1. Hybrid System Controlled by a  -Synthesis Method for a Seismically Excited Cable-Stayed Bridge 2004 추계 학술대회 소음진동분야 NRL 2 지진하중을 받는 사장교를 위한  - 합성법을 이용한 복합시스템 2004. 11. 19 박규식, 한국과학기술원 건설 및 환경공학과 박사 후 연수과정 문영종, 한국과학기술원 건설 및 환경공학과 박사과정 정형조, 세종대학교 토목환경공학과 교수 이종헌, 경일대학교 토목공학과 교수 이인원, 한국과학기술원 건설 및 환경공학과 교수

2. Structural Dynamics & Vibration Control Lab., KAIST 2 Introduction Robust hybrid control system Numerical examples Conclusions Contents

3. Structural Dynamics & Vibration Control Lab., KAIST 3 Introduction Hybrid control system (HCS)  A combination of passive and active/semiactive control devices Passive devices: insure the control system robustness Active/semiactive devices: improve the control performances  The overall system robustness may be negatively impacted by active/semiactive device or active/semiactive controller may cause instability due to small margins.

4. Structural Dynamics & Vibration Control Lab., KAIST 4 Objective  Apply a hybrid control system for vibration control of a seismically excited cable-stayed bridge  Apply a robust control algorithm to improve the controller robustness

5. Structural Dynamics & Vibration Control Lab., KAIST 5 Robust Hybrid Control System Control devices  Passive control devices Lead rubber bearings (LRBs) Design procedure: Ali and Abdel-Ghaffar (1995) Bouc-Wen model

6. Structural Dynamics & Vibration Control Lab., KAIST 6  Active control devices Hydraulic actuators (HAs) An actuator capacity has a capacity of 1000 kN. The actuator dynamics are neglected.

7. Structural Dynamics & Vibration Control Lab., KAIST 7 Control algorithm:  -synthesis method where : structured singular value : transfer function of closed-loop system : perturbation  Cost function (1)  Advantages Combine uncertainty in the design procedure Guarantee the stability and performance (robust performance)  Shortcomings Nonconvex problem Large controller size

8. Structural Dynamics & Vibration Control Lab., KAIST 8  Frequency dependent filters Kanai-Tajimi filter (2)

9. Structural Dynamics & Vibration Control Lab., KAIST 9 High-pass and low-pass filters (3), (4)

10. Structural Dynamics & Vibration Control Lab., KAIST 10 Additive uncertainty filter (5) Multiplicative uncertainty filter (6)

11. Structural Dynamics & Vibration Control Lab., KAIST 11 LRB-installed structure Sensor  -synthesis method HA Block diagram of robust hybrid control system

12. Structural Dynamics & Vibration Control Lab., KAIST 12 Analysis model  Bridge model Bill Emerson Memorial Bridge · Benchmark control problem · Located in Cape Girardeau, MO, USA · 16 shock transmission devices (STDs) are employed between the tower-deck connections. Numerical Examples

13. Structural Dynamics & Vibration Control Lab., KAIST 13 Configuration of control devices (LRBs+HAs) 142.7 m350.6 m 142.7 m

14. Structural Dynamics & Vibration Control Lab., KAIST 14 Bent 1 4 actuators 2 actuators Pier 2 Pier 3 Pier 4 bottom view of bridge deck edge girder tower deck LRB Placement of control devices

15. Structural Dynamics & Vibration Control Lab., KAIST 15 PGA: 0.348g PGA: 0.143g PGA: 0.265g  Historical earthquake excitations

16. Structural Dynamics & Vibration Control Lab., KAIST 16 - Max. responses J 1 : Base shear J 2 : Shear at deck level J 3 : Base moment J 4 : Moment at deck level J 5 : Cable deviation J 6 : Deck dis. - Normed responses J 7 : Base shear J 8 : Shear at deck level J 9 : Base moment J 10 : Moment at deck level J 11 : Cable deviation  Evaluation criteria

17. Structural Dynamics & Vibration Control Lab., KAIST 17 Analysis results  Control performances Displacement under El Centro earthquake (a) STDs(b) RHACS

18. Structural Dynamics & Vibration Control Lab., KAIST 18 Cable tension under El Centro earthquake (a) STDs(b) RHACS

19. Structural Dynamics & Vibration Control Lab., KAIST 19 Base shear force under El Centro earthquake (a) STDs(b) RHACS

20. Structural Dynamics & Vibration Control Lab., KAIST 20 Evaluation criteria PassiveActiveSemiactiveHybrid IHybrid II J 1. Max. base shear 0.5460.523 0.468 0.4850.497 J 2. Max. deck shear 1.4621.146 1.283 0.9211.170 J 3. Max. base moment 0.6190.416 0.485 0.4430.454 J 4. Max. deck moment 1.2660.821 1.184 0.6560.752 J 5. Max. cable deviation 0.2080.154 0.219 0.1430.144 J 6. Max. deck dis. 3.8301.465 3.338 1.5531.117 J 7. Norm base shear 0.4210.368 0.370 0.3770.360 J 8. Norm deck shear 1.5501.005 1.351 0.8990.976 J 9. Norm base moment 0.4820.316 0.404 0.3380.307 J 10. Norm deck moment 1.4430.682 1.607 0.7280.617 J 11. Norm cable deviation0.0220.0160.0190.0170.015 Maximum evaluation criteria for all the three earthquakes Passive: LRB, Active: HA/ , Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/ 

21. Structural Dynamics & Vibration Control Lab., KAIST 21  Controller robustness The dynamic characteristic of as-built bridge is not identical to the numerical model. There are large differences at high frequencies between full-order and reduced-order models. There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.  Robust analysis should be performed to verify the applicability of the control system

22. Structural Dynamics & Vibration Control Lab., KAIST 22 where: nominal stiffness matrix : perturbed stiffness matrix : perturbation amount Stiffness matrix perturbation Mass matrix perturbation · Additional snow loads (97.7 kg/m 2, UBC) are added to the deck. where: time delay : time delay amount : sampling time (0.02 sec) Time delay of actuator (7) (8)

23. Structural Dynamics & Vibration Control Lab., KAIST 23 Max. variation of evaluation criteria vs. variation of stiffness perturbation

24. Structural Dynamics & Vibration Control Lab., KAIST 24 Max. variation of evaluation criteria vs. variation of time delay

25. Structural Dynamics & Vibration Control Lab., KAIST 25 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/o snow)

26. Structural Dynamics & Vibration Control Lab., KAIST 26 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow)

27. Structural Dynamics & Vibration Control Lab., KAIST 27 Robust hybrid control system  Control performances is superior to passive control system and slightly better than active and semiactive control systems.  Has excellent robustness without loss of control performances Conclusions  could be used for cable-stayed bridges containing many uncertainties

28. Structural Dynamics & Vibration Control Lab., KAIST 28 Thank you for your attention! This research is supported by the National Research Laboratory program from the Ministry of Science of Technology and the Grant for Pre- Doctoral Students from the Korea Research Foundation in Korea. Acknowledgements