 - 합성법을 이용한 사장교의 지진응답 제어 년도 한국전산구조공학회 가을 학술발표회 박규식, 한국과학기술원 건설 및 환경공학과 박사후과정 정형조, 세종대학교 토목환경공학과 조교수 윤우현, 경원대학교 산업환경대학원 부교수 이인원, 한국과학기술원 건설 및 환경공학과 교수 Seismic Response Control of a Cable-Stayed Bridge using a  -Synthesis Method

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  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, Korea 4 Objective of this study Apply a  -synthesis method 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 capacity has a capacity of 1000 kN. The actuator dynamics are neglected.

Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 Control algorithm:  -synthesis method where : structured singular value : transfer function of closed-loop system : perturbation  Cost Function (1)  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, Korea 7  Design of Filters Kanai-Tajimi filter (2)

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

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

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

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 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, 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 15 Configuration of control devices (LRBs+HAs)

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

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 PGA: 0.348g PGA: 0.143g PGA: 0.265g  Historical earthquake excitations

Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 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 : Deck dis. at abutment  Evaluation criteria

Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 Analysis results  Control performances Displacement under El Centro earthquake (a) Uncontrolled(b) RHCS

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 Base shear force under El Centro earthquake (a) Uncontrolled(b) RHCS

Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 Evaluation criteria PassiveActiveSemiactiveHybrid IHybrid II 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 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, Korea 24 Maximum evaluation criteria for all the three earthquakes Passive: LRB, Active: HA/ , Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/  Evaluation criteria PassiveActiveSemiactiveHybrid IHybrid II 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 25 Maximum evaluation criteria for all the three earthquakes Passive: LRB, Active: HA/ , Semiactive: MRD/SMC, Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/  Evaluation criteria PassiveActiveSemiactiveHybrid IHybrid II 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 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea 26  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, Korea 27 where: nominal stiffness matrix : perturbed stiffness matrix : perturbation amount Stiffness matrix perturbation Mass matrix perturbation · additional snow loads (97.7 kg/m 2, UBC) are added to the deck. where: time delay : time delay amount : sampling time (0.02 sec) Time delay of actuator (7) (8)

Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 Max. variation of evaluation criteria vs. variation of stiffness perturbation

Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 Max. variation of evaluation criteria vs. variation of time delay

Structural Dynamics & Vibration Control Lab., KAIST, Korea 30 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay

Structural Dynamics & Vibration Control Lab., KAIST, Korea 31 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/o snow)

Structural Dynamics & Vibration Control Lab., KAIST, Korea 32 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow)

Structural Dynamics & Vibration Control Lab., KAIST, Korea 33 Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow) 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.

Structural Dynamics & Vibration Control Lab., KAIST, Korea 34 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, Korea 35 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.