MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법

1. 한국전산구조공학회 춘계 학술발표회 서울대학교, 서울 2002년 4월 13일 MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법 정형조, 한국과학기술원 건설환경공학과 문영종,한국과학기술원 건설환경공학과 고만기, 공주대학교 토목공학과 이인원, 한국과학기술원 건설환경공학과

2. OUTLINE • Introduction • Benchmark Problem Statement • Seismic Control System Using MR Dampers • Numerical Simulation Results • Conclusions

3. INTRODUCTION • The control of cable-stayed bridges is a unique and challenging problem. • During the 2nd International Workshop on Structural Control (Hong Kong, 1996), a working group was formed to develop a benchmark control problem for bridges. • Dyke et al. have developed a benchmark control problem for seismically excited cable-stayed bridges (2000).

4. Semiactive Control Using MR Dampers • Magnetorheological (MR) fluid dampers: new class of semiactive control devices that utilize MR fluids to provide controllable damping forces.

5. Semiactive Control Using MR Dampers • Magnetorheological (MR) fluid dampers: new class of semiactive control devices that utilize MR fluids to provide controllable damping forces.

6. Semiactive Control Using MR Dampers • Magnetorheological (MR) fluid dampers: new class of semiactive control devices that utilize MR fluids to provide controllable damping forces. • MR damper-based control strategies • Reliability of passive control devices • Versatility and adaptability of fully active control system • Attractive features • Bounded-input, bounded-output stability • Small energy requirements

7. Objective of This Study: to investigate the effectiveness of semiactive control strategies using MR fluid dampers for seismic protection of cable-stayed bridges

8. 636 m 570 m BENCHMARK PROBLEM STATEMENT • Benchmark Bridge Model • Under construction in Cape Griardeau, Missouri, USA. • To be completed in 2003. • Missouri Side • 350 m main span • 142m side span • 128 Cables • Illinois Approach • 12 additional piers • 570 m

9. K(s) Control Design Problem • Longitudinal excitation applied simultaneously. • For proposed controllers, designers must define • Sensor models and locations • Device models and locations • Control algorithm

10. El Centro PGA = 0.36g Historical Earthquakes Considered

11. El Centro PGA = 0.36g Mexico City PGA = 0.14g Historical Earthquakes Considered

12. El Centro PGA = 0.36g Mexico City PGA = 0.14g Gebze Turkey PGA = 0.26g Historical Earthquakes Considered

13. Evaluation Criteria • Peak Responses (J1 – J6) • Base shear – Shear at deck level • Overturning moment – Moment at deck level • Cable tension • Deck displacement at abutment • Normed Responses (J7 – J11) • Base shear – Shear at deck level • Overturning moment – Moment at deck level • Cable tension • Control Strategy (J12 – J18) • Peak control force and device stroke • Peak and total power required • Number of control devices and sensors

14. SEISMIC CONTROL SYSTEM USING MR DAMPERS • Sensors • Five accelerometers • Four displacement transducers • 24 force transducers for measuring control forces • Control Devices • 24 MR dampers (capacity: 1000 kN/each)

15. Dynamic Model of MR Dampers • Previous methods: based on the small-scale damper • Bingham model (Stanway et al. 1985, 1987) • Simple Bouc-Wen model (Spencer et al. 1997) • Modified Bouc-Wen model (Spencer et al. 1997) • Proposed method: based on the large-scale damper • Modified Bouc-Wen model (Spencer et al. 1997)

16. Dynamic Model of MR Dampers • Previous methods: based on the small-scale damper • Bingham model (Stanway et al. 1985, 1987) • Simple Bouc-Wen model (Spencer et al. 1997) • Modified Bouc-Wen model (Spencer et al. 1997) • Proposed method: based on the large-scale damper • Modified Bouc-Wen model (Spencer et al. 1997)

17. Modified Bouc-Wen Model (Spencer et al. 1997) • Control force: where and , • First-order filter:

18. Optimized Parameters of Dynamic Model for MR Dampers

19. Physical Structure

20. Detailed F.E. Model ~ 105 - 106 DOF Physical Structure

21. Detailed F.E. Model ~ 105 - 106 DOF Evaluation Model ~ 102 - 103 DOF Physical Structure

22. Detailed F.E. Model ~ 105 - 106 DOF Evaluation Model ~ 102 - 103 DOF Control Design Model ~ 10- 102 DOF Physical Structure

23. Control Design Model • Reduced-Order Model (30 states) • By forming a balanced realization and condensing out the states with relatively small controllability and observability grammians

24. MR Structure Damper Decision Block Nominal Controller Control Law Control Strategy for Semiactive Control

25. LQG / H2 Linear Output Feedback Controller MR Structure Damper Alternatively, H¥, Cumulant Control, Risk Sensitive, etc., can be employed. Decision Block Nominal Controller Control Law Control Strategy for Semiactive Control

26. Clipped-Optimal Control MR Structure Damper u = 0 u = umax Decision u = 0 Block Nominal Controller Control Law Control Strategy for Semiactive Control

27. Weighting Parameters for Semiactive Control • Performance Index where Q: Response weighing matrix R: Control force weighting matrix (identity matrix) • Appropriate Weighting Parameters by Stochastic Response Analyses • Overturning moment (Qover_mom) • Deck displacement (Qdeck_disp)

28. NUMERICAL SIMULATIONS • Comparison Methods • Ideal active control • Ideal semiactive control • Passive control using MR dampers • Passive-off (command signal u = 0 Volts) • Passive-on (command signal u = 10 Volts) • Semiactive control using MR dampers • Values of Optimized Weighting Parameters • Qover_mom = 6×10-9;Qdeck_disp = 6×103

29. kN • El Centro earthquake: 71% reduction in peak kN • Mexico City earthquake: 54% reduction in peak kN • Gebze Turkey earthquake: 64% reduction in peak Time-History Responses(Base Shear Force)

30. Maximum Evaluation Criteria(Peak Responses)

31. Maximum Evaluation Criteria(Normed Responses)

32. Maximum Evaluation Criteria(Control Strategy)

33. Robustness to Earthquake Motion Intensities

34. CONCLUSIONS • A semiactive control strategy using MR dampers has been proposed for the benchmark bridge problem. • The performance of the proposed semiactive control design using MR dampers nearly achieves the same performance as that of the ideal active or semiactive control system. • MR dampers show great promise for response control of seismically excited cable-stayed bridges.