1. Comparative Study on Performances of Various Semiactive Control Algorithms for Stay Cables 2004 년도 강구조공학회 학술발표대회 2004 년 6 월 5 일 장지은, 한국과학기술원 건설 및 환경공학과 석사과정 정형조, 세종대학교 토목환경공학과 조교수 윤우현, 경원대학교 산업환경대학원 부교수 이인원, 한국과학기술원 건설 및 환경공학과 교수

2. 2 Structural Dynamics & Vibration Control Lab., KAIST, Korea Introduction System Characteristics Control Algorithms Numerical Analysis Conclusions Contents

3. 3 Structural Dynamics & Vibration Control Lab., KAIST, Korea Introduction Cable Extremely low damping inherent in cables Proneness to vibration Necessity to mitigate cable vibration causing reduced cable and connection life

4. 4 Structural Dynamics & Vibration Control Lab., KAIST, Korea Several methods to mitigate cable vibration Tying multiple cables together Changes to cable roughness Discrete passive viscous dampers Active transverse and/or axial control Semiactive dampers

5. 5 Structural Dynamics & Vibration Control Lab., KAIST, Korea Control algorithms for semiactive technology Control strategy based on Lyapunov stability theory Decentralized bang-bang control Maximum energy dissipation algorithm Clipped-optimal control Modulated homogeneous friction control

6. 6 Structural Dynamics & Vibration Control Lab., KAIST, Korea Objectives Comparative study on performance of semiactive control strategies for vibration control of cable

7. 7 Structural Dynamics & Vibration Control Lab., KAIST, Korea System Characteristics Cable L T, m where, : transverse deflection of the cable : cable tension : transverse damper force at location : cable mass per unit length

8. 8 Structural Dynamics & Vibration Control Lab., KAIST, Korea Partial Differential Equation of Motion where, (1)

9. 9 Structural Dynamics & Vibration Control Lab., KAIST, Korea - Approximation of the transverse deflection using a finite series Solution by Series Approximation (2)

10. 10 10 Structural Dynamics & Vibration Control Lab., KAIST, Korea The static deflection shape function (3) - First shape function : mode shape induced by damper force

11. 11 11 Structural Dynamics & Vibration Control Lab., KAIST, Korea - Other shape functions : cable mode shape (4)

12. 12 12 Structural Dynamics & Vibration Control Lab., KAIST, Korea Standard Galerkin approach where, (5)

13. 13 13 Structural Dynamics & Vibration Control Lab., KAIST, Korea without magnetic fields with magnetic fields Semiactive Damper MR damper

14. 14 14 Structural Dynamics & Vibration Control Lab., KAIST, Korea t v v max - Change of voltage input - Various algorithms to determine the command voltage Semiactive mode

15. 15 15 Structural Dynamics & Vibration Control Lab., KAIST, Korea - equations governing the damper force (6) Bouc-Wen Shear-mode MR damper

16. 16 16 Structural Dynamics & Vibration Control Lab., KAIST, Korea Control Algorithms (8) (7) (9) Ideal clipped optimal control algorithm damper force Passive off voltage input Passive on voltage input

17. 17 17 Structural Dynamics & Vibration Control Lab., KAIST, Korea Modulated homogeneous friction algorithm voltage input (12) (10) (11) Control based on Lyapunov stability theory voltage input Maximum energy dissipation alogorithm voltage input Clipped-optimal control algorithm voltage input (13)

18. 18 18 Structural Dynamics & Vibration Control Lab., KAIST, Korea parametersvaluesparametersvalues L12.65 m m0.747 kg/m T2172 N2.89 Hz Numerical Analysis Parameters for the flat-sag cable model Tested by Christenson

19. 19 19 Structural Dynamics & Vibration Control Lab., KAIST, Korea 항목상수 값항목상수 값 125 70 700 70 50 Parameters for the shear-mode MR damper Tested by Christenson

20. 20 20 Structural Dynamics & Vibration Control Lab., KAIST, Korea Damper Capacity Maximum damper force = 10 N Maximum voltage input = 3 V

21. 21 21 Structural Dynamics & Vibration Control Lab., KAIST, Korea External Load Distributed load (14)

22. 22 22 Structural Dynamics & Vibration Control Lab., KAIST, Korea Gaussian white noise process Wind load ( 3rd generation benchmarks for building) Wind load (N/m) Time (sec)

23. 23 23 Structural Dynamics & Vibration Control Lab., KAIST, Korea Performance of Various Control Algorithms Measurements - Max. displacement at mid-span - Max. displacement at quarter-span - RMS displacement - RMS velocity

24. 24 24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Ideal clipped passive off passive on Lyapunov MEDA clipped optimal MHF Max. Displ. (midspan) 0.320.660.490.420.47 0.44 Max. Displ. (quartspan) 0.320.680.570.450.530.570.60 RMS Displ. 0.250.530.370.36 0.400.38 RMS Velocity 0.260.870.580.540.510.560.58 Gaussian white noise process - normalized value by uncontrolled case

25. 25 25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Normalized value Ideal clipped Passive off passive on LyapunovMEDA clipped optimal MHF

26. 26 26 Structural Dynamics & Vibration Control Lab., KAIST, Korea Wind load ( 3rd generation benchmarks for building) - normalized value by uncontrolled case Ideal clipped passive off passive on Lyapunov MEDA clipped optimal MHF Max. Displ. (midspan) 0.310.490.360.340.36 0.38 Max. Displ. (quartspan) 0.300.510.40 0.440.380.40 RMS Displ. 0.200.390.250.270.280.290.26 RMS Velocity 0.190.560.35 0.340.360.35

27. 27 27 Structural Dynamics & Vibration Control Lab., KAIST, Korea Normalized value Ideal clipped Passive off Passive on LyapunovMEDA Clipped optimal MHF

28. 28 28 Structural Dynamics & Vibration Control Lab., KAIST, Korea Conclusions Several recently proposed semiactive control algorithms have been evaluated for application in cable vibration control using shear-mode MR dampers Semi-active dampers significantly improved mitigation of stay cable vibration over uncontrolled case Control algorithm based on Lyapunov stability theory is most efficient control strategy for control of stay cable vibration with gaussian white noise process among the evaluated control algorithms