Download - 모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어
Structural Dynamics & Vibration Control Lab. 1
모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어
최강민 , 한국과학기술원 건설 및 환경공학과조상원 , 한국과학기술원 건설 및 환경공학과오주원 , 한남대학교 토목공학과이인원 , 한국과학기술원 건설 및 환경공학과
2004 년도 한국전산구조공학회 춘계 학술발표회국민대학교 , 서울2004 년 4 월 10 일
Structural Dynamics & Vibration Control Lab. 2
Outline
• Introduction
• Proposed Method
• Numerical Example
• Conclusions
Structural Dynamics & Vibration Control Lab. 3
Introduction
Fuzzy theory has been recently proposed for the active structural control of civil engineering systems.
The uncertainties of input data from the external loads and structural responses are treated in a much easier way by the fuzzy controller than by classical control theory.
If offers a simple and robust structure for the specification of nonlinear control laws.
Structural Dynamics & Vibration Control Lab. 4
Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes.
Because civil structures has hundred or even thousand DOFs and its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil engineering structure.
Structural Dynamics & Vibration Control Lab. 5
Conventional Fuzzy Controller
One should determine state variables which are used as inputs of the fuzzy controller.
- It is very complicated and difficult for the designer to select state variables used as inputs among a lot of state variables.
One should construct the proper fuzzy rule.
- Control performance can be varied according to many kinds of fuzzy rules.
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Objectives
Development of active fuzzy controller on modal coordinates
- An active modal-fuzzy control algorithm can be magnified efficiency caused by belonging their’ own advantages together.
Structural Dynamics & Vibration Control Lab. 7
Proposed Method
Modal Approach• Equations of motion for MDOF system
• Using modal transformation
• Modal equations
gxMtftKxtxCtxM )()()()(
n
iiiqtqtx
1
)()(
(1)
(2)
(3)gT
iT
iiiiii xftqtqtq )()()( 22
),,1( ni
Structural Dynamics & Vibration Control Lab. 8
• Displacement
where
• State space equation
where
gCCCCC xEtFBtwAtw )()()(
T
CCT
CC
CC
CC EB
IA
0,
0,
02
)()()( txtxtx RC
.:)( dsipcontrolledtxC )(,1
nlxm
iiiC
.:)( dsipresidualtxR
(4)
(5)
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•Control force
•Modal approach is desirable for civil engineering structure
)()( twKtF CC
- Involve hundred or thousand DOFs- Vibration is dominated by the first few modes
(6)
Structural Dynamics & Vibration Control Lab. 10
Structure Modal Structure
dfFuzzy controller
qq ,
Force output
Active Modal-fuzzy Control System
Structural Dynamics & Vibration Control Lab. 11
Modal-fuzzy control system design
Input variables
Output variables
Fuzzification
Defuzzification
Fuzzy inference
• Fuzzy inference : membership functions, fuzzy rule
• Input variables : mode coordinates• Output variable : desired control force
),( qq )( df
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Six-Story Building (Jansen and Dyke 2000)
Numerical Example
2cm/sN227.0im
cmN297ik
005.0
11
10
00
00
00
00
1
1
1
1
1
1
gx
Structural Dynamics & Vibration Control Lab. 13
Frequency Response Analysis• Under the scaled El Centro earthquake
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2.0
2.5
3.0
PS
D
frequency, Hz
102
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
x 105
PS
D
frequency, Hz0 1 2 3 4 5 6 7 8 9 10
0
2
4
6
8
10
12
14
16
x 106
PS
D
frequency, Hz
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
PS
D
frequency, Hz0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
PS
D
frequency, Hz
104
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
x 106
PS
D
frequency, Hz
PSD of Displacement PSD of Velocity PSD of Acceleration
1st F
loor
6th F
loor
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• In frequency analysis, the first mode is dominant.
-The responses can be reduced by modal-fuzzy control using the lowest one mode.
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Active Modal-fuzzy Controller Design
• input variables : first mode coordinates• output variable : desired control force
),( 11 qq
• Fuzzy inference
)( df
• Membership function
- A type : triangular shapes (inputs: 5MFs, output: 5MFs)
- B type : triangular shapes (inputs: 5MFs, output: 7MFs)
A type : for displacement reduction B type : for acceleration reduction
Structural Dynamics & Vibration Control Lab. 16
• Fuzzy rule
- A type
NL NS ZE PS PL
NL PL PL PM PS ZE
NS PL PM PS ZE NS
ZE PM PS ZE NS NM
PS PS ZE NS NM NL
PL ZE NS NM NL NL
- B type
1q
1q
NL NS ZE PS PL
NL PL PL PS PS ZE
NS PL PS PS ZE NS
ZE PS PS ZE NS NS
PS PS ZE NS NS NL
PL ZE NS NL NL NL
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- Fuzzy rule surface (A type)
Structural Dynamics & Vibration Control Lab. 18
Acc
el.
(m/s
ec2
)A
ccel
. (m
/sec
2)
Time(sec)
Acc
el.
(m/s
ec2
)
Kobe(PGA: 0.834g)
California(PGA: 0.156g)
El Centro(PGA: 0.348g)
0 10 20 30 40
-8
-4
0
4
8
- 8
- 4
0
4
8
0 4 8 12 16 20
-8
-4
0
4
8
- 8
- 4
0
4
8
0 10 20 30 40
-8
-4
0
4
8
- 8
- 4
0
4
8
Input Earthquakes
Structural Dynamics & Vibration Control Lab. 19
max,1
)(max
x
txJ i
it
max,2
/)(max
n
ii
it d
htdJ
max,3
)(max
ai
ai
it x
txJ
W
tfJ i
it
)(max
,4
Normalized maximum floor displacement
Normalized maximum inter-story drift
Normalized peak floor acceleration
Maximum control force normalized by the weight of the structure
- This evaluation criteria is used in the second generation linear control problem for buildings (Spencer et al. 1997)
Evaluation Criteria
Structural Dynamics & Vibration Control Lab. 20
Control Results
0
1
2
3
4
5
6
0 0.1 0.2 0.3
Peak interstory drif t (cm)
Flo
or o
f str
uctu
re
Uncontrolled
Fuzzy
Modal-f uzzy A
Modal-f uzzy B
0
1
2
3
4
5
6
0 100 200Peak absolute acceleration
Flo
or o
f str
uctu
re
Uncontrolled
Fuzzy
Modal-f uzzy A
Modal-f uzzy B
Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake
Structural Dynamics & Vibration Control Lab. 21
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Evaluation criteria
Red
uct
ion
fac
tor
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active Fuzzy control
0.343
0.548
0.600
0.562
0.635
0.756
1.186
0.601
0.660
0.0178
0.0134
0.0178
• Normalized Controlled Maximum Response due to Scaled El Centro Earthquake• Normalized Controlled Maximum Response due to Scaled El Centro Earthquake
J1 J2 J3
A typeFuzzy
B type
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Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.449
0.729
0.745
0.727
0.762
0.885
1.856
0.842
0.939
0.0178
0.0134
0.0178
• High amplitude (the 120% El Centro earthquake)• High amplitude (the 120% El Centro earthquake)
0
0.5
1
1.5
2
Evaluation criteria
Red
uct
ion
fac
tor A type
Fuzzy
B type
Structural Dynamics & Vibration Control Lab. 23
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.231
0.403
0.473
0.467
0.509
0.640
1.110
0.619
0.531
0.0178
0.0134
0.0178
• Low amplitude (the 80% El Centro earthquake)• Low amplitude (the 80% El Centro earthquake)
0
0.2
0.4
0.6
0.8
1
1.2
Evaluation criteria
Red
uct
ion
fac
tor A type
Fuzzy
B type
Structural Dynamics & Vibration Control Lab. 24
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.294
0.360
0.430
0.321
0.366
0.402
0.677
0.660
0.614
0.0178
0.0134
0.0178
• Scaled Kobe earthquake (1995)• Scaled Kobe earthquake (1995)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Evaluation criteria
Red
uct
ion
fac
tor A type
Fuzzy
B type
Structural Dynamics & Vibration Control Lab. 25
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.175
0.173
0.178
0.485
0.268
0.244
1.144
0.561
0.260
0.0100
0.0070
0.0076
• Scaled California earthquake (1994)• Scaled California earthquake (1994)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Evaluation criteria
Red
uct
ion
fac
tor A type
Fuzzy
B type
Structural Dynamics & Vibration Control Lab. 26
Conclusions
• A new active modal-fuzzy control strategy for seismic response reduction is proposed.
• Verification of the proposed method has been investigated according to various amplitudes and frequency components.
• The performance of the proposed method is comparable to that of conventional method.
• The proposed method is more convenient and easy to apply to real system