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Chapter 4 Discription of Computer- Controlled System

Chapter 4 Discription of Computer- Controlled System. Contents. 4.1 Description of Linear Discrete Systems 4.2 Pulse Response Function 4.3 Pulse Transfer Function 4.4 Open/closed-loop Pulse Transfer Function 4.5 Response of the CCS 4.6 Performance Specifications of the CCS

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Chapter 4 Discription of Computer- Controlled System

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  1. Chapter 4 Discription of Computer- Controlled System

  2. Contents 4.1 Description of Linear Discrete Systems 4.2 Pulse Response Function 4.3 Pulse Transfer Function 4.4 Open/closed-loop Pulse Transfer Function 4.5 Response of the CCS 4.6 Performance Specifications of the CCS 4.7 State Space Description of the CCS

  3. 4.1 Description of Linear Discrete Systems

  4. 4.1 Description of Linear Discrete Systems 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,…

  5. y(t) x(t) x*(t) G(s) y*(t) 4.2 Pulse Response Function • Pulse response function is the basis for studying pulse transfer function. Fig. 4.1 Continuous system with impulse sampling signal input

  6. 4.2 Pulse Response Function

  7. 4.2 Pulse Response Function

  8. 4.2 Pulse Response Function

  9. 4.2 Pulse Response Function

  10. 4.3 Pulse Transfer Function

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

  12. 4.3 Pulse Transfer Function

  13. 4.3 Pulse Transfer Function

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

  15. 4.4 Open/closed-loop Pulse Transfer Function

  16. 4.4 Open/closed-loop Pulse Transfer Function

  17. 4.4 Open/closed-loop Pulse Transfer Function 4.4.2 Properties of X*(s)

  18. 4.4 Open/closed-loop Pulse Transfer Function

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

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

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

  22. 4.4 Open/closed-loop Pulse Transfer Function 4.4.4 Pulse transfer function and difference equation • Pulse transfer function can be converted to the difference equation, and vice versa.

  23. 4.4 Open/closed-loop Pulse Transfer Function

  24. 4.4 Open/closed-loop Pulse Transfer Function

  25. 4.4 Open/closed-loop Pulse Transfer Function

  26. 4.4 Open/closed-loop Pulse Transfer Function 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

  27. 4.4 Open/closed-loop Pulse Transfer Function

  28. G(z) T (s) R(s) R*(s) C(s) C*(s) C1(s) G1(s) G2(s) R(z) C(z) 4.4 Open/closed-loop Pulse Transfer Function 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

  29. 4.4 Open/closed-loop Pulse Transfer Function

  30. G(z) T R(s) R*(s) C1(s) C1*(s) C(s) C*(s) G1(s) G2(s) R(z) C1(z) C(z) 4.4 Open/closed-loop Pulse Transfer Function (2) Pulse transfer function of cascaded elements with sampler between them Fig. 4.6 cascade connection with sampler

  31. 4.4 Open/closed-loop Pulse Transfer Function

  32. 4.4 Open/closed-loop Pulse Transfer Function

  33. Y1(s) U*(s) G1(s) Y*(s) Y(s) U(s)  U*(s) G2(s) Y2(s) 4.4 Open/closed-loop Pulse Transfer Function (3) Pulse transfer function of parallel elements

  34. Y1(s) U*(s) G1(s) Y*(s) Y(s) U(s)  G2(s) Y2(s) 4.4 Open/closed-loop Pulse Transfer Function

  35. Ф(z) R*(s) C*(s) R(z) C(z) E*(s) R(s) E(s) G(s) C(s) E(z) - B(s) H(s) 4.4 Open/closed-loop Pulse Transfer Function 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

  36. 4.4 Open/closed-loop Pulse Transfer Function

  37. 4.4 Open/closed-loop Pulse Transfer Function

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

  39. 4.4 Open/closed-loop Pulse Transfer Function

  40. 4.4 Open/closed-loop Pulse Transfer Function (3) Sampler is located at the forward channel T R*(s) R(z) C*(s) E*(s) R(s) E(s) G(s) E(z) - C(z) B(s) H(s) Fig. 4.9 sampler is located at the forward channel

  41. 4.4 Open/closed-loop Pulse Transfer Function

  42. 4.4 Open/closed-loop Pulse Transfer Function

  43. E(s) E*(s) U(s) R(s) G2(s) G1(s) C(s) - 4.4 Open/closed-loop Pulse Transfer Function

  44. 4.4 Open/closed-loop Pulse Transfer Function

  45. Gh(s) G1(s) Gp(s) x(t) x*(t) y*(t) H(s) 4.5 Response of the CCS (1) System response at sampling instant Fig. 4.10 Open loop sampling system

  46. 4.5 Response of the CCS

  47. 4.5 Response of the CCS

  48. 4.5 Response of the CCS

  49. 4.5 Response of the CCS The response of the open-loop control system

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