Robust Hybrid Control System 2003년도 한국지진공학회 추계 학술발표회 2003. 9. 19. Robust Hybrid Control System 박규식, 한국과학기술원 건설 및 환경공학과 박사과정 정형조, 세종대학교 토목환경공학과 조교수 오주원, 한남대학교 토목환경공학과 교수 이인원, 한국과학기술원 건설 및 환경공학과 교수

Contents Introduction Robust hybrid control system Numerical examples Conclusions

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  However, the robustness of HCS could be decreased by the active control devices.

Objective of this study Apply robust control algorithms to improve the controller robustness of HCS

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.

Control algorithm  RHCS I • Primary control scheme · Linear quadratic Gaussian (LQG) algorithm • Secondary control scheme · On-off type controller according to LRB’s responses

Bridge Model Sensor LQG On/Off HA LRB MUX Block diagram of RHCS I

 RHCS II • H2 control algorithm with frequency weighting filters • Frequency weighting filters

Block diagram of RHCS II Bridge Model Sensor H2 HA LRB MUX DM Wg kg R Wu Wz Q K Block diagram of RHCS II

 RHCS III • H control algorithm with frequency weighting filters

Numerical examples Analysis model  Bridge model • Bill Emerson Memorial Bridge · Benchmark control problem · Under construction in Cape Girardeau, MO, USA · 16 Shock transmission devices (STDs) are employed between the tower-deck connections.

Schematic of the Bill Emerson Memorial Bridge

Configuration of sensors 142.7 m 350.6 m : Accelerometer : Displacement sensor Configuration of sensors

Configuration of control devices (HAs+LRBs) 142.7 m 350.6 m 2+3 4+3 Configuration of control devices (HAs+LRBs)

 Historical earthquake excitations PGA: 0.348g

 Historical earthquake excitations PGA: 0.348g PGA: 0.143g

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

 Evaluation criteria • Structural response J1/J7 : Peak/Normed base shear J2/J8 : Peak/Normed shear at deck level J3/J9 : Peak/Normed overturning moment J4/J10 : Peak/Normed moment at deck level J5/J11 : Peak/Normed cable tension deviation J6: Deck dis. at abutment • Control strategy J12: Peak control force, J13: Device stroke J14: Peak power, J15: Total power J16: No. of control devices, J17: No. of sensors J18:

Displacement under El Centro earthquake Analysis results  Control performances (a) Uncontrolled (b) RHCS III Displacement under El Centro earthquake

Cable tension under El Centro earthquake (a) Uncontrolled (b) RHCS III Cable tension under El Centro earthquake

Base shear force under El Centro earthquake (a) Uncontrolled (b) RHCS III Base shear force under El Centro earthquake

• Maximum evaluation criteria for all the three earthquakes CHCS* RHCS I RHCS II RHCS III J1. Max. base shear 0.4841 0.4810 0.5319 0.4808 J2. Max. deck shear 0.9476 0.9508 0.9607 0.9579 J3. Max. base moment 0.4444 0.4426 0.5057 0.4380 J4. Max. deck moment 0.6750 0.6739 0.6441 0.5750 J5. Max. cable deviation 0.1468 0.1469 0.1252 0.1473 J6. Max. deck dis. 1.6702 1.6787 1.0652 1.1923 J7. Norm base shear 0.3744 0.3749 0.3929 0.3514 J8. Norm deck shear 0.9261 0.9352 0.7868 0.9301 J9. Norm base moment 0.3345 0.3389 0.3590 0.3132 J10. Norm deck moment 0.7806 0.8055 0.5404 0.7458 J11. Norm cable deviation 1.819e-2 1.769e-2 1.275e-2 1.782e-2 *Conventional HCS (HCS with LQG)

 Controller robustness • The dynamic characteristic of as-built bridge is not identical to the numerical model. • To verify the applicability of RHCS, the controller robustness is investigated to perturbation of stiffness parameter. where : nominal stiffness matrix : perturbed stiffness matrix : perturbation amount

Max. variation of evaluation criteria for variations of stiffness perturbation

• Maximum variations of evaluation criteria for all three earthquake (%, 5% perturbation) Evaluation criteria CHCS RHCS I RHCS II RHCS III J1. Max. base shear 9.75 10.34 9.20 7.69 J2. Max. deck shear 16.62 16.26 4.42 14.34 J3. Max. base moment 16.68 15.97 4.93 5.01 J4. Max. deck moment 4.46 5.37 6.21 8.91 J5. Max. cable deviation 13.08 14.22 13.96 15.68 J6. Max. deck dis. 7.51 4.06 1.48 3.52 J7. Norm base shear 50.00 6.54 6.12 7.02 J8. Norm deck shear 139.17 7.94 10.68 J9. Norm base moment 39.94 5.98 5.54 10.36 J10. Norm deck moment 42.15 10.37 7.56 21.82 J11. Norm cable deviation 41.32 18.65 13.78 30.31

• Maximum variations of evaluation criteria for all three earthquake (%, 20% perturbation) Evaluation criteria RHCS II RHCS III J1. Max. base shear 36.51 27.33 J2. Max. deck shear 22.93 38.66 J3. Max. base moment 33.08 30.86 J4. Max. deck moment 34.48 40.75 J5. Max. cable deviation 50.07 31.97 J6. Max. deck dis. 5.02 18.86 J7. Norm base shear 31.78 29.98 J8. Norm deck shear 39.33 35.21 J9. Norm base moment 29.70 32.17 J10. Norm deck moment 45.34 33.66 J11. Norm cable deviation 72.35 47.83

Conclusions Hybrid control system with robust control algorithms  Has excellent robustness for stiffness perturbation without loss of control performances  Could be used to seismically excited cable-stayed bridges

Thank you for your attention! Acknowledgements This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST). Thank you for your attention!