Control of a Hybrid System using a -Synthesis Method 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

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

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

Objective of this study Apply a -synthesis method to improve the controller robustness of HCS Structural Dynamics & Vibration Control Lab., KAIST

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

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

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

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

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

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

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

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

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

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

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

Analysis results  Maximum evaluation criteria for all the three earthquakes Evaluation criteria Passive Active Semiactive Hybrid I Hybrid II J1. Max. base shear 0.546 0.523 0.468 0.485 0.497 J2. Max. deck shear 1.462 1.146 1.283 0.921 1.170 J3. Max. base moment 0.619 0.416 0.443 0.454 J4. Max. deck moment 1.266 0.821 1.184 0.656 0.752 J5. Max. cable deviation 0.208 0.154 0.219 0.143 0.144 J6. Max. deck dis. 3.830 1.465 3.338 1.553 1.117 J7. Norm base shear 0.421 0.368 0.370 0.377 0.360 J8. Norm deck shear 1.550 1.005 1.351 0.899 0.976 J9. Norm base moment 0.482 0.316 0.404 0.338 0.307 J10. Norm deck moment 1.443 0.682 1.607 0.728 0.617 J11. Norm cable deviation 0.022 0.016 0.019 0.017 0.015 Passive: LRB, Active: HA/, Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/ Structural Dynamics & Vibration Control Lab., KAIST

Analysis results  Maximum evaluation criteria for all the three earthquakes Evaluation criteria Passive Active Semiactive Hybrid I Hybrid II J1. Max. base shear 0.546 0.523 0.468 0.485 0.497 J2. Max. deck shear 1.462 1.146 1.283 0.921 1.170 J3. Max. base moment 0.619 0.416 0.443 0.454 J4. Max. deck moment 1.266 0.821 1.184 0.656 0.752 J5. Max. cable deviation 0.208 0.154 0.219 0.143 0.144 J6. Max. deck dis. 3.830 1.465 3.338 1.553 1.117 J7. Norm base shear 0.421 0.368 0.370 0.377 0.360 J8. Norm deck shear 1.550 1.005 1.351 0.899 0.976 J9. Norm base moment 0.482 0.316 0.404 0.338 0.307 J10. Norm deck moment 1.443 0.682 1.607 0.728 0.617 J11. Norm cable deviation 0.022 0.016 0.019 0.017 0.015 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

 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

• Stiffness matrix perturbation • Time delay of actuator (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) Structural Dynamics & Vibration Control Lab., KAIST

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

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

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

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

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

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

Thank you for your attention! 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