조상원 * : 박사과정, 한국과학기술원 건설환경공학과 조상원 * : 박사과정, 한국과학기술원 건설환경공학과 정형조 : 교수, 세종대학교 토목환경공학과 정형조 : 교수, 세종대학교 토목환경공학과 이종헌 : 교수, 경일대학교 토목공학과 이종헌 : 교수, 경일대학교 토목공학과 이인원 : 교수, 한국과학기술원 건설환경공학과 이인원 : 교수, 한국과학기술원 건설환경공학과 Maximum Energy Dissipation Algorithm 을 이용한 벤치마크 사장교의 제어 한국지진공학회 추계 학술발표회 2003 년 9 월 19 일

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

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 =,

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 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 -

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 Objective and Scope Objective and Scope Implementation of maximum energy dissipation algorithm for benchmark cable-stayed bridge using MR dampers and Prove the applicability in point of the performance and robustness comparing with previous algorithms

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 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)

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 8 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 10 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 12 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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 Results for normal system under El Centro earthquake Evaluation criteria Normalized value

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 14 under Mexico earthquake Evaluation criteria Normalized value

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 system under El Centro earthquake Evaluation criteria Normalized value Results for  7% stiffness perturbed system

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 Evaluation criteria Normalized value under El Centro earthquake Results for  30% stiffness perturbed system

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 under Mexico earthquake Evaluation criteria Normalized value

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

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 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 algorithms Robustness: for  7%,  30% stiffness perturbed, stable and perform well stable and perform well MEDA is efficient and robust controller especially for large MEDA is efficient and robust controller especially for large size structure like cable-stayed bridge size structure like cable-stayed bridge

Structural Dynamics & Vibration Control Lab., KAIST, Korea Structural Dynamics & Vibration Control Lab., KAIST, Korea 21 Thank you for your attention.