen-Coon and Ziegler-Nichols.

38. Chapter 12

39. Chapter 12

40. Approach (b) - Criteria • Integral of absolute value of error (IAE) • Integral of square error (ISE) • Time-weighted IAE (ITAE)

41. Approach (b) - Remarks Pick controller parameters to minimize integral. • IAE allows larger overall deviation than ISE (with smaller overshoots). • ISE needs longer settling time • ITAE weights errors occurring later more heavily Approximate optimum tuning parameters are correlated with K, ,  (Table 12.3).

42. Chapter 12

45. Chapter 12

46. Example 1

47. Example 1

49. Example 2

50. Chapter 12