Controller Design, Tuning

1. Controller Design, Tuning

6. Performance Criteria for Closed-loop systems • Must be stable. • Provide good disturbance rejection---minimizing the effects of disturbance. • Have good set-point tracking---Rapid, smooth responses to set-point changes • Eliminate steady state error (zero offset) • Avoid excessive control action. • Must be robust( or insensitive) to process changes or model inaccuracies.

10. Methods for PID controller settings Classical methods: • By reaction curve for a quarter decay ratio. • By on-line cycling experiment for quarter decay ratio. • By tuning rules using reaction curve and integral performance criteria.

12. Reaction Curve Reaction curve L Manual input y + + + - R

14. Classical methods

15. Classical methods

16. Classical methods

17. Classical methods

18. Tyler-Luyben’s Tuning Rule

19. Tyler-Luyben vs Z-N Tuning

20. Model characterization by reaction curve • FOPDT (First Order Plus Dead Time) model • Fit 1

21. Model characterization by reaction curve • FOPDT (First Order Plus Dead Time) model • Fit 2

22. Model characterization by reaction curve • FOPDT (First Order Plus Dead Time) model • Fit 3

23. Model-based tuning rules for QDR

24. Hagglund & Astrom’s PI Tuning Rules

25. Integral performance indices • ISE : • IAE: • ITSE: • ITAE:

26. Tuning rules for optimal integral performance measures • Optimal tuning parameters are obtained via simulating a basic loop: • The results apply specifically to set-point change or to disturbance change. GL=GP

27. Tuning rules for optimal integral performance measures • The controller used is considered as of parallel and ideal form; • Parameters are Dimensionless groups, such as : KcKp, tR/t, tD/t;

28. Tuning rules for optimal integral performance measures • The resulted tuning parameters are fitted into the following forms: • The values of a and b are tabularized.

29. Model based tuning rules for optimal integral performance measures ---II • Optimal tuning parameters are obtained via simulating a basic loop: • The results apply specifically to set-point change or to disturbance change. GL=GP

30. Model based tuning rules for optimal integral performance measures ---III • The resulted tuning parameters are fitted into the following forms: • The values of a and b are tabularized.

36. Remarks on tuning rules with integral performance indices: • Remember that conversions between a series PID controller and the parallel PID controller is necessary in order to use the tuning rules. • The tuning parameters for disturbance change will be too aggressive when controlling a set-point change. The reverse happens in using set-point tuning parameters to disturbance regulation. • No significance in difference among rules of different integral criteria.

37. Late methods • Method of Synthesis • Using IMC tuning (internal model control ) or other model based rules • Using ATV test to characterize the process dynamics.

38. Direct synthesis method • Specify desired closed-loop transfer function. • Derive PID controller follows. • Tuning parameters are directly synthesized. • Exactly PID controller form applies to FOPDT or SOPDT processes.

40. r y + Gc(s) Gp(s) - y r Go(s) Specified to meet requirement r y H(s)

42. In order to be implementable, the reference H(s) should: • not allow to be assigned as “1”, in other words, a system can not be perfect in control. • contain all RHP zeros of Gp(s) • contain the dead time of Gp(s)

44. Example Choose:f = t3

45. Structure evolution from direct synthesis d y + r + + Gp(s) 1/Gp(s) H(s) - +

46. d y r + + H(s) Gp(s) Gp(s) 1/Gp(s) - + d r + y H(s) + 1/Gp(s) Gp(s) - + - Gp(s) Gp(s)

47. d y r + + 1/Gp(s) H(s) Gp(s) - + - Gp(s) C(s) d y r + + 1/Gp(s) H(s) Gp(s) - + - Gp(s) Gp(s)

48. d y r + Gp(s) C(s) - - Gp(s) Known as IMC d y r + + 1/Gp(s) H(s) Gp(s) - + C(s) - Gp(s)

49. d y r + C(s) Gp(s) - - Gp(s)