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Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge

JSSI 10th Anniversary Symposium on Performance of Response Controlled Buildings. Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge. Kyu-Sik Park , Post-Doctoral Researcher , KAIST, Korea Hyung-Jo Jung, Assistant Professor , Sejong Univ., Korea

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Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge

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  1. JSSI 10th Anniversary Symposium on Performance of Response Controlled Buildings Robust Hybrid Control ofa Seismically Excited Cable-Stayed Bridge Kyu-Sik Park, Post-Doctoral Researcher, KAIST, Korea Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea Woon-Hak Kim, Professor, Hankyong National Univ., Korea In-Won Lee, Professor, KAIST, Korea

  2. Contents • Introduction • Robust hybrid control system • Numerical examples • Conclusions

  3. Introduction • Hybrid control system (HCS)  A combination of passive and active/semiactivecontrol 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/semiactivedevice or active/semiactive controller may cause instability due to small margins.

  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. 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.  Active control devices • Hydraulic actuators (HAs) • An actuator capacity has a capacity of 1000 kN. • The actuator dynamics are neglected.

  7. Control algorithm: -synthesis method Cost function (1) where : structured singular value : transfer function of closed-loop system : perturbation Advantages • Combine uncertainty in the design procedure • Guarantee the stability and performance (robust performance)

  8. Frequency dependent filters • Kanai-Tajimi filter (2)

  9. • High-pass and low-pass filters (3), (4)

  10. • Additive uncertainty filter (5) • Multiplicative uncertainty filter (6)

  11. LRB-installed structure -synthesis method Sensor HA Block diagram of robust hybrid control system

  12. Numerical Examples • 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.

  13. 142.7 m 350.6 m 142.7 m Configuration of control devices (LRBs+HAs)

  14. Pier 3 Bent 1 Pier 2 Pier 4 bottom view of bridge deck edge girder 4 actuators 2 actuators tower deck LRB Placement of control devices

  15.  Historical earthquake excitations PGA: 0.348g PGA: 0.143g PGA: 0.265g

  16.  Evaluation criteria - Max. responses J1: Base shear J2: Shear at deck level J3: Base moment J4: Moment at deck level J5: Cable deviation J6: Deck dis. - Normed responses J7: Base shear J8: Shear at deck level J9: Base moment J10: Moment at deck level J11: Cable deviation

  17. Analysis results  Control performances (a) STDs (b) RHCS Displacement under El Centro earthquake

  18. (a) STDs (b) RHCS Cable tension under El Centro earthquake

  19. (a) STDs (b) RHCS Base shear force under El Centro earthquake

  20. • 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.  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. • Stiffness matrix perturbation (7) where : nominal stiffness matrix : perturbed stiffness matrix : perturbation amount • Mass matrix perturbation · Additional snow loads (97.7 kg/m2, UBC) are added to the deck. • Time delay of actuator (8) where : time delay : time delay amount : sampling time (0.02 sec)

  23. Max. variation of evaluation criteria vs. variation of stiffness perturbation

  24. Max. variation of evaluation criteria vs. variation of time delay

  25. Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/o snow)

  26. Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/ snow)

  27. Conclusions • 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 could be used for cable-stayed bridges containing many uncertainties

  28. Acknowledgements • 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. Thank you for your attention!

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