The Asian-Pacific Symposium on Structural Reliability and its Applications Seoul, Korea, August 18-20, 2004 Kyu-Sik Park Kyu-Sik Park, Ph. D. Candidate, KAIST, Korea Hyung-Jo Jung Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea Woon-Hak Kim Woon-Hak Kim, Professor, Hankyong Nat. Univ., Korea In-Won Lee In-Won Lee, Professor, KAIST, Korea Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 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  However, the robustness of HCS could be decreased by the active control devices.

Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 Objective of this study Apply robust control algorithms to improve the controller robustness of HCS

Structural Dynamics & Vibration Control Lab., KAIST, Korea 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 has a capacity of 1000 kN. The actuator dynamics are neglected.

Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 Control algorithm  RHCS I Primary control scheme · Linear quadratic Gaussian (LQG) algorithm Secondary control scheme · On-off type controller according to LRB’s responses

Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 Bridge Model Sensor LQG On-Off HA LRB MUX Block diagram of RHCS I

Structural Dynamics & Vibration Control Lab., KAIST, Korea 8  RHCS II H 2 control algorithm with frequency weighting filters Frequency weighting filters

Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 Bridge Model Sensor H2H2 HA LRB MUX Block diagram of RHCS II DM WgWg kgkg R WuWu WzWz Q K

Structural Dynamics & Vibration Control Lab., KAIST, Korea 10  RHCS III H  control algorithm with frequency weighting filters

Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 Numerical examples Analysis model  Bridge model Bill Emerson Memorial Bridge · Benchmark control problem (Dyke et al., 2003) · Located in Cape Girardeau, MO, USA · 16 shock transmission devices (STDs) are employed between the tower-deck connections.

Structural Dynamics & Vibration Control Lab., KAIST, Korea m350.6 m m Schematic of the Bill Emerson Memorial Bridge

Structural Dynamics & Vibration Control Lab., KAIST, Korea m350.6 m m Configuration of sensors : Accelerometer : Displacement sensor

Structural Dynamics & Vibration Control Lab., KAIST, Korea m350.6 m m Configuration of control devices (HAs+LRBs)

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 PGA: 0.348g PGA: 0.143g  Historical earthquake excitations

Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 PGA: 0.348g PGA: 0.143g PGA: 0.265g  Historical earthquake excitations

Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 J 1 /J 7 : Peak/Normed base shear J 2 /J 8 : Peak/Normed shear at deck level J 3 /J 9 : Peak/Normed overturning moment J 4 /J 10 : Peak/Normed moment at deck level J 5 /J 11 : Peak/Normed cable tension deviation J 6 : Peak Deck dis. at abutment  Evaluation criteria

Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 Analysis results  Control performances Displacement under El Centro earthquake (a) Uncontrolled(b) RHCS III

Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 Cable tension under El Centro earthquake (a) Uncontrolled(b) RHCS III

Structural Dynamics & Vibration Control Lab., KAIST, Korea 21 Shear force under El Centro earthquake (a) Uncontrolled(b) RHCS III

Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 Evaluation criteria CHCS * RHCS IRHCS IIRHCS III J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation1.707e e e e-2 Maximum evaluation criteria for all three earthquakes * Conventional HCS controlled by LQG algorithm

Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 Evaluation criteria CHCS * RHCS IRHCS IIRHCS III J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation1.707e e e e-2 Maximum evaluation criteria for all three earthquakes * Conventional HCS controlled by LQG algorithm

Structural Dynamics & Vibration Control Lab., KAIST, Korea 24  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 (  5% ~  20 %)

Structural Dynamics & Vibration Control Lab., KAIST, Korea 25 Maximum variations of evaluation criteria for all three earthquakes (%,  5% perturbation) Evaluation criteria RHCS IRHCS IIRHCS III J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation

Structural Dynamics & Vibration Control Lab., KAIST, Korea 26 Maximum variations of evaluation criteria for all three earthquakes (%,  20% perturbation) Evaluation criteria RHCS IIRHCS III J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation

Structural Dynamics & Vibration Control Lab., KAIST, Korea 27 Max. variation of evaluation criteria for variations of stiffness perturbation

Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 Conclusions Hybrid control system with robust control algorithms  Has excellent robustness for stiffness perturbation without loss of control performances RHCS I obtains robustness only for  5% stiffness perturbations. RHCS III is more robust than RHCS II.  Robust hybrid control system could effectively be used to seismically excited cable-stayed bridge.

Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST) and the Grant for Pre-Doctoral Students from the Korea Research Foundation (KRF) in Korea. Thank you for your attention! Acknowledgements