Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers

Modified Bang-Bang Control of Seismically Modified Bang-Bang Control of Seismically

Excited Structures Using MR Dampers Excited Structures Using MR Dampers

Sang-Won Cho* : Ph.D. Student, KAISTSang-Won Cho* : Ph.D. Student, KAIST Ji-Sung Jo : Ph.D. Student, KAISTJi-Sung Jo : Ph.D. Student, KAIST In-Won Lee : Professor, KAIST In-Won Lee : Professor, KAIST

KAIST-Kyoto Univ. Joint SeminarKAIST-Kyoto Univ. Joint Seminar

Daejeon, KoreaDaejeon, Korea

February 25, 2002February 25, 2002

2 2Structural Dynamics & Vibration Control Lab., KAIST, Korea

CONTENTSCONTENTS

IntroductionIntroduction

Semi-Active ControlSemi-Active Control

Proposed Control AlgorithmProposed Control Algorithm

Numerical ExampleNumerical Example

Conclusions and Further StudiesConclusions and Further Studies


14,491 of death and 13 trillion won of damage14,491 of death and 13 trillion won of damage

• Chi-Chi, Taiwan (1999)Chi-Chi, Taiwan (1999)• Chi-Chi, Taiwan (1999)Chi-Chi, Taiwan (1999)

Recent EarthquakesRecent Earthquakes

5,400 of death and 1.5 trillion won of damage5,400 of death and 1.5 trillion won of damage• Kobe, Japan (1995)Kobe, Japan (1995)• Kobe, Japan (1995)Kobe, Japan (1995)

2,161 of death and 9.2 trillion won of damage2,161 of death and 9.2 trillion won of damage

Introduction Introduction

• Gebze, Turkey (1999)Gebze, Turkey (1999)• Gebze, Turkey (1999)Gebze, Turkey (1999)

To increase the safety and reliability,To increase the safety and reliability, structural control is required structural control is required


Structural Control StrategiesStructural Control Strategies

• Active control Active control

– Use external control force to reduce the responses Use external control force to reduce the responses

– Large external powerLarge external power

– The problem of reliability under earthquakeThe problem of reliability under earthquake

– Active Mass Damper (AMD)Active Mass Damper (AMD)

• Passive controlPassive control– Increase the capacity of energy dissipation of Increase the capacity of energy dissipation of

structurestructure– No external powerNo external power– No adaptability to various external loadNo adaptability to various external load– Lead Rubber Bearing (LRB)Lead Rubber Bearing (LRB)


• Semi-active controlSemi-active control

– Change the characteristics of control devicesChange the characteristics of control devices

– Small external powerSmall external power

– Reliability of passive system with adaptability of Reliability of passive system with adaptability of

active systemactive system

– Variable-orifice damper, MR/ER damperVariable-orifice damper, MR/ER damper


Semi-Active Control DevicesSemi-Active Control Devices

• Variable-orifice damper Variable-orifice damper

Feng and ShinozukaFeng and Shinozuka (1990), Kawashima et al. (19 (1990), Kawashima et al. (1992)92)

• Variable-friction damper Variable-friction damper

Akbay and AktanAkbay and Aktan (1990), (1990), Kannan et al.Kannan et al. (1995) (1995)

• Semi-active impact damperSemi-active impact damper

Masri and YangMasri and Yang (1973), (1973), Papalou and MasriPapalou and Masri(1996)(1996)


• Controllable fluid damperControllable fluid damper

– Electrorheorogical fluid damperElectrorheorogical fluid damper (ER damper) (ER damper)

Ergott and MasriErgott and Masri(1992)(1992)

– Magnetorheorogical fluid damperMagnetorheorogical fluid damper (MR damper) (MR damper)

Carlson et al. Carlson et al. (1994)(1994)

PropertyProperty MR FluidsMR Fluids ER FluidsER Fluids

Response TimeResponse Time millisecondsmilliseconds millisecondsmilliseconds

Operable Temp. RangeOperable Temp. Range -40 to 150°C-40 to 150°C +10 to 90°C+10 to 90°C

StabilityStabilityUnaffected by most Unaffected by most

impuritiesimpuritiesCannot tolerate Cannot tolerate

impuritiesimpurities

Table 1 Properties of MR and ER Table 1 Properties of MR and ER FluidsFluids


MR DamperMR Damper

• Characteristics of MR fluidCharacteristics of MR fluid

Without Magnetic Fields With Magnetic Fields

Bearing &

Seal

CoilAccumulator

MR FluidDiaphragm

Wires to

Electromgnet


zxc 0f

• Modeling of MR damperModeling of MR damper

– Model of the parallel-plate MR damper Model of the parallel-plate MR damper (Jansen et al. (Jansen et al.

2000)2000)

– Voltage dependence of the damper parametersVoltage dependence of the damper parametersuu ba )(uccucc ba 0000 )(

)( vuu vv : commanded voltage : commanded voltage

Indirect control command is usedIndirect control command is used

(1)

(2)

xAzxzzx nn |||||| 1 z

x

f

c0

0c


Objective and ScopeObjective and Scope

To develop an efficient semi-active control strategiesTo develop an efficient semi-active control strategies

considering the characteristics of MR damperconsidering the characteristics of MR damper


Semi-Active Control AlgorithmsSemi-Active Control Algorithms

• Karnopp et al. Karnopp et al. ((19741974) )

““Skyhook” damper control algorithmSkyhook” damper control algorithm

• Feng and Shinozukah Feng and Shinozukah ((19901990))Bang-Bang controller for a hybrid controller onBang-Bang controller for a hybrid controller onbridge bridge

• Brogan Brogan ((19911991)), Leitmann , Leitmann ((19941994))Lyapunov stability theory for ER dampersLyapunov stability theory for ER dampers

•

McClamroch and Gavin McClamroch and Gavin ((19951995) )

Decentralized Bang-Bang controllerDecentralized Bang-Bang controller

Semi-Active ControlSemi-Active Control


• Inaudi Inaudi ((19971997) :) :

Modulated homogeneous friction algorithm for Modulated homogeneous friction algorithm for a a variable friction device variable friction device

• Sack et al.Sack et al. ( (19941994), ), DykeDyke ( (1991996) :6) :Clipped optimal controllers for semi-active devicClipped optimal controllers for semi-active devic

eses


(3)

(4)

Clipped-Optimal Control (Dyke et al. 1996)Clipped-Optimal Control (Dyke et al. 1996)

• Optimal control with clipped algorithmOptimal control with clipped algorithm

• Optimal controlOptimal control– State-space equationState-space equation

– Cost functionCost function

BuAxx

ft

TT dttRututQxtxJ0

)]()()()([2

1


– Optimal control algorithmOptimal control algorithm

KK : solution of Ricatti equation : solution of Ricatti equation

)()( 1 tKBt T xru (5)

0 KBKBQKAKA TT 1r (6)

- Control force is linear to the state of structureControl force is linear to the state of structure- No consideration of saturation - No consideration of saturation


• Clipped algorithmClipped algorithm

– Indirect control command to MR damperIndirect control command to MR damper

– Control voltage Control voltage vv , instead of control , instead of control forceforce

)}({ iicii fffHv (7)maxV

0v

maxVv

maxVv

0v

Cf

if0v

0v

fc : calculated optimal control force

fi : control force of MR damper

H : Heaviside step function

vi : control voltage

ici ff maxVv i

ici ff 0iv


Proposed Control Strategy : Proposed Control Strategy :

Decentralized Bang-Bang ControlDecentralized Bang-Bang Control

• To use full capacity of MR damperTo use full capacity of MR damper

• To consider the saturation of MR damperTo consider the saturation of MR damper

• High speed switching control commandHigh speed switching control command

Clipped algorithmClipped algorithm

• Indirect control commandIndirect control command

Clipped Decentralized Bang-Bang Control Clipped Decentralized Bang-Bang Control (CDBBC)(CDBBC)


Decentralized Bang-Bang Control Decentralized Bang-Bang Control

((McClamroch and Gavin, 1995McClamroch and Gavin, 1995))

• Based on Lyapunov stability theoryBased on Lyapunov stability theory

• Lyapunov function V(z) Lyapunov function V(z)

• Derivative of Lyapunov function Derivative of Lyapunov function

)()(2

1

2

1)( g

Tg

T xxMxxKxxzV (8)

)()(2

1)( fKxxCxxxKxzV T

gT (9)


• Control law which minimize Eq.(9)Control law which minimize Eq.(9)

• Approximate sign functionApproximate sign function

• Modified decentralized bang-bang controlModified decentralized bang-bang control

))(sgn(max fxxuu Tg (10)

(11)

(12) max)( utum

x

x

e

exsign

1

1)(

x

x

e

e

1

1

fxxx Tg )( where


• Clipped algorithmClipped algorithm

– Indirect control command to MR damperIndirect control command to MR damper

– Control voltage Control voltage vv , instead of control , instead of control forceforce

)}({ iicii fffHv (13)maxV0v

maxVv

maxVv

0v

Cf

if0v

0v

fc : calculated CMBB Control force

fi : control force of MR damper (nonlinear)

H : Heaviside step function

vi : control voltage


• Block diagram of proposed control algorithmBlock diagram of proposed control algorithm

`

Modified Modified DBBDBB

ControlControl

StructureStructureMR DamperMR Damper

ClippedClippedAlgorithmAlgorithm

gx

f

cf

Clipped Modified Decentralized Bang-Bang Control Clipped Modified Decentralized Bang-Bang Control (CMDBBC)(CMDBBC)

v

y


Three-Story Building (Dyke at al. 1996)Three-Story Building (Dyke at al. 1996) Numerical ExamplesNumerical Examples

ControlComputer

f

gx

1ax

2ax

3axv


• System matricesSystem matrices

,

3.9800

03.980

003.98

kgM s

m

NC s

sec

50500

5010050

050175

m

NK s

84.684.60

84.67.1384.6

084.60.12


• Damper modeling and parametersDamper modeling and parameters

Value Value

coa 21.0 Nsec/cm a 140 N/cm

cob3.50

Nsec/cmVb 695 N/cmV

ko 46.9 N/cm 363 cm-2

c1a 283 Nsec/cm 363 cm-2

c1b2.95

Nsec/cmVA 301

k1 5.00 N/cm n 2

xo 14.3 cm 190 sec-1

c0 c1 k1

k0

Bouc-Wen

c0 c1 k1

k0

Modified Bouc-Wen Model


• 3 Modes of MR damper3 Modes of MR damper– Passive-offPassive-off : input Voltage = 0 V: input Voltage = 0 V

– Passive-onPassive-on : input Voltage = 2.5 V: input Voltage = 2.5 V

– Semi-ActiveSemi-Active : switching on and off according: switching on and off according

to control algorithmto control algorithm


0 1 2 3 4 5Time(sec)

- 1

0

1

-1.5

-0.5

0.5

1.5

Dis

plac

emen

t(cm

)

0 1 2 3 4 5Time(sec)

- 1

0

1

-1.5

-0.5

0.5

1.5

Acc

eler

atio

n(g

)• Structural responses by CMDBBCStructural responses by CMDBBC

(Under El Centro Earthquake, at 3(Under El Centro Earthquake, at 3rdrd floor) floor)

Uncontrolled

CMDBBC


• Peak responses under El Centro EarthquakePeak responses under El Centro Earthquake

aix

ControlStrategy

Uncont.Passive-

OffPassive-

OnClip.-Opt.

ControlCMBBC

xi

(cm)

0.5380.8200.962

0.2110.3570.455

0.0760.1960.306

0.1140.1850.212

0.0800.1960.306

di

(cm)

0.5380.3190.201

0.2110.1530.103

0.0760.1580.110

0.1140.0900.101

0.0800.1580.111

(cm/sec2)

85610301400

420480717

281494767

696739703

310507772

F(N)

- 258 979 941 982


DiscussionsDiscussions

• Performance of CMDBBC Performance of CMDBBC

• Measured control forcesMeasured control forces

• Capacity of MR damper : 3000N (104% of total Capacity of MR damper : 3000N (104% of total weight)weight)

Unsaturated condition !!Unsaturated condition !!

ControlStrategy Uncont.

Passive-Off

Passive-On

Clip.-Opt.Control

CMBBC

F(N) - 258 979 941 982


• Peak responses under Peak responses under scaledscaled El Centro earthquake El Centro earthquake

ControlStrategy

Uncont.Passive-

OffPassive-

OnClip.-Opt.

ControlCMDBBC

xi

(cm)

2.7424.1794.863

3.2094.2114.869

0.8591.4741.862

1.3212.2232.818

0.8641.5031.876

di

(cm)

2.7421.5911.014

3.2091.9351.632

0.8590.6460.394

1.3211.0350.805

0.8640.6420.373

(cm)

439953427053

142769321

11354

223525742741

598647115599

212625322598

f(N)

- 1500 1500 1500 1500

aix


• Proposed Clipped modified decentralized bang-bangProposed Clipped modified decentralized bang-bang control reduce the structural responses from thecontrol reduce the structural responses from the uncontrolled valueuncontrolled value

• Performance of proposed is not better than clippedPerformance of proposed is not better than clipped optimal control under optimal control under unsaturated conditionunsaturated condition

• For the strong earthquake (i.e. For the strong earthquake (i.e. saturated conditionsaturated condition),), proposed control is superior in reducing the responsesproposed control is superior in reducing the responses

ConclusionsConclusions


Clipped Modified Decentralized Bang-Bang ControlClipped Modified Decentralized Bang-Bang Control

• Improve the performanceImprove the performance

• Apply to full-scale MR damperApply to full-scale MR damper

Experimental StudiesExperimental Studies

• Shaking table testShaking table test

• Full-scale MR damper testFull-scale MR damper test

Further StudiesFurther Studies

Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers

Documents

control force7fc

optimal control dyke

modified bangbang control

optimal control forcefi

control force of mr

semiactive devices

damper parametersv

mr dampers