1. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-1 (p. 235) Basic time-domain test signals for control systems. (a) Step function. (b) Ramp-function. (c) Parabolic function.

2. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-2 (p. 236) Typical unit-step response of a control system illustrating the time-domain specifications.

3. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-3 (p. 238) Nonunity feedback control system.

4. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-4 (p. 239) System with disturbance input.

5. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-5 (p. 240) Typical steady-state error due to a step input.

6. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-6 (p. 241) Typical steady-state error due to a ramp-function input.

7. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-7 (p. 242) Typical steady-state error due to a parabolic-function input.

8. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-8 (p. 249) Typical input-output characteristics of an amplifier with dead zone and saturation.

9. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-9 (p. 250) Typical input-output characteristics of a quantizer.

10. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-10 (p. 250) Torque-angle curve of a motor or closed-loop system with Coulomb friction.

11. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-11 (p. 251) State diagram of the speed control of a first-order dc motor system.

12. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-12 (p 252) Unit-step responses of a first-order dc motor speed-control system.

13. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-13 (p. 252) Pole configuration of the transfer function of a first-order dc motor speed- control system.

14. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-14 (p. 253) Prototype second-order control system.

15. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-15 (p. 254) Unit-step responses of the prototype second-order system with various damping ratios.

16. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-16 (p. 255) Relationship between the characteristic-equation roots of the prototype second-order system and α, ζ, ω n, and ω.

17. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-17 (p. 256) (a) Constant-natural-undamped-frequency loci. (b) Constant-damping-ratio loci. (c) Constant-damping-factor loci. (d) Constant-conditional-frequency loci.

18. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-18 (p. 257) Locus of roots of the characteristic equation of the prototype second-order system. Eq. (7-94), when ω n is held constant while the damping ratio is varied from (–  to  ).

19. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-19 (p. 258) Step-response comparison for various characteristic-equation- root locations in the s-plane.

20. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-20 (p. 259) Unit-step response illustrating that the maxima and minima occur at periodic intervals.

21. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-21 (p. 260) Percent overshoot as a function of damping ratio for the step response of the prototype second-order system.

22. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-22 (p. 260) Normalized delay time versus ζ for the prototype second-order system.

23. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-23 (p. 261) Normalized rise time versus ζ for the prototype second-order system.

24. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-24 (p. 262) Settling time of the unit-step response.

25. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-24 (cont., p. 263)

26. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-25 (p. 265) Block diagram of an attitude-control system of an aircraft.

27. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-26 (p. 266) Transfer-function block diagram of the system shown in Fig. 7-25.

28. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-27 (p. 269) Unit-step responses of the attitude-control system in Fig. 7-26; L a = 0.

29. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-28 (p. 270) Root loci of the characteristic equation in Eq. (7-129) as K varies.

30. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-29 (p. 272) Unit-ramp responses of the attitude-control system in Fig. 7-26; L a = 0.

31. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-30 (p. 274) Root loci of the third-order attitude-control system.

32. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-31 (p. 275) Unit-step responses of the third-order attitude-control system.

33. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-32 (p. 277) Unit-step responses of the system with the closed-loop transfer function in Eq. (7-155): ζ = 1, ω n = 1, and T p = 0, 1, 2, and 5.

34. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-33 (p. 278) Unit-step responses of the system with the closed-loop transfer function in Eq. (7-155); ζ = 0.25, ω n = 1, and T p = 0, 0.2, 0.667, and 1.0.

35. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-34 (p. 278) Unit-step responses of the system with the closed-loop transfer function in Eq. (7-156); ζ = 0.5, ω n = 1, and T p = 0, 0.5, 1.0, 2.0, and 4.0.

36. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-35 (p. 279) Unit-step responses of the system with the closed-loop transfer function in Eq. (7-157); T z = 0, 1, 2, 3, 6, and 10.

37. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-36 (p. 280) Unit-step responses showing the effect of adding a zero to the closed-loop transfer function.

38. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-37 (p. 280) Unit-step responses of the system with the closed-loop transfer function in Eq. (7-161); T z = 0, 0.2, 0.5, 2, 5, and 10.

39. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-38 (p. 281) Regions of dominant and insignificant poles in the s-plane.

40. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-39 (p. 282) Regions of dominant and insignificant poles in the s-plane for design purposes.

41. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-40 (p. 287) Approximation of a third-order system by a first-order system and a second-order system.

42. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-41 (p. 289) Approximation of a third-order system by a second-order system.

43. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-42 (p. 290) Approximation of a third-order system by a second-order system.

44. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-43 (p. 290) Approximation of a third-order system by a second-order system.

45. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-44 (p. 291) Approximation of a third-order system by a second-order system.

46. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-45 (p. 292) Comparison of the unit-step responses of the system in Example 7-11.

47. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-46 (p. 294) Main GUI for Time Response Tool.

48. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-47 (p. 295) (a) Transfer Function Input window. (b) Entering transfer function G after clicking the G button.

49. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-48 (p. 296) Closed-loop system transfer function in polynomial form and system poles- zeros form.

50. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-50 (p. 298) (a) Unit-step response of the closed- loop system, (b) Unit-ramp response.

51. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-51 (p. 300) (a) Root locus of Eq. (7-201), (b) G and H poles and zeros.

52. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-52 (p. 301) (a) Unit-step response of Eq. (7-201) for K = 1; (b) poles and zeros of Eq. (7-201) for K = 1.

53. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-53 (p. 302) (a) Root locus of Eq. (7-201); (b) poles and zeros of (7-201) for K = 181.2.

54. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-54 (p. 303) (a) The unit-step response of Eq. 7-200 for K = 180.2, (b) the Property Editor window for the response characteristics.

55. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-56 (p. 304) Adding a real pole at s = 10 6 to the open-loop system.

56. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-57 (p. 305) (a) Root locus of the third-order system with an added pole at s = 106, (b) poles and zeros for K = 181.2.

57. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-58 (p. 306) Unit-step response of the third-order system with an added pole at s = -10 6.

58. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-59 (p. 306) Unit-step response of the third-order system with an added pole at s = -2000.

59. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-7 (p. 310)

60. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-10 (p. 310)

61. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-11 (p. 311)

62. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-12 (p. 311)

63. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-23 (p. 312)

64. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-25 (p. 313)

65. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-26 (p. 313)

66. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-28 (p. 314)

67. Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7P-29 (p. 315)