modified bang-bang control of seismically excited structures using mr dampers
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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
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
Three-Story Building (Dyke at al. 1996)Three-Story Building (Dyke at al. 1996) Numerical ExamplesNumerical Examples
ControlComputer
f
gx
1ax
2ax
3axv
22 22Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
23 23Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
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
• 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
27 27Structural Dynamics & Vibration Control Lab., KAIST, Korea
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
28 28Structural Dynamics & Vibration Control Lab., KAIST, Korea
• 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
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),), proposed control is superior in reducing the responsesproposed control is superior in reducing the responses
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
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