1. Chapter 7 Adjusting Controller Parameters Professor Shi-Shang Jang Chemical Engineering Department National Tsing-Hua University Hsin Chu, Taiwan

2. 7-1 Basic Requirement of a controller The closed loop system must be stable The effects of disturbance must be minimized, good disturbance rejection (regulation performance) Rapid, smooth responses to set-point changes are required, good servo performance Steady state error (offset) is eliminated Excessive control action is avoided (control action should avoid oscillation, input stable) The control system robust, that is, insensitive to changes in process

3. 7-1 Quarter Decay Ratio By Ultimate Properties Ziegler- Nicho ls Kc II DD P0.5K u -- PIK u /2.2P u /1.2- PIDK u /1.7P u /2P u /8

4. 7-1 Example (Example 6-1.1 K u =10.4 P u =4.6min

5. 7-1 Example (Example 6-1.1- Cont.

6. 7-2 Open Loop Characterization

8. 7-2 Open Loop Characterization -Example 7.2 61.5

9. 7-2 Tuning for Quarter Decay Ratio

10. 7-2 Tuning for Quarter Decay Ratio - Example

11. 7-2.2 Tuning for Integral Criteria Integral of absolute value of the error (IAE) Integral of the square error (ISE) Integral of the time-weighted abolute error (ITAE)

12. 7-2.2 Tuning for Integral Criteria - IAE

14. 7-2.2 Tuning for Integral Criteria – IAE : Example

15. Example – Cont.

19. Step Response Test; FOPDT Fit 2

20. Response; C Time (min) Regression Test

21. time Response; C Step Response Test; SOPDT, Smith’s Method

22. Response; C Time (min)

23. FOPTD SOPTD PID Control Comparison Temperature; C Time, min

24. 7-3 Summary A control loop should be stable, fast responding and robust Z-N QD tuning and IAE tuning are widely used in the industries On-Line tuning is also widely used

25. Homeworks Text p 271 7-3,, 7-12, 7-15, 7-19, 7-22

26. Supplemental Materials

27. Synthesis of Feedback Controllers Controller synthesis ◦ Given the transfer functions of the components of a feedback loop, synthesize the controller required to produce a specific closed-loop response Formula derivation Chapter 7

28. For perfect control ◦ This says that in order to force the output to equal the set point at all times, the controller gain must be infinite. ◦ In other words, perfect control cannot be achieved with feedback control. ◦ This is because any feedback corrective action must be based on an error. Chapter 7

29. Specification of the Closed-Loop Response The simplest achievable closed-loop response is a first- order lag response τ c is the time constant of the closed-loop response ◦ The single tuning parameter for the synthesized controller ◦ Design parameter τ c provides a convenient controller tuning parameter that can be used to make the controller more aggressive (small τ c ) or less aggressive (large τ c ). Chapter 7

30. This controller has integral mode ◦ No offset ◦ i.e. unity gain Chapter 7 ~

31. Notes Although second- and higher-order closed-loop responses could be specified, it is seldom necessary to do so. When the process contains dead time, the closed-loop response must also contain a dead-time term, with the dead time equal to the process dead time. Chapter 7

32. If the process transfer function contains a known time delay θ, a reasonable choice for the desired closed-loop transfer function is: The time-delay term is essential because it is physically impossible for the controlled variable to respond to a set-point change at t = 0, before t = θ. If the time delay is unknown, θ must be replaced by an estimate. Chapter 7

33. Although this controller is not in a standard PID form, it is physically realizable. Using a truncated Taylor series expansion: Note that this controller also contains integral control action. Chapter 7

34. FOPDT Model Consider the standard FOPDT model, Chapter 7

35. SOPDT Model Consider a SOPTD model, where:

36. Example Use the DS design method to calculate PID controller settings for the process: Chapter 7 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 G d = G. Repeat the evaluation for two cases: a.The process model is perfect ( = G). b.The model gain is = 0.9, instead of the actual value, K = 2. Thus,

37. The controller settings for this example are: 3.75 1.88 0.682 8.33 4.17 1.51 15 3.33 Chapter 7

38. The values of K c decrease as increases, but the values of and do not change.

39. Perfect process model Chapter 7

40. With model mismatch Chapter 7

41. Comparison to quarter decay ratio response Chapter 7

42. Set the parameters of the PID controller according to Table 7-1.1

43. Chapter 7