케이블 진동 감쇠를 위한 반능동 제어 장치 성능의 실험적 평가

케이블 진동 감쇠를 위한

반능동 제어 장치 성능의 실험적 평가

케이블 진동 감쇠를 위한

반능동 제어 장치 성능의 실험적 평가

2004 년도 한국전산구조공학회 추계 학술발표회목포해양대학교 2004 년 10 월 9 일

장지은 , 한국과학기술원 건설 및 환경공학과 석사과정정형조 , 세종대학교 토목환경공학과 조교수정 운 , 현대건설기술개발원 주임연구원이인원 , 한국과학기술원 건설 및 환경공학과 교수

22Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Introduction

Cable Damping Experimental Setup

Experimental Results

Conclusions

Contents

33Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Introduction

Cable

• Cables are efficient structural elements that are used in cable-stayed bridges, suspension bridges and other cable structures.

• Steel cables are flexible and have low inherent damping, resulting in high susceptibility to vibration.

• Vibration can result in premature cable or connection

failure and/or breakdown of the cable corrosion protection

systems, reducing the life of the cable structure.

• Numerous passive and active cable damping studies have been performed and full-scale applications realized.

44Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Semiactive damping system

- Johnson et al. (1999, 2000): verification of the efficacy of

a semiactive damper for a taut/sagged cable model

- Christenson (2001): experimental verification of the

performance of an MR damper in mitigating cable

responses by using a medium-scale cable

- Ni et al. (2002), Ko et al. (2002), Duan et al. (2002): field

comparative tests of cable vibration control using

MR dampers (the world’s first time implementation

of MR-based smart damping technology in civil

engineering structures)

55Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Objectives

• To experimentally verify the performance of the MR

damper-based control systems for suppressing vibration of

real-scaled stay cables using various semiactive control

algorithms

66Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Cable Damping Experimental Setup

Schematic of smart cable damping experiment

Where, )(tFs

: displacement at damper location

: shaker force

)(tFd : damper force

: evaluation displacement

shakershaker flat-sagcable

flat-sagcable

spectrumanalyzer

spectrumanalyzer

MR dampers

MR dampers

digital controller

digital controller

)(tFd

)(tFs

dw

dw

u

u

ew

ew: control signal

77Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Cable

Real-scaled cable at HICT

parameters values

L 44.7 m

m 89.86 N/m

T 500 KN

1.34 m

13.4 m

8.37

2.53 Hz

dx

0005.0

0015.0

2

1

i

0

sx

88Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Cable model

• Transverse motion of cable could be modeled by

the motion of a taut string because of small sag

(0.1% sag-to-span ratio with tension of 500 kN).

99Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

dx sx

),( txvx

where ),( txv

)(tFd dxx : transverse deflection of the cable

: transverse damper force at location

)(tFd )(tFs

)(tFs sxx

L

: transverse shaker force at location

: angle of inclination

1010Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

MR damper

• MR controllable friction damper

(RD-1097-01 from Lord Corporation)

• Maximum force level: 100 N

• Maximum voltage: 1.4 V

1111Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

MR damper installation

• Twin damper setup

• Location : 1.34m

from bottom support

• Measurement : Damper force,

displacement, and

acceleration

1212Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Cable exciting system (Kim et al. 2002)

temtF sin)( force exciting Harmonic 2

mass exciting :

frequency exciting : where

m

(1)

1313Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Controller

• The controller is constructed by the Matlab Real-Time

Workshop executed in real time using MS Visual C++.

• The measured responses are acquired from displacement

and acceleration sensors at damper location and converted into digital data by NI DAQ Card-6062E.

1414Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Control algorithms:

to calculate the command voltage input

• Passive-mode cases

- passive-off (v=0V),

- passive-on (v= 1.4V)

- other passive-modes (v= 0.6V, 1.0V, 1.1V, 1.2V, 1.3V)

1515Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

• Semiactive control cases (Jansen and Dyke 2000)

- Clipped-optimal control algorithm

where, Vmax=1.4V, Fd ci= the desired control force, and

Fd = the measured control force

- Control based on Lyapunov stability theory

where, z = the state vector, and

P = the matrix to be found using the Lyapunov equation

)}({max ddcidi FFFHVv

))((max dT

i PBFzHVv

(2)

(3)

1616Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

- Maximum energy dissipation algorithm

where, vd = the velocity at the damper location

- Modulated homogeneous friction algorithm

)(max ddi FvHVv

|)|(max ddi FFHVvn

)(tiPgF ndn

P[i(t)] = i(t-s),

where s = {min x0: i(t-x)=0}

(4)

(5)

1717Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Experimental Results

Displacement in free vibration

Time (sec)

Dis

plac

emen

t (m

)

1818Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Damping ratios for verification of performances

• The amplitude-dependent damping ratios are calculated by

the Hilbert transform-based identification method

(Duan et al. 2002)

1919Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Damping ratios in the passive-mode casesD

ampi

ng r

atio

(%

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25

passive V=1.4 passive V=1.3 passive V=1.2passive V=1.1passive V=1.0passive V=0.6passive V=0.0uncontrolled

Amplitude (mm) at the location of 10.2 m away from the bottom support

2020Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Damping ratios in the semiactive control cases

Amplitude (mm) at the location of 10.2 m away from the bottom support

Dam

ping

rat

io

(%)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3 5 7 9 11 13 15 17

Passive offPassive onClipped optimalLyapunovMHFMEDA

2121Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea

Conclusions

Semiactive control systems significantly improve the

mitigation of stay cable vibration over the uncontrolled

and the passive-off cases.

Semiactive control systems significantly improve the

mitigation of stay cable vibration over the uncontrolled

and the passive-off cases.

The Modulated homogeneous friction algorithm shows

nearly the same performance as the passive-on case.

The Modulated homogeneous friction algorithm shows

nearly the same performance as the passive-on case.

The performance of MR damper-based control systems for suppressing vibration of stay cables is experimentally verified.

The performance of MR damper-based control systems for suppressing vibration of stay cables is experimentally verified.

The control based on Lyapunov stability and the clipped-

optimal control show slightly better performance than

the passive-on case.

The control based on Lyapunov stability and the clipped-

optimal control show slightly better performance than

the passive-on case.