1. HYBRID SYSTEM CONTROLLED BY A  -SYNTHESIS METHOD International Symposium on Earthquake Engineering Commemorating 10 th Anniversary of the 1995 Kobe Earthquake Kyu-Sik Park, Post-Doctoral Researcher, KAIST, Korea Namihiko Inoue, Senior Researcher, BRI, Japan Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea In-Won Lee, Professor, KAIST, Korea

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  -synthesis method to improve the controller robustness

5. Structural Dynamics & Vibration Control Lab., KAIST 5 Robust Hybrid Control System (RHCS) 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)

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) RHCS

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

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

20. Structural Dynamics & Vibration Control Lab., KAIST 20 PassiveActiveSemiactiveHybrid IHybrid II Max. dis (cm) 0.27450.1054 0.1091 0.11170.0804 Max. deck shear (kN) 55334344 5206 33754408 Max. base moment (kN  m) 349754249586 267714 244316244582 Max. (T max /T f ) 0.47730.4561 0.4611 0.45860.4556 Min. (T min /T f ) 0.27050.2822 0.2774 0.28530.2821 Max. (  T) 784453 527 453438 Max. control force (kN) 11021000 13381493 Normed control force (kN)11014112112093 Important responses of bridge and the peak and normed control forces for all the three earthquakes T f : failure tension of cable Passive: LRB, Active: HA/ , Semiactive: MRD/ , 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 evaluation and design 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 and time delay (w/o snow)

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

27. Structural Dynamics & Vibration Control Lab., KAIST 27 Robust hybrid control system  Control performance is improved consuming similar control forces.  Has excellent robustness without loss of control performances  could be used for cable-stayed bridges containing many uncertainties Conclusions

28. Structural Dynamics & Vibration Control Lab., KAIST 28 Thank you for your attention! This presentation is supported by the Japan Association for Earthquake Engineering (JAEE). Acknowledgements