Presentation on theme: "MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법"— Presentation transcript:
1 MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법 한국전산구조공학회 춘계 학술발표회서울대학교, 서울2002년 4월 13일MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법정형조, 한국과학기술원 건설환경공학과문영종, 한국과학기술원 건설환경공학과고만기, 공주대학교 토목공학과이인원, 한국과학기술원 건설환경공학과
2 OUTLINE Introduction Benchmark Problem Statement Seismic Control System Using MR DampersNumerical Simulation ResultsConclusions
3 INTRODUCTIONThe 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 strategiesReliability of passive control devicesVersatility and adaptability of fully active control systemAttractive featuresBounded-input, bounded-output stabilitySmall 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 BENCHMARK PROBLEM STATEMENT Benchmark Bridge ModelUnder construction in Cape Griardeau, Missouri, USA.To be completed in 2003.636 m570 mMissouri Side350 m main span142m side span128 CablesIllinois Approach12 additional piers570 m
9 Control Design Problem Longitudinal excitation applied simultaneously.For proposed controllers, designers must defineSensor models and locationsDevice models and locationsControl algorithmK(s)
10 Historical Earthquakes Considered El CentroPGA = 0.36g
11 Historical Earthquakes Considered El CentroPGA = 0.36gMexico CityPGA = 0.14g
12 Historical Earthquakes Considered El CentroPGA = 0.36gMexico CityPGA = 0.14gGebze TurkeyPGA = 0.26g
13 Evaluation Criteria Peak Responses (J1 – J6) Base shear – Shear at deck levelOverturning moment – Moment at deck levelCable tensionDeck displacement at abutmentNormed Responses (J7 – J11)Base shear – Shear at deck levelOverturning moment – Moment at deck levelCable tensionControl Strategy (J12 – J18)Peak control force and device strokePeak and total power requiredNumber of control devices and sensors
14 SEISMIC CONTROL SYSTEM USING MR DAMPERS SensorsFive accelerometersFour displacement transducers24 force transducers for measuring control forcesControl Devices24 MR dampers (capacity: 1000 kN/each)
15 Dynamic Model of MR Dampers Previous methods: based on the small-scale damperBingham 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
16 Dynamic Model of MR Dampers Previous methods: based on the small-scale damperBingham 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
17 Modified Bouc-Wen Model (Spencer et al. 1997) Control force:where,andFirst-order filter:
18 Optimized Parameters of Dynamic Model for MR Dampers ParameterValuea46.2 kN/mk00.002 kN/mb41.2 kN/m/Vk1kN/mc0a110 kNs/m164 m-2c0b114 kNs/m/Vc1a8359 kNs/mA1107.2c1b7483 kNs/m/Vn2x00.0 m100
21 Physical Structure Detailed F.E. Model Evaluation Model ~ DOFEvaluation Model~ DOF
22 Physical Structure Detailed F.E. Model Evaluation Model ~ DOFEvaluation Model~ DOFControl Design Model~ DOF
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 Control Strategy for Semiactive Control Control LawMRDamperStructureDecisionBlockNominalController
25 Control Strategy for Semiactive Control Alternatively, H¥, Cumulant Control, Risk Sensitive, etc., can be employed.LQG / H2 Linear Output Feedback ControllerControl LawMRDamperStructureDecisionBlockNominalController
26 Control Strategy for Semiactive Control Control LawMRDamperStructureDecisionBlockNominalControllerClipped-Optimal Controlu = 0u = umax
27 Weighting Parameters for Semiactive Control Performance Indexwhere Q: Response weighing matrixR: Control force weighting matrix (identity matrix)Appropriate Weighting Parameters by Stochastic Response AnalysesOverturning 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.
28 NUMERICAL SIMULATIONS Comparison MethodsIdeal active controlIdeal semiactive controlPassive control using MR dampersPassive-off (command signal u = 0 Volts)Passive-on (command signal u = 10 Volts)Semiactive control using MR dampersValues of Optimized Weighting ParametersQover_mom = 6×10-9; Qdeck_disp = 6×103
29 Time-History Responses (Base Shear Force) El Centro earthquake: 71% reduction in peakGebze Turkey earthquake: 64% reduction in peakkNMexico City earthquake: 54% reduction in peak
30 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.
31 Maximum Evaluation Criteria (Normed Responses) This slide is for normed responses.It shows the similar results to the peak responses case.
32 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.
34 CONCLUSIONSA 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.