MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법 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

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

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).

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

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

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

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

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

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

Historical Earthquakes Considered El Centro PGA = 0.36g

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

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

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

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)

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

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) Control force: where , and First-order filter:

Optimized Parameters of Dynamic Model for MR Dampers   Parameter Value a 46.2 kN/m k0 0.002 kN/m b 41.2 kN/m/V k1 0.0097 kN/m c0a 110 kNs/m  164 m-2 c0b 114 kNs/m/V  c1a 8359 kNs/m A 1107.2 c1b 7483 kNs/m/V n 2 x0 0.0 m  100

Physical Structure

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

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

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

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

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

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

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

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) In this study, the following performance index is considered. In this equation, Q means the response weighting matrix and R is the control force weighting matrix, here assumed an identity matrix. To design well performed controllers, we have to obtain the appropriate weighting parameters. In this study, the appropriate weighting parameters were obtained by stochastic response analyses. Following the extensive parametric study, this combination of weighting parameters are considered: That is, the combination of overturning moment and deck displacement.

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

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

Maximum Evaluation Criteria (Peak Responses) This slide shows the maximum evaluation criteria for peak responses. Each bar represents each control case, like this. As you can see, proposed smart damping strategy shows better performance compared with Professor Dyke’s sample controller. And, the proposed method shows nearly the same performance as the active control case.

Maximum Evaluation Criteria (Normed Responses) This slide is for normed responses. It shows the similar results to the peak responses case.

Maximum Evaluation Criteria (Control Strategy) This slide shows the maximum evaluation criteria related to the control strategy. The control force of the proposed smart damping case is a little bit larger than that of Professor Dyke’s method. On the other hand, the stroke of the device is quite smaller than that of the Professor Dyke’s method.

Robustness to Earthquake Motion Intensities

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.