1. 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

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. 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

9. 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)

10. Historical Earthquakes Considered
El Centro
PGA = 0.36g

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

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

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

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

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
Parameter
Value a
46.2 kN/m k0
0.002 kN/m b
41.2 kN/m/V k1
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

19. Physical Structure

20. Physical Structure Detailed F.E. Model
~ DOF

21. Physical Structure Detailed F.E. Model Evaluation Model
~ DOF
Evaluation Model
~ DOF

22. Physical Structure Detailed F.E. Model Evaluation Model
~ DOF
Evaluation Model
~ DOF
Control 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 Law MR
Damper
Structure
Decision
Block
Nominal
Controller

25. 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

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

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)
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 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. 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

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.

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.