comparative study on performances of various semiactive control algorithms for stay cables 2004...

Comparative Study on Performances of Various Semiactive Control Algorithms

for Stay Cables

Comparative Study on Performances of Various Semiactive Control Algorithms

for Stay Cables

2004 년도 강구조공학회 학술발표대회2004 년 6 월 5 일

장지은 , 한국과학기술원 건설 및 환경공학과 석사과정정형조 , 세종대학교 토목환경공학과 조교수윤우현 , 경원대학교 산업환경대학원 부교수이인원 , 한국과학기술원 건설 및 환경공학과 교수

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

Introduction

System Characteristics

Control Algorithms

Numerical Analysis

Conclusions

Contents


Introduction

Cable

• Extremely low damping inherent in cables

• Proneness to vibration

• Necessity to mitigate cable vibration

causing reduced cable and connection life


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


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


Objectives

• Comparative study on performance of

semiactive control strategies for vibration control of cable


System Characteristics

Cable

L

T, m

dx

),( txv

x

where, ),( txv

T

)(tFd dxx

: transverse deflection of the cable

: cable tension

: transverse damper force at location

)(tFd

m : cable mass per unit length


Partial Differential Equation of Motion

where,

damper oflocation

forcedamper

load external

tensioncable

cabletheoflength

lengthunit per damping viscous

lengthunitpermasscable

d

d

x

F

f

T

L

c

m

(1))()(),(),(),(),( dd xxtFtxftxvTtxvctxvm


- Approximation of the transverse deflection

using a finite series

m

jjj tqxtxv

1

)()(),(

ntsdisplaceme dgeneralize: )(tq j

functionsshapeofseta:)( where, xj

Solution by Series Approximation

(2)


The static deflection shape function

LxxxLxL

xxxxx

dd

dd

)/()(

0/)(1 (3)

dx

- First shape function

: mode shape induced by damper force


jxxj sin)(1

- Other shape functions

: cable mode shape

(4)


dxxxTK

dxxxM

j

L

iij

j

L

iij

)()(][

)()(][

0

0

Standard Galerkin approach

)]()()([)( 21 dmddd xxxx

where,

(5)(t) FfKqqCqM d

dxxtxff i

L

i )(),(0


without magnetic fields with magnetic fields

Semiactive Damper

MR damper


t

v

vmax

- Change of voltage input

- Various algorithms to determine the command voltage

Semiactive mode


- equations governing the damper force

)(

||||||

000

1

0

vuu

uccc

where

xAzxzzxz

zxcf

ba

ba

nn

(6)

Bouc-Wen 0c

Shear-mode MR damper


Control Algorithms

(8)

(7)

(9)

Ideal clipped optimal control algorithm

damper force

Passive off

voltage input

Passive on

voltage input

0iv

maxVvi

)),()(( txvtFHFF dactive

ddd


Modulated homogeneous friction algorithmvoltage input |)|(max ddi FFHVv

ni

(12)

(10)

(11)

Control based on Lyapunov stability theory

voltage input

Maximum energy dissipation alogorithm

voltage input

Clipped-optimal control algorithm

voltage input

))((max dT

i PBFHVv

)}({max ddcidi FFFHVv

)(max ddT

i FqHVv

(13)


parameters values parameters

values

L 12.65 m

m 0.747 kg/m

T 2172 N 2.89 Hz

0005.0

005.0

003.0

0015.0

4

3

2

1

i

0

Numerical Analysis

Parameters for the flat-sag cable model Parameters for the flat-sag cable model

Tested by Christenson


항목 상수 값 항목 상수 값

125

70

700

70

50

5103.1

n 1

5103.1

A 200

ac0

bc0

a

b

Parameters for the shear-mode MR damper Parameters for the shear-mode MR damper

Tested by Christenson


Damper Capacity

Maximum damper force = 10 N

Maximum voltage input = 3 V


External Load

),( txf

L

xtWtxf sin)(),(

L

Distributed load

(14)


Gaussian white noise process

Wind load (3rd generation benchmarks for building)

-2

-1.5

-1

-0.5

0

0.5

1

0 10 20 30 40 50 60 70 80 90 100

Win

d lo

ad

(N/m

)

Time (sec)


Performance of Various Control Algorithms

Measurements

- Max. displacement at mid-span- Max. displacement at quarter-span- RMS displacement- RMS velocity


Ideal clipped

passive off

passive on

Lyapunov MEDA

clipped optimal

MHF

Max.

Displ. (midspan)

0.32 0.66 0.49 0.42 0.47 0.47 0.44

Max.

Displ. (quartspan)

0.32 0.68 0.57 0.45 0.53 0.57 0.60

RMS

Displ.0.25 0.53 0.37 0.36 0.36 0.40 0.38

RMS

Velocity0.26 0.87 0.58 0.54 0.51 0.56 0.58

Gaussian white noise process

- normalized value by uncontrolled case


Nor

mal

ized

valu

e

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7

Max.displ at mid span

Max.displ at quarter span

RMS velocity

RMS displ

Ideal clippe

d

Passive off

passive on

Lyapunov MEDA

clipped

optimal

MHF


Wind load (3rd generation benchmarks for building)

- normalized value by uncontrolled case

Ideal clipped

passive off

passive on

Lyapunov MEDAclipped optimal

MHF

Max.

Displ. (midspan)

0.31 0.49 0.36 0.34 0.36 0.36 0.38

Max.

Displ. (quartspan)

0.30 0.51 0.40 0.40 0.44 0.38 0.40

RMS

Displ.0.20 0.39 0.25 0.27 0.28 0.29 0.26

RMS

Velocity0.19 0.56 0.35 0.35 0.34 0.36 0.35


Nor

mal

ized

valu

e

0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7

Max.displ at mid span

Max.displ at quarter span

RMS displ

RMS velocity

Ideal clippe

d

Passive off

Passive on

Lyapunov MEDAClippedoptimal MHF


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 vibrat

ion with gaussian white noise process among the evaluated co

ntrol algorithms

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 vibrat

ion with gaussian white noise process among the evaluated co

ntrol algorithms

comparative study on performances of various semiactive control algorithms for stay cables 2004...

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