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한국지진공학회 츤계학술발표 연세대학교 2002 년 3 월 23 일. 지진 하중을 받는 구조물의 수정된 분산뱅뱅 제어기법을 이용한 MR Damper 제어. 조 상 원* : KAIST 건설 · 환경공학과 박사과정 김 병 완 : KAIST 건설 · 환경공학과 박사과정 김 운 학 : 한경대학교 토목공학과 교수 이 인 원 : KAIST 건설 · 환경공학과 교수. CONTENTS. Introduction Semi-Active Control - PowerPoint PPT Presentation
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지진 하중을 받는 구조물의 수정된 분산뱅뱅지진 하중을 받는 구조물의 수정된 분산뱅뱅
제어기법을 이용한 제어기법을 이용한 MR DamperMR Damper 제어제어
조 상 원조 상 원 * : KAIST * : KAIST 건설건설 ·· 환경공학과 환경공학과 박사과정 박사과정 김 병 완 김 병 완 : KAIST : KAIST 건설건설 ·· 환경공학과 환경공학과 박사과정 박사과정 김 운 학 김 운 학 : : 한경대학교 토목공학과 교수한경대학교 토목공학과 교수 이 인 원 이 인 원 : KAIST : KAIST 건설건설 ·· 환경공학과 환경공학과 교수 교수
한국지진공학회 츤계학술발표한국지진공학회 츤계학술발표연세대학교 연세대학교 20022002 년 년 33 월 월 2323 일일
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
3 3Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
4 4Structural Dynamics & Vibration Control Lab., KAIST, Korea
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)
5 5Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
6 6Structural Dynamics & Vibration Control Lab., KAIST, Korea
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)
7 7Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
8 8Structural Dynamics & Vibration Control Lab., KAIST, Korea
MR DamperMR Damper
• Characteristics of MR fluidCharacteristics of MR fluid
Without Magnetic Fields With Magnetic Fields
Bearing &
Seal
CoilAccumulator
MR FluidDiaphragm
Wires to
Electromgnet
9 9Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
10 10Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
11 11Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
12 12Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
13 13Structural Dynamics & Vibration Control Lab., KAIST, Korea
(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
14 14Structural Dynamics & Vibration Control Lab., KAIST, Korea
– 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
15 15Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
16 16Structural Dynamics & Vibration Control Lab., KAIST, Korea
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)
17 17Structural Dynamics & Vibration Control Lab., KAIST, Korea
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)
18 18Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
19 19Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
20 20Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
21 21Structural Dynamics & Vibration Control Lab., KAIST, Korea
Six-Story Building (Jansen and Dyke 2000)Six-Story Building (Jansen and Dyke 2000) Numerical ExamplesNumerical Examples
ControlComputer
f1
gx
6ax
5ax
4ax
3ax
2ax
1ax
f2
LVDT
LVDTv1
v2
MR Damper
22 22Structural Dynamics & Vibration Control Lab., KAIST, Korea
• System dataSystem data
– Mass of each floor Mass of each floor : 0.277 N/(cm/sec: 0.277 N/(cm/sec22))
– Stiffness Stiffness : 297 N/cm: 297 N/cm
– Damping ratioDamping ratio : each mode of 0.5%: each mode of 0.5%
23 23Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Damper modeling and parametersDamper modeling and parameters
,
Parameter Value Parameter Value
coa0.0064
Nsec/cma 8.66 N/cm
cob
0.0052 Nsec/cm
Vb
8.86 N/cmV
A 120 300 cm-2
n 2 300 cm-2
190 sec-1
x
F-f
Bouc-Wen Model
24 24Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
25 25Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
26 26Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Unsaturated condition under El Centro earthquakeUnsaturated condition under El Centro earthquake
,|)(|
maxmax,
1
x
txJ i
it,
|/)(|max
max,2
n
ii
it d
htdJ ,
|)(|max
max,3
a
ai
it x
txJ
W
tfJ i
it
|)(|max
,4
Control Strategy J1 J2 J3 J4
Passive-Off 0.862 0.801 0.904 0.00292
Passive-On 0.506 0.696 1.41 0.0178
Lyapunov A 0.686 0.788 0.756 0.0178
Lyapunov B 0.326 0.548 1.39 0.0178
Clipped Optimal A 0.631 0.640 0.636 0.01095
Clipped Optimal B 0.405 0.547 1.25 0.0178
Modified DecentralizedBang-Bang
0.567 0.673 1.18 0.0119
0.591 0.618 1.24 0.0115
27 27Structural Dynamics & Vibration Control Lab., KAIST, Korea
DiscussionsDiscussions
• Maximum measured control forces : 24.03 NMaximum measured control forces : 24.03 N
• Capacity of MR damper : 29N (1.8% of total weight)Capacity of MR damper : 29N (1.8% of total weight)
Unsaturated condition !!Unsaturated condition !!
28 28Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Saturated condition under Saturated condition under magnifiedmagnified El Centro earthquake El Centro earthquake
,|)(|
maxmax,
1
x
txJ i
it,
|/)(|max
max,2
n
ii
it d
htdJ ,
|)(|max
max,3
a
ai
it x
txJ
W
tfJ i
it
|)(|max
,4
Control Strategy J1 J2 J3 J4
Passive-Off 19.84 19.817 20.034 0.0036
Passive-On 19.108 17.8 19.775 0.0217
Lyapunov B 18.816 18.401 18.191 0.0217
Clipped Optimal B 19.112 17.814 18.864 0.0217
Modified DecentralizedBang-Bang
19.623 19.577 19.56 0.0122
29 29Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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),), clipped optimal control is not better than othersclipped optimal control is not better than others
ConclusionsConclusions
30 30Structural Dynamics & Vibration Control Lab., KAIST, Korea
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