a Bang-Bang Type Controller 2003년도 한국전산구조공학회 봄 학술발표회 2003. 4. 12. Hybrid Control with a Bang-Bang Type Controller 박규식, 한국과학기술원 건설 및 환경공학과 박사과정 정형조, 세종대학교 토목환경공학과 조교수 조상원, 한국과학기술원 건설 및 환경공학과 박사과정 이인원, 한국과학기술원 건설 및 환경공학과 교수

Contents Introduction HCS with a bang-bang type controller Numerical examples Conclusions

Introduction Hybrid control system (HCS) Cable-stayed bridge  A combination of passive and active devices  Higher level of performance  Reliable and robust Cable-stayed bridge  Aesthetic shape, structural efficiency and economical construction  Very flexible due to low structural damping  Vibration control is needed to protect the bridge.

Objective of this study Apply robust hybrid control system for seismic protection of a cable-stayed bridge

HCS with a bang-bang type controller 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  Primary control scheme • Linear quadratic Gaussian (LQG) algorithm • Optimal weighting matrix: Maximum response approach  Secondary control scheme • Bang-Bang type controller according to LRB’s responses

Block diagram of hybrid control system Bridge Model HCS Block diagram of hybrid control system

Hybrid control with a bang-bang type controller Bridge Model Sensor LQG On/Off HA LRB MUX Hybrid control with a bang-bang type controller

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

: Accelerometer : Displacement sensor Location of sensor 142.7 m

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:

Analysis results  Control performances (a) Time-history response (b) Frequency response Base shear force record at pier 2 under El Centro earthquake

Restoring force record of LRB at pier 2

• Maximum evaluation criteria for all the three earthquakes Passive Active Hybrid J1. Max. base shear 0.5459 0.4898 0.5125 J2. Max. deck shear 1.4616 1.1706 0.9510 J3. Max. base moment 0.6188 0.4562 0.4439 J4. Max. deck moment 1.2656 0.8803 0.6737 J5. Max. cable deviation 0.2077 0.1469 0.1479 J6. Max. deck dis. 3.8289 1.8079 1.6787 J7. Norm base shear 0.4211 0.3820 0.3824 J8. Norm deck shear 1.5502 0.9737 0.9366 J9. Norm base moment 0.4815 0.3591 0.3435 J10. Norm deck moment 1.4429 0.7659 0.8196 J11. Norm cable deviation 2.233e-2 1.622e-2 1.718e-2

• Actuator requirements Earthquake Max. Active Hybrid 1940 El Centro NS Force(kN) 1000 Stroke(m) 0.0984 0.0740 Vel. (m/s) 0.5502 0.5480 1985 Mexico City 649.37 332.13 0.0403 0.0278 0.2452 0.2003 1990 Gebze NS 924.57 0.1300 0.1207 0.4197 0.4226 Actuator requirement constraints Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

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

*: Active control system using 32 HAs (-synthesis) • Maximum variations of evaluation criteria for the ±7% stiffness perturbation systems under El Centro earthquake (%) Evaluation criteria Turan (2001)* Active Hybrid J1. Max. base shear 36.9 9.1 J2. Max. deck shear 52.0 68.0 21.8 J3. Max. base moment 22.5 50.1 6.2 J4. Max. deck moment 31.0 27.3 5.1 J5. Max. cable deviation 9.2 7.0 5.6 J6. Max. deck dis. 19.0 16.3 2.3 J7. Norm base shear 47.4 196.4 7.2 J8. Norm deck shear 35.3 335.2 5.3 J9. Norm base moment 28.5 138.1 7.4 J10. Norm deck moment 18.7 84.5 13.3 J11. Norm cable deviation 31.3 71.0 17.1 *: Active control system using 32 HAs (-synthesis)

(a) Time-history response (b) Frequency response Base shear force record at pier 2 in the 7% stiffness perturbed bridge model under El Centro earthquake 23

 Could be used to seismically excited cable-stayed bridges Conclusions HCS with a bang-bang type controller  More effective than passive or active control system in reducing structural responses  Robust for stiffness matrix perturbation due to the passive control part and bang-bang type controller  Could be used to seismically excited cable-stayed bridges

Thank you for your attention! Acknowledgements This research is supported by the National Research Laboratory and Smart Infra-Structure Technology Center. Thank you for your attention!