MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법

Structural Dynamics & Vibration Control Lab. 1

MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법

정형조 , 한국과학기술원 건설환경공학과문영종 , 한국과학기술원 건설환경공학과고만기 , 공주대학교 토목공학과이인원 , 한국과학기술원 건설환경공학과

한국전산구조공학회 춘계 학술발표회서울대학교 , 서울2002 년 4 월 13 일


OUTLINE

IntroductionBenchmark Problem StatementSeismic Control System Using MR

DampersNumerical Simulation ResultsConclusions


INTRODUCTIONThe control of cable-stayed bridges is a unique and

challenging problem. During the 2nd International Workshop on

Structural Control (Hong Kong, 1996),

a working group was formed to develop a benchmark control problem for bridges.

Dyke et al. have developed a benchmark control problem for seismically excited cable-stayed bridges (2000).


Semiactive Control Using MR Dampers– Magnetorheological (MR) fluid dampers: new class of semiactive control devices that utilize

MR fluids to provide controllable damping forces.



MR fluids to provide controllable damping forces.



MR fluids to provide controllable damping forces. MR damper-based control strategies

• Reliability of passive control devices• Versatility and adaptability of fully active control system

– Attractive features• Bounded-input, bounded-output stability• Small energy requirements


Objective of This Study:

to investigate the effectiveness of semiactive control strategies using MR fluid dampers for seismic protection of cable-stayed bridges


BENCHMARK PROBLEM STATEMENT

Missouri Side– 350 m main span

– 142m side span

– 128 Cables

Illinois Approach– 12 additional piers

– 570 m

570 m636 m

Benchmark Bridge Model– Under construction in Cape Griardeau, Missouri, USA.– To be completed in 2003.


Longitudinal excitation applied simultaneously.For proposed controllers, designers must define

– Sensor models and locations

– Device models and locations

– Control algorithm

Control Design Problem

K(s)


El CentroPGA = 0.36g

Historical Earthquakes Considered



Mexico CityPGA = 0.14g




Mexico CityPGA = 0.14g

Gebze TurkeyPGA = 0.26g



Peak Responses (Peak Responses (JJ11 – – JJ66))– Base shear Base shear –– Shear at deck level Shear at deck level – Overturning moment Overturning moment –– Moment at deck level Moment at deck level– Cable tensionCable tension– Deck displacement at abutmentDeck displacement at abutment

Normed Responses (Normed Responses (JJ77 – – JJ1111))– Base shear Base shear –– Shear at deck level Shear at deck level – Overturning moment Overturning moment –– Moment at deck level Moment at deck level– Cable tensionCable tension

Evaluation Criteria

Control Strategy (Control Strategy (JJ1212 – – JJ1818))– Peak control force and device strokePeak control force and device stroke– Peak and total power requiredPeak and total power required– Number of control devices and sensorsNumber of control devices and sensors


SEISMIC CONTROL SYSTEM USING MR DAMPERS

Sensors

– Five accelerometers

– Four displacement transducers

– 24 force transducers for measuring control forcesControl Devices

– 24 MR dampers (capacity: 1000 kN/each)


Previous methods: based on the small-scale damper Bingham model (Stanway et al. 1985, 1987) Simple Bouc-Wen model (Spencer et al. 1997) Modified Bouc-Wen model (Spencer et al. 1997)

Proposed method: based on the large-scale damper Modified Bouc-Wen model (Spencer et al. 1997)

Dynamic Model of MR Dampers


Previous methods: based on the small-scale damper Bingham model (Stanway et al. 1985, 1987) Simple Bouc-Wen model (Spencer et al. 1997) Modified Bouc-Wen model (Spencer et al. 1997)

Proposed method: based on the large-scale damper Modified Bouc-Wen model (Spencer et al. 1997)

Dynamic Model of MR Dampers


0 0 1 0 1 1 0( ) ( ) ( ) ( )f z c x y k x y k x x c y k x x

)()(1

yxAzyxzzyxznn

)}({1

0010

yxkxczcc

y

vba vccc ba 000 vccc ba 111

wherewhere

Control force:Control force:

First-order filter:First-order filter:

,, andand

Modified Bouc-Wen Model (Spencer et al. 1997)

)( uvv


Parameter Value Parameter Value

a 46.2 kN/m k0 0.002 kN/m

b 41.2 kN/m/V k1 0.0097 kN/m

c0a 110 kNs/m 164 m-2

c0b 114 kNs/m/V 164 m-2

c1a 8359 kNs/m A 1107.2

c1b 7483 kNs/m/V n 2

x0 0.0 m 100

Optimized Parameters of Dynamic Model for MR Dampers


Physical Structure


Physical Structure

Detailed F.E. Model ~ 105 - 106 DOF


Physical Structure


Evaluation Model ~ 102 - 103 DOF


Physical Structure


Evaluation Model ~ 102 - 103 DOF

Control Design Model ~ 10 - 102 DOF


Control Design Model

Reduced-Order Model (30 states)

– By forming a balanced realization and condensing out the states with relatively small controllability and observability grammians

gddddd x EuBxAx

gzd

zdd

zd xFuDxCz

vFfDxCDy )( gy

dydd

ydss x


Control Law

MRDamper Structure

DecisionBlock

NominalController

f f

cf

fu

y

gx

dd x,x

Control Strategy for Semiactive Control


Control Law

MRDamper Structure

DecisionBlock

NominalController

f f

cf

fu

y

gx

dd x,x

Alternatively, H, Cumulant Control,

Risk Sensitive, etc., can be employed.

LQG / H2 Linear Output Feedback Controller

ccc

Tcccc

zCf

fyBzAz



Control Law

MRDamper Structure

DecisionBlock

NominalController

f f

cf

fu

y

gx

dd x,x

Clipped-Optimal Control

])[( cmax fffHuu

u = 0

u = 0

u = umax

cf

f



Weighting Parameters for Semiactive Control

Appropriate Weighting Parameters by Stochastic Response Analyses

– Overturning moment (Qover_mom)

– Deck displacement (Qdeck_disp)

Performance Index

where Q: Response weighing matrix R: Control force weighting matrix (identity matrix)

dtEJ

0

uRuzQz1

lim TT


NUMERICAL SIMULATIONS

Comparison Methods

– Ideal active control

– Ideal semiactive control

– Passive control using MR dampers• Passive-off (command signal u = 0 Volts)

• Passive-on (command signal u = 10 Volts)

– Semiactive control using MR dampersValues of Optimized Weighting Parameters

– Qover_mom = 6×10-9; Qdeck_disp = 6×103


Time-History Responses(Base Shear Force)

• El Centro earthquake: 71% reduction in peak

• Gebze Turkey earthquake: 64% reduction in peak

kNkN

kNkN

• Mexico City earthquake: 54% reduction in peakkNkN


Maximum Evaluation Criteria(Peak Responses)

0

1

2

3

4

5

6

7

8

9

No

rmal

ized

res

po

nse

s

Base shear Shear atdeck level

Shear atdeck level

Moment atdeck level

Cabletension

Deckdisplacment

Ideal active

Ideal semiactive

Passive-off using MR

Passsive-on using MR

Semiactive using MR


0

0.5

1

1.5

2

2.5

3

3.5

4

No

ma

lize

d R

es

po

ns

es

Base shear Shear at decklevel

Overturningmoment

Moment atdeck level

Cable tension

Ideal active

Ideal semiactive

Passive-off using MR

Passive-on using MR

Semiactive using MR

Maximum Evaluation Criteria(Normed Responses)


Maximum Evaluation Criteria(Control Strategy)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Stroke0.0E+00

2.0E- 04

4.0E- 04

6.0E- 04

8.0E- 04

1.0E- 03

1.2E- 03

1.4E- 03

1.6E- 03

1.8E- 03

2.0E- 03

Control force

Ideal activeIdeal semiactivePassive- off using MRPassive- on using MRSemiactive using MR


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

No

rma

lize

d R

es

po

ns

es

Base shear Shear at decklevel

Overturningmoment

Moment at decklevel

Cable tension Deckdisplacement

Passive-on (1.0*Eq.)Semiactive (1.0*Eq.)Passive-on (0.5*Eq.)Semiactive (0.5*Eq.)Passive-on (0.25*Eq.)Semiactive (0.25*Eq.)

Robustness to Earthquake Motion Intensities


CONCLUSIONSA semiactive control strategy using MR dampers

has been proposed for the benchmark bridge problem.

The performance of the proposed semiactive control design using MR dampers nearly achieves the same performance as that of the ideal active or semiactive control system.

MR dampers show great promise for response control of seismically excited cable-stayed bridges.

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MR 유체 감쇠기를 이용한 사장교의 지진응답 제어 기법