1. ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ (22Δ802) Β΄ ΕΞΑΜΗΝΟ 2014-15 Καθηγητής Πέτρος Π. Γρουμπός  2610 996449 Ώρες Γραφείου: Τετάρτη Πέμπτη Παρασκευή 11:00-12:00 Γραφείο: 1 ος όροφος Τομέας Συστημάτων & Αυτομάτου Ελέγχου Τμήμα ΗΜ&ΤΥ ΚΕΦΑΛΑΙΟ 4

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3. 3 Contents 1 Description of Linear Discrete Systems 2 Pulse Response Function 3 Pulse Transfer Function 4 Open/closed-loop Pulse Transfer Function 5 Response of the CCS 6 Performance Specifications of the CCS 7 State Space Description of the CCS

4. 4 1 Description of Linear Discrete Systems

5. 5 The system considered in the class is the linear time-invariant system, i.e. the relation between the output and input is unchangeable over time. r(kT)→y(kT); r(kT-iT)→y(kT-iT), k=0,1,2,…; i=…,-2,-1,0,1,2,…

6. 6 2 Pulse Response Function Pulse response function is the basis for studying pulse transfer function. G(s) x(t)x * (t) y(t) y * (t) Fig. 4.1 Continuous system with impulse sampling signal input

7. 7 2 Pulse Response Function

8. 8

9. 9 4.2 Pulse Response Function

10. 10 4.2 Pulse Response Function

11. 11 4.3 Pulse Transfer Function

12. 12 4.3 Pulse Transfer Function G(z) X(z)Y(z) Fig. 4.2. Diagram of Pulse Transfer System

13. 13 4.3 Pulse Transfer Function

14. 14 4.3 Pulse Transfer Function

15. 15 4.4 Open/closed-loop Pulse Transfer Function 4.4.1 Laplace transform of the sampled signal G(s) x(t)x * (t) y(t) Y(s) X*(s)X(s)

16. 16 4.4 Open/closed-loop Pulse Transfer Function

17. 17 4.4 Open/closed-loop Pulse Transfer Function

18. 18 4.4.2 Properties of X*(s) 4.4 Open/closed-loop Pulse Transfer Function

19. 19 4.4 Open/closed-loop Pulse Transfer Function

20. 20 4.4.3 How to get pulse transfer function (1) System with sampler G(s) x(t)x * (t) y(t) y * (t) Fig. 4.3 system with sampler 4.4 Open/closed-loop Pulse Transfer Function

21. 21 4.4 Open/closed-loop Pulse Transfer Function Fig. 4.4 system without sampler G(s) x(t)y(t) X(s) Y(s) (2) System without sampler

22. 22 G(s) x(t)x * (t) y(t) y * (t) 4.4 Open/closed-loop Pulse Transfer Function (3) The methods to get pulse transfer function

23. 23 4.4.4 Pulse transfer function and difference equation  Pulse transfer function can be converted to the difference equation, and vice versa. 4.4 Open/closed-loop Pulse Transfer Function

24. 24 4.4 Open/closed-loop Pulse Transfer Function

25. 25 4.4 Open/closed-loop Pulse Transfer Function

26. 26 4.4 Open/closed-loop Pulse Transfer Function

27. 27 4.4.5 Pulse transfer function of the system with ZOH The transfer function of the zero order holder is The transfer function of the system with zero order holder is 4.4 Open/closed-loop Pulse Transfer Function

28. 28 4.4 Open/closed-loop Pulse Transfer Function

29. 29 4.4.6 Open loop pulse transfer function of the system (1) Pulse transfer function of cascaded elements without sampler between them Fig. 4.5 cascade connection without sampler G 1 (s)G 2 (s) R(s) C 1 (s) C * (s)C(s) C(z)R(z) R*(s) G(z) T (s) 4.4 Open/closed-loop Pulse Transfer Function

30. 30 4.4 Open/closed-loop Pulse Transfer Function

31. 31 (2) Pulse transfer function of cascaded elements with sampler between them Fig. 4.6 cascade connection with sampler G 1 (s)G 2 (s) R(s)C 1 (s)C * (s)C(s) C(z)R(z) R*(s) G(z) T C 1* (s) C 1 (z) 4.4 Open/closed-loop Pulse Transfer Function

32. 32 4.4 Open/closed-loop Pulse Transfer Function

33. 33 4.4 Open/closed-loop Pulse Transfer Function

34. 34 (3) Pulse transfer function of parallel elements G 1 (s) U*(s) G 2 (s) Y(s) Y*(s) U(s) U*(s)  Y 1 (s) Y 2 (s) 4.4 Open/closed-loop Pulse Transfer Function

35. 35 G 1 (s) U*(s) G 2 (s) Y(s) Y*(s) U(s)  Y 1 (s) Y 2 (s) 4.4 Open/closed-loop Pulse Transfer Function

36. 36 4.4.7 Closed-loop pulse transfer function of the system (1) Sampler is located after the comparator Fig. 4.7 sampler is located after the comparator G (s) E(s) C(s) E(z) E*(s) Ф(z) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - 4.4 Open/closed-loop Pulse Transfer Function

37. 37 4.4 Open/closed-loop Pulse Transfer Function

38. 38 4.4 Open/closed-loop Pulse Transfer Function

39. 39 (2) Sampler is located at the feedback channel Fig. 4.8 Sampler is located at the feedback channel G (s) E(s) C(s) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - 4.4 Open/closed-loop Pulse Transfer Function

40. 40 4.4 Open/closed-loop Pulse Transfer Function

41. 41 (3) Sampler is located at the forward channel Fig. 4.9 sampler is located at the forward channel G (s) E(s) E(z) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - T 4.4 Open/closed-loop Pulse Transfer Function

42. 42 (3) Sampler is located at the forward channel Fig. 4.9 sampler is located at the forward channel G (s) E(s) E(z) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - T 4.4 Open/closed-loop Pulse Transfer Function

43. 43 4.4 Open/closed-loop Pulse Transfer Function

44. 44 G 2 (s) E(s) C(s) R(s) - G 1 (s) E*(s)U(s) 4.4 Open/closed-loop Pulse Transfer Function

45. 45 4.4 Open/closed-loop Pulse Transfer Function

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47. . ΕΥΧΑΡΙΣΤΩ ΓΙΑ ΤΗΝ ΠΡΟΣΟΧΗ ΣΑΣ Καθ.Γρουμπός Π. Πέτρος groumpos@ece.upatras.gr