Feedback control systems characteristics Solutions-chapter 4

1. Feedback control systems characteristics  Solutions-chapter 4 Prof. Marian S. Stachowicz Laboratory for Intelligent Systems ECE Department, University of Minnesota Duluth February 23, 2010

2. References for reading R.C. Dorf and R.H. Bishop, Modern Control Systems, 11th Edition, Prentice Hall, 2008, Chapter 4.1 - 4.11 2. J.J. DiStefano, A. R. Stubberud, I. J. Williams, Feeedback and Control Systems, Schaum's Outline Series, McGraw-Hill, Inc., 1990 Chapter 9 2 Control Systems

3. Outline Introduction Error signal analysis Sensitivity of control systems to parameter variations Disturbance signals in a feedback control system 3 Control Systems Objectives The main topic of Chapters 2 and 3 was the mathematical modeling of physical systems. In this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal. This signal is used to control the process using the notion of feedback. Generally speaking, the goal is to minimize the error signal. We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved. We wish to reduce the effect of unwanted input signals, called disturbances, on the output signal. We will show how we may design a control system to reduce the impact of disturbance signals. Of course, the benefits of a control system come with an attendant cost. We will demonstrate how the cost of using feedback in a control system is associated with the selection of the feedback sensor device. The chapter concludes with a system performance analysis of the Sequential Design Example: Disk Drive Read System. Objectives The main topic of Chapters 2 and 3 was the mathematical modeling of physical systems. In this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal. This signal is used to control the process using the notion of feedback. Generally speaking, the goal is to minimize the error signal. We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved. We wish to reduce the effect of unwanted input signals, called disturbances, on the output signal. We will show how we may design a control system to reduce the impact of disturbance signals. Of course, the benefits of a control system come with an attendant cost. We will demonstrate how the cost of using feedback in a control system is associated with the selection of the feedback sensor device. The chapter concludes with a system performance analysis of the Sequential Design Example: Disk Drive Read System.

4. Goal We extend the ideas of modeling to include control system characteristics: - sensitivity to model uncertainties, - steady-state errors, - transient response characteristics to input test signals, - disturbance rejection. Control Systems 4

5. Feedback control 5 Control Systems Negative feedbackNegative feedback

6. 6 Control Systems Figure: 04-01Figure: 04-01

7. Advantages of the closed-loop feedback control Decreased sensitivity of the system to variations in the parameters of the process Improved rejection of the disturbances Improved measurement noise attenuation Improved reduction of the steady-state error of the system Easy control and adjustment of the transient response 7 Control Systems

8. System sensitivity 8 Control Systems

9. System sensitivity 9 Control Systems

10. 10 Control Systems it confirms that the T changes by the same percentage as the process gain.it confirms that the T changes by the same percentage as the process gain.

11. 11 Control Systems Figure: 04-02Figure: 04-02

12. 12 Control Systems

13. The sensitivity of the feedback system to change in the G(s) 13 Control Systems

14. The sensitivity of the feedback system to change in the H(s) 14 Control Systems

15. 15 Control Systems Figure: 04-03abFigure: 04-03ab

16. Closed-loop control system 16 Control Systems

17. Closed-loop control system 17 Control Systems

18. 18 Control Systems

19. 19 Control Systems

20. 20 Control Systems Tracking the sun to obtain maximum power from a photovoltaic array. May be represented by Fig. 4.3 with H(s) = 1 and G(s)= 100/(? s + 1), where ? = 3 sec. Tracking the sun to obtain maximum power from a photovoltaic array. May be represented by Fig. 4.3 with H(s) = 1 and G(s)= 100/(? s + 1), where ? = 3 sec.

21. Sensitivity 21 Control Systems

22. Time-constant 22 Control Systems for Laplace Table (? s + 1) = ? (s +1/?)for Laplace Table (? s + 1) = ? (s +1/?)

23. Step responses 23 Control Systems

24. 24 Control Systems Compute : T(s), Tracking error E(s) = R(s) - Y(s), Steady state tracking error due to a unit step input, R(s) = 1/s, Transfer function Y(s)/Td(s) of the output due to a unit step disturbance input Td(s) =1/s Sensitivity T(s,K)Compute : T(s), Tracking error E(s) = R(s) - Y(s), Steady state tracking error due to a unit step input, R(s) = 1/s, Transfer function Y(s)/Td(s) of the output due to a unit step disturbance input Td(s) =1/s Sensitivity T(s,K)

25. The transfer function 25 Control Systems

26. Tracking error 26 Control Systems

27. The steady-state error 27 Control Systems

28. Sensitivity 28 Control Systems

29. 29 Control Systems Is to be controlled so that it closes to an angle ? by using a DC motor system. Determine: the response ?(t) to a step change in ?d(t) when K = 20 Find the effect of a load disturbance Td(s0 = A/s Determine the steady state err or essr when the input is r(t) t, t>0 ( assume that Td(s) = 0)Is to be controlled so that it closes to an angle ? by using a DC motor system. Determine: the response ?(t) to a step change in ?d(t) when K = 20 Find the effect of a load disturbance Td(s0 = A/s Determine the steady state err or essr when the input is r(t) t, t>0 ( assume that Td(s) = 0)

30. ECE 3151 Figure: 04-16 The DLR German Aerospace Center is developing an advanced robotic hand. The hand operator receives stereo video feedback and force feedback. This information is employed in conjunction with a data glove equipped with force feedback and an input devise to control robotFigure: 04-16 The DLR German Aerospace Center is developing an advanced robotic hand. The hand operator receives stereo video feedback and force feedback. This information is employed in conjunction with a data glove equipped with force feedback and an input devise to control robot

31. Control Systems 31

32. Transfer function 32 Control Systems

33. Disturbance 33 Control Systems

34. Final value 34 Control Systems

35. AP 4.3 The machine tool 35 Control Systems A machine tool is designed to follow a desired path so that r(t) = (1 - t) u(t) Determine: The steady-state error when r(t) is the desired path and Td(s)=0 Plot the error e(t) for r(t) for 0< t <10 sec Find the steady -state error when Td(s) = 1/s and r(t) = 0 Plot the error e(t) for previous partA machine tool is designed to follow a desired path so that r(t) = (1 - t) u(t) Determine: The steady-state error when r(t) is the desired path and Td(s)=0 Plot the error e(t) for r(t) for 0< t <10 sec Find the steady -state error when Td(s) = 1/s and r(t) = 0 Plot the error e(t) for previous part

36. Error plot 36 Control Systems

37. 37 Control Systems

38. 38 Control Systems

39. 39 Control Systems Figure: 04-38-34UNAP4.6Figure: 04-38-34UNAP4.6

40. 40 Control Systems

41. 41 Control Systems

42. 42 Control Systems

43. 43 Control Systems

44. CP 4.3 Family of step responses 44 Control Systems

45. 45 Control Systems To regulate the level h in response to a disturbance change q3.To regulate the level h in response to a disturbance change q3.

46. 46 Control Systems

47. 47 Control Systems

48. 48 Control Systems The temperature T of the process is controlled by the heater with resistance RThe temperature T of the process is controlled by the heater with resistance R

49. Open-loop response of the system 49 Control Systems It is not a transfer function. Rather it is a Y(s). The linearized open-loop response of the system. Determine and compare the open-loop and closed-loop system for Sensitivity to changes to constant K=k1kaEb b) The ability to to reduce the effects of a step disturbance in the environmental temperature ?Te(s) c) The steady state error of the temperature controller for a step change in the input e-desired. It is not a transfer function. Rather it is a Y(s). The linearized open-loop response of the system. Determine and compare the open-loop and closed-loop system for Sensitivity to changes to constant K=k1kaEb b) The ability to to reduce the effects of a step disturbance in the environmental temperature ?Te(s) c) The steady state error of the temperature controller for a step change in the input e-desired.

50. 50 Control Systems

51. 51 Control Systems

52. 52 Control Systems

53. 53 Control Systems