Control of a Hybrid System using μ-Synthesis Method

1. 2004. 10. 21. 2004년도 학술발표회 Session B1 : 동적해석내진설계 I -합성법을 이용한 복합시스템의 제어 Control of a Hybrid System using a -Synthesis Method 박규식, 한국과학기술원 건설 및 환경공학과 박사 후 연수과정 윤우현,경원대학교 산업환경대학원 부교수 고만기,공주대학교 토목공학과 교수 이인원,한국과학기술원 건설 및 환경공학과 교수

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

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

4. Objective of this study Apply a -synthesis method to improve the controller robustness of HCS 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  Active control devices • Hydraulic actuators (HAs) • An actuator capacity has a capacity of 1000 kN. • The actuator dynamics are neglected. Structural Dynamics & Vibration Control Lab., KAIST

6. 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) Shortcomings • Nonconvex problem • Large controller size Structural Dynamics & Vibration Control Lab., KAIST

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

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

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

10. Wu MUX Wz P noise K Block diagram of -controller with various filters Structural Dynamics & Vibration Control Lab., KAIST

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

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. Structural Dynamics & Vibration Control Lab., KAIST

13. 142.7 m 350.6 m 142.7 m : Accelerometer : Displacement sensor Configuration of sensors Structural Dynamics & Vibration Control Lab., KAIST

14. Configuration of control devices (LRBs+HAs) Structural Dynamics & Vibration Control Lab., KAIST

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

16. Analysis results  Maximum evaluation criteria for all the three earthquakes Passive: LRB, Active: HA/, Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/ Structural Dynamics & Vibration Control Lab., KAIST

17. Analysis results  Maximum evaluation criteria for all the three earthquakes The performance of robust hybrid control system - better than that of passive, active, semiactive control systems - similar to that of performance-oriented hybrid control system Passive: LRB, Active: HA/, Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/ Structural Dynamics & Vibration Control Lab., KAIST

18.  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. Structural Dynamics & Vibration Control Lab., KAIST

19. : nominal stiffness matrix : perturbed stiffness matrix : perturbation amount : time delay : time delay amount : sampling time (0.02 sec) • Stiffness matrix perturbation (7) where • Mass matrix perturbation · additional snow loads (97.7 kg/m2, UBC) are added to the deck. • Time delay of actuator (8) where Structural Dynamics & Vibration Control Lab., KAIST

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

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

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

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

24. The hybrid system controlled by a -synthesis method - shows good robustness w.r.t perturbation of stiffness and mass matrices and time delay of actuator - robustness is more affected by perturbation of stiffness matrix than others. Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow) Structural Dynamics & Vibration Control Lab., KAIST

25. Conclusions • Hybrid control system with a -synthesis method  Has excellent robustness without loss of control performances  Could effectively be used to seismically excited cable- stayed bridges which contains many uncertainties Structural Dynamics & Vibration Control Lab., KAIST

26. 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. Thank you for your attention! Structural Dynamics & Vibration Control Lab., KAIST