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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
33Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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
44Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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
55Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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
66Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
Objectives
• Comparative study on performance of
semiactive control strategies for vibration control of cable
77Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
88Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
99Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
- 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)
1010Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
The static deflection shape function
LxxxLxL
xxxxx
dd
dd
)/()(
0/)(1 (3)
dx
- First shape function
: mode shape induced by damper force
1111Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
jxxj sin)(1
- Other shape functions
: cable mode shape
(4)
1212Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
1313Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
without magnetic fields with magnetic fields
Semiactive Damper
MR damper
1414Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
t
v
vmax
- Change of voltage input
- Various algorithms to determine the command voltage
Semiactive mode
1515Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
- equations governing the damper force
)(
||||||
000
1
0
vuu
uccc
where
xAzxzzxz
zxcf
ba
ba
nn
(6)
Bouc-Wen 0c
Shear-mode MR damper
1616Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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
0iv
maxVvi
)),()(( txvtFHFF dactive
ddd
1717Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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)
1818Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
1919Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
2020Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
Damper Capacity
Maximum damper force = 10 N
Maximum voltage input = 3 V
2121Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
External Load
),( txf
L
xtWtxf sin)(),(
L
Distributed load
(14)
2222Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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)
2323Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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
2424Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
2525Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
2626Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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 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
2727Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea
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
2828Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural 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 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
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