LNG

1
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Contents

• Introduction
• System Characteristics
• Control Algorithms
• Numerical Analysis
• Conclusions

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• Introduction

• Cable

• Extremely low damping inherent
• Proneness to vibration
• Rain-wind induced vibration
• Necessity to mitigate cable vibration
• causing reduced life of cable and connection

4

• 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

5

• 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

6

• Objectives

• Comparative study on performance of
• semiactive control strategies for vibration
  control of cable

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• System Characteristics

• Cable

L
T, m
where,
transverse deflection of the cable
transverse damper force at location
transverse shaker force at location
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• Partial Differential Equation of Motion

(1)
where,
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• Solution by Series Approximation

• - Approximation of the transverse deflection
• using a finite series

(2)
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• The static deflection shape function

- First shape function mode shape induced
by damper force
(3)
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- Second shape function mode shape
induced by shaker force
(4)
- Other shape functions cable mode shape
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• Standard Galerkin approach

(5)
where,
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• Damper

• MR damper

• with magnetic fields

without magnetic fields
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• Passive mode

• - Passive-on
• - Passive-off

v
vmax
t
v
0
t
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• Semiactive mode

• Change of voltage input
• Various algorithms to determine the command
  voltage

v
vmax
t
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• Shear-mode MR damper

• equations governing the damper force

(6)
Bouc-Wen
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• Control Algorithms

• Ideal clipped optimal control
• Other control algorithms

Ideal clipped optimal control
Damper force
Cable
Control algorithm
Voltage
Damper force
Cable
Damper
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• Ideal clipped optimal control
• damper force
• Passive off
• voltage input
• Passive on
• voltage input

(7)
(8)
(9)
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• Control based on Lyapunov stability theory
• voltage input
• Maximum energy dissipation alogorithm
• voltage input
• Clipped-optimal control algorithm
• voltage input

(10)
(11)
(12)

• Modulated homogeneous friction algorithm
• voltage input

(13)
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• Numerical Analysis

• Parameters for the flat-sag cable model

• Tested by Christenson et al. (2001)

parameters values parameters values
L 12.65 m
m 0.747 kg/m
T 2172 N 2.89 Hz
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• Parameters for the shear-mode MR damper

• Tested by Christenson et al. (2001)

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125
70
700
70
50
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• Shaker force

• Gaussian white noise process through a series of
  filters

• Series of filters

- Low-pass filter for low frequency
roll-off - Excitation filter to excite
primarily first symmetric mode - Elliptical
low-pass filter to attenuate the signal at
higher frequencies
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• Frequency content of shaker force

Elliptical Low-pass filter
Excitation filter
Low-pass filter
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• Shaker Force

• RMS of shaker force 5.0 N

• Damper Capacity

• Maximum damper force 10 N
• Maximum voltage input 3 V

• Location of shaker and damper

• Location of shaker 2 of the cable length
  from support
• Location of damper 3 of the cable length
• from other support

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• Performance of Various Control Algorithms

• Maximum Displacement at Mid-Span

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• Maximum Displacement at Quarter-Span

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• RMS (Root mean square) Displacement

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• RMS (Root mean square) Velocity

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• Control Performances normalized by uncontrolled
  values

Ideal clipped passive on passive off Lyapu nov MEDA clipped optimal MHF
Max. Displ. (midspan) 0.52 0.76 0.69 0.61 0.79 0.72 0.64
Max. Displ. (quartspan) 0.53 0.71 0.75 0.72 0.81 0.84 0.74
RMS Displ. 0.42 0.78 0.78 0.74 0.82 0.80 0.74
RMS Velocity 0.39 0.81 0.78 0.75 0.82 0.81 0.74
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Ideal clipped Passive on passive off Lyapunov MEDA clipped optimal MHF
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• Conclusions

• Several semiactive control algorithms have been
  evaluated
• for application in cable vibration control
  using shear-mode
• MR dampers
• Semi-active control system mitigated stay cable
  vibration
• over uncontrolled case
• The Control algorithm based on Lyapunov
  stability theory
• is most efficient control strategy for
  vibration control of stay
• cable among the evaluated control algorithms
  in this study