1. Slide# 1 212 Ketter Hall, North Campus, Buffalo, NY 14260 www.civil.buffalo.edu Fax: 716 645 3733 Tel: 716 645 2114 x 2400 Control of Structural Vibrations Lecture #7_2 Active Control - Special Algorithms Instructor: Andrei M. Reinhorn P.Eng. D.Sc. Professor of Structural Engineering

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3. Slide# 3 Issues in Active Control  Control Logic - Algorithms  Control Considerations - Stability, etc.  Control Implementations - Force Generation  Physical Implementations  Full Scale Implementations

4. Slide# 4 Control Considerations  Stability  Controllability  Observability

5. Slide# 5 Reduced Order Models

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7. Slide# 7 Stability of Control  Addition of energy to system  Control may produce “negative” damping

8. Slide# 8 Stability of Control

9. Slide# 9 Stability of Control

10. Slide# 10 Stability of Control

11. Slide# 11 Stability of Control

12. Slide# 12 Stability of Control

13. Slide# 13 Stability of Control

14. Slide# 14 Controllability Is it possible to modify the state (displacement and velocity) of system under the control input? For: R must have rank n n x nm

15. Slide# 15 Controllability

16. Slide# 16 Controllability

17. Slide# 17 Controllability above

18. Slide# 18 Observability Is it possible to determine the state, z, variables if the control forces, u, and the output vector, y, is known Must have rank n rn x n

19. Slide# 19 Observability

20. Slide# 20 Issues in Active Control  Control Logic - Algorithms  Control Considerations - Stability, etc.  Control Implementations - Force Generation  Physical Implementations  Full Scale Implementations

21. Slide# 21 Control Implementations  Force Generation  Time Delay  Robustness

22. Slide# 22 Time Delay Effect

23. Slide# 23 Time Delay Effect

24. Slide# 24 Time Delay Effect

25. Slide# 25 Time Delay Effect

26. Slide# 26 Time Delay Effect

27. Slide# 27 Time Delay Effect

28. Slide# 28 Time Delay Effect

29. Slide# 29 Time Delay in Feedback Vectors

30. Slide# 30 Time Delay Compensation

31. Slide# 31 Time Delay - Phase Lag  =   or  [sec]=  /2  f [Hz]

32. Slide# 32 Issues in Active Control  Control Logic - Algorithms  Control Considerations - Stability, etc.  Control Implementations - Force Generation  Physical Implementations  Full Scale Implementations

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34. Slide# 34 Three Stories Controlled Model

35. Slide# 35 Active Tendon System

36. Slide# 36 Control Equipment

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38. Slide# 38 Structural Properties

39. Slide# 39 Instrumentation

40. Slide# 40 Control System of Three Stories Structure

41. Slide# 41 Control Properties

42. Slide# 42 Transfer Functions

43. Slide# 43 Challenges

44. Slide# 44 First Floor Response

45. Slide# 45 Second Floor Response

46. Slide# 46 Third Floor Response

47. Slide# 47 First Floor Response

48. Slide# 48 Second Floor Response

49. Slide# 49 Third Floor Response

50. Slide# 50 Summary of Three Stories Model - System Uncontrolled Controlled Modal Frequencies 2.24 2.25 (Hz) 6.83 6.54 11.5311.56 Modal Damping 1.8212.77 Factors (%) 0.5912.27 0.36 5.45

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58. Slide# 58 Characteristics of Six Stories Model - System

59. Slide# 59 Six Stories Model - Control Configurations

60. Slide# 60 Six Stories Model - Control Configurations ExperimentalSimulations

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64. Slide# 64 Comparison of AMD abd ATS/ABS

65. Slide# 65 Estimates of Full Scale

66. Slide# 66 Issues in Active Control  Control Logic - Algorithms  Control Considerations - Stability, etc.  Control Implementations - Force Generation  Physical Implementations  Full Scale Implementations

67. Slide# 67 Full Scale Implementations

68. Slide# 68 Full Scale Implementations

69. Slide# 69 Six Story Test Structure

70. Slide# 70 ABS Actuator Detail

71. Slide# 71 Control System Components

72. Slide# 72 Significant Results  System operational for one year.  Verified with forced vibrations.  Subjected to three earthquakes. –Magnitudes of 4.9 to 5.6.  System performed well. –Moderate reduction of the peak response. –Excellent reduction of the RMS intensity of the response.  Not operational during fourth earthquake due to a hardware failure.

73. Slide# 73 Response of Controlled Structure

74. Slide# 74 Lessons Learned  Active bracing systems can be implemented with current technology.  System has reasonable energy requirements.  Need for improvements: –Linear controller not effective on first response peak. –Need redundancy in the control hardware.  Learned a great deal about computer and digital hardware communication.

75. Slide# 75 Control Algorithms  Method 1: Optimal Control  Method 2: Poles Assignment  Method 3: Instantaneous optimum  Method 4: Independent Modal Space Control  Method 5: Bounded State Control  Method 6: H 2 and H  Control Method 6: H 2 and H  Control  Method 7: Sliding Mode Control  Method 8: Fuzzy Logic Control

76. Slide# 76 Control Algorithms  Method 1: Optimal Control  Method 2: Poles Assignment  Method 3: Instantaneous optimum  Method 4: Independent Modal Space Control  Method 5: Bounded State Control  Method 6: H 2 and H  Control  Method 7: Sliding Mode Control Method 7: Sliding Mode Control  Method 8: Fuzzy Logic Control

77. Slide# 77 Control Algorithms  Method 1: Optimal Control  Method 2: Poles Assignment  Method 3: Instantaneous optimum  Method 4: Independent Modal Space Control  Method 5: Bounded State Control  Method 6: H 2 and H  Control  Method 7: Sliding Mode Control  Method 8: Fuzzy Logic Control

78. Slide# 78 Linear and Nonlinear Control