1. 조상원 * : 박사과정, 한국과학기술원 건설환경공학과 조상원 * : 박사과정, 한국과학기술원 건설환경공학과 정형조 : 교수, 세종대학교 토목환경공학과 정형조 : 교수, 세종대학교 토목환경공학과 박선규 : 교수, 성균관대학교 토목공학과 박선규 : 교수, 성균관대학교 토목공학과 이인원 : 교수, 한국과학기술원 건설환경공학과 이인원 : 교수, 한국과학기술원 건설환경공학과 Maximum Energy Dissipation Algorithm 을 이용한 벤치마크 구조물의 MR 댐퍼 제어 대한토목학회 학술대회 2003 년 10 월 25 일

2. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 1 CONTENTS Introduction Introduction Maximum Energy Dissipation Algorithm Maximum Energy Dissipation Algorithm Numerical Examples Numerical Examples Conclusions Conclusions Further Study Further Study

3. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 2 Backgrounds Backgrounds Introduction Introduction Semi-active control device hasSemi-active control device has reliability of passive and adaptability of active system. MR dampers are quite promising semi-active device forMR dampers are quite promising semi-active device for small power requirement, reliability, and inexpensive to manufacture. It is not possible to directly control the MR damper.It is not possible to directly control the MR damper. Control Force of MR Damper Control Force of MR Damper Input voltage Structural Response =,

4. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 Without Magnetic Fields With Magnetic Fields Bearing & Seal Coil Accumulator MR Fluid Diaphragm Wires to Electromgnet Characteristics of MR damper Characteristics of MR damper

5. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 Previous Studies Previous Studies Karnopp et al. (1974)Karnopp et al. (1974) “Skyhook” damper control algorithm Feng and Shinozukah (1990)Feng and Shinozukah (1990) Bang-Bang controller for a hybrid controller on bridge Brogan (1991), Leitmann (1994)Brogan (1991), Leitmann (1994) Lyapunov stability theory for ER dampers McClamroch and Gavin (1995)McClamroch and Gavin (1995) Decentralized Bang-Bang controller - - - -

6. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 Inaudi (1997)Inaudi (1997) Modulated homogeneous friction algorithm for a variable friction device Dyke, Spencer, Sain and Carlson (1996)Dyke, Spencer, Sain and Carlson (1996) Clipped optimal controller for semi-active devices Jansen and Dyke (2000)Jansen and Dyke (2000) - Formulate previous algorithms for use with MR dampers - Compare the performance of each algorithm - - Difficulties in designing phase of controller - Efficient control design method is required -

7. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 Objective and Scope Objective and Scope Implementation of maximum energy dissipation algorithm for benchmark structures using MR dampers Prove the applicability in performance and robustness comparing with previous algorithms

8. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 Lyapunov Direct Method Maximum Energy Dissipation Algorithm Lyapunov function, V(z)Lyapunov function, V(z) If the V(z) is positive definite and If the V(z) is positive definite and then V(z) is Lyapunov function then V(z) is Lyapunov function Lyapunov direct methodLyapunov direct method If the Lyapunov function,V(z), exists for the system If the Lyapunov function,V(z), exists for the system origin (z=0) of system is stable origin (z=0) of system is stable z1z1 z2z2 V z(t)z(t) Fig.1 Illustrating Lyapunov Direct Method

9. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 8 Equation of motionEquation of motion Define Lyapunov function, V(z)Define Lyapunov function, V(z) Derivative of Lyapunov function,Derivative of Lyapunov function, Maximum Energy Dissipation Algorithm (MEDA) (1) (2) (3)

10. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 Control law which minimize the derivative of eq.(3)Control law which minimize the derivative of eq.(3) (4) where U max : maximum control force H : step function x: state  : location vector f: control force - No weighting matrix - Control force is determined form state and control force - Simple controller

11. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 10 Numerical Examples Numerical Examples Benchmark Cable-Stayed Bridge 142.7m 350.6m (Pier1) FEM model of cable-stayed bridge Element :162 beam elements 420 rigid links 128 cable elements Node :579 nodes

12. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 MR damper Total number :24Total number :24 Capacity :1000 KNCapacity :1000 KN Location:PerformanceLocation:Performance 8 MR dampers on bent1 and pier3 8 MR dampers on bent1 and pier3 4 MR dampers on pier2 and pier4 4 MR dampers on pier2 and pier4Robustness 8 MR dampers on bent1 and pier4 8 MR dampers on bent1 and pier4 4 MR dampers on pier2 and pier3 4 MR dampers on pier2 and pier3

13. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 12 Evaluation Criteria Peak Responses (J 1 ~ J 6 )Peak Responses (J 1 ~ J 6 ) Base shear, shear at deck level, overturning moment, moment at deck level, cable tension, deck displacement at abutment Normed responses (J 7 ~ J 11 )Normed responses (J 7 ~ J 11 ) Base shear, shear at deck level, overturning moment, Moment at deck level, cable tension

14. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 Analysis Control methodsControl methods –Passive on/off –LQG –Sliding mode control (SMC) (S. J. Moon et al 2003) PerformancesPerformances El Centro, Mexico, Gebze earthquakes RobustnessRobustness –  7% stiffness perturbed system –  30% stiffness perturbed system

15. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 14 Results for normal system under El Centro earthquake Evaluation criteria Normalized value

16. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 15 under Mexico earthquake Evaluation criteria Normalized value

17. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 under Gebze earthquake Normalized value Evaluation criteria

18. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 system under El Centro earthquake Evaluation criteria Normalized value Results for  7% stiffness perturbed system

19. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 Evaluation criteria Normalized value under El Centro earthquake Results for  30% stiffness perturbed system

20. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 under Mexico earthquake Evaluation criteria Normalized value

21. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 under Gebze earthquake Evaluation criteria Normalized value

22. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 21 Nonlinear Benchmark Building Nonlinear benchmark building Plan : 30.48  36.58 (m) Height: 80.77 (m) 20-story building MR damper –Capacity : 1000 KN –Number of dampers : 25 (4, 2, 2, 1, 1, …, 1)

23. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 Evaluation Criteria J 1, J 2, J 3 : Drift, Acceleration, Base shearJ 1, J 2, J 3 : Drift, Acceleration, Base shear J 4, J 5, J 6 : Normed drift, Acceleration, Base shearJ 4, J 5, J 6 : Normed drift, Acceleration, Base shear J 7, J 8, J 9 : Ductility, Dissipated energy, Plastic connectionJ 7, J 8, J 9 : Ductility, Dissipated energy, Plastic connection J 10, J 11 : Normed ductility, Control forceJ 10, J 11 : Normed ductility, Control force

24. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 Analysis Control methods –Clipped-optimal control –Maximum energy dissipation algorithm (MEDA) Performances –El Centro, Hachinohe:50%, 100%, 150% –Northridge, Kobe earthquakes:50%, 100%

25. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 24 50% intensity of El Centro earthquake Results J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

26. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 25 J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. 100% intensity of El Centro earthquake Evaluation criteria Normalized value A

27. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 26 150% intensity of El Centro earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

28. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 27 50% intensity of Hachnohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

29. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 100% intensity of Hachinohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

30. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 150% intensity of Hachinohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

31. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 30 50% intensity of Northridge earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

32. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 31 100% intensity of Northridge earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

33. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 32 50% intensity of Kobe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

34. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 33 100% intensity of Kobe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value A

35. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 34 Discussions Discussions MEDA based semi-active control system - Inter-story drifts and plastic connections reduced. - Accelerations and base shears increased over uncontrolled case. Number and location of MR damper need to be changed.

36. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 35 50% intensity of El Centro earthquake Modified number and location (total 10: 1,0,1,0,1,0…) J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

37. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 36 J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. 100% intensity of El Centro earthquake Evaluation criteria Normalized value

38. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 37 150% intensity of El Centro earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

39. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 38 50% intensity of Hachnohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

40. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 39 100% intensity of Hachinohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

41. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 40 150% intensity of Hachinohe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

42. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 41 50% intensity of Northridge earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

43. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 42 100% intensity of Northridge earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

44. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 43 50% intensity of Kobe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

45. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 44 100% intensity of Kobe earthquake J 1 : Drift J 2 : Accel J 3 : B. shear J 4 : N. drift J 5 : N. accel J 6 : N. B. shear J 7 : Ductility J 8 : D. Energy J 9 : Plastic Connection Connection J 10 : N. ductility J 11 : Control F. Evaluation criteria Normalized value

46. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 45 Conclusions Conclusions Maximum energy dissipation algorithm(MEDA) is Maximum energy dissipation algorithm(MEDA) is implemented to seismically excited structures using MR implemented to seismically excited structures using MR dampers dampers Applicability of MEDA is exploited Applicability of MEDA is exploited Performance : comparable performance with previous algorithms for cable-stayed bridge algorithms for cable-stayed bridge Robustness: for  7%,  30% stiffness perturbed, stable and perform well stable and perform well MEDA is MEDA is - Efficient and robust controller especially for cable-stayed - Efficient and robust controller especially for cable-stayed bridge bridge - Not adequate for building structures - Not adequate for building structures

47. Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 46 Thank you for your attention.