Robust Hybrid Control of a Seismically Excited Cable- Stayed Bridge JSSI 10th Anniversary Symposium on Performance of Response Controlled Buildings Kyu-Sik Park , Post-Doctoral Researcher, KAIST, Korea Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea Woon-Hak Kim, Professor, Hankyong National Univ., Korea In-Won Lee, Professor, KAIST, Korea
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Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge
JSSI 10th Anniversary Symposium on Performance of Response Controlled Buildings. Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge. Kyu-Sik Park , Post-Doctoral Researcher , KAIST, Korea Hyung-Jo Jung, Assistant Professor , Sejong Univ., Korea - PowerPoint PPT Presentation
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Robust Hybrid Control of
a Seismically Excited Cable-Stayed Bridge
JSSI 10th Anniversary Symposium on
Performance of Response Controlled Buildings
Kyu-Sik Park, Post-Doctoral Researcher, KAIST, Korea
Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea
Woon-Hak Kim, Professor, Hankyong National Univ., Korea
In-Won Lee, Professor, KAIST, Korea
Structural Dynamics & Vibration Control Lab., KAIST 2 2
Introduction
Robust hybrid control system
Numerical examples
Conclusions
Contents
Structural Dynamics & Vibration Control Lab., KAIST 3 3
Introduction
Hybrid control system (HCS)
A combination of passive and active/semiactive control devices
• Passive devices: insure the control system robustness
• Active/semiactive devices: improve the control performances
The overall system robustness may be negatively impacted
by active/semiactive device or active/semiactive controller
may
cause instability due to small margins.
A combination of passive and active/semiactive control devices
• Passive devices: insure the control system robustness
• Active/semiactive devices: improve the control performances
The overall system robustness may be negatively impacted
by active/semiactive device or active/semiactive controller
may
cause instability due to small margins.
Structural Dynamics & Vibration Control Lab., KAIST 4 4
Objective
Apply a hybrid control system for vibration control of
a seismically excited cable-stayed bridge
Apply a robust control algorithm to improve the controller robustness
Apply a hybrid control system for vibration control of
a seismically excited cable-stayed bridge
Apply a robust control algorithm to improve the controller robustness
Structural Dynamics & Vibration Control Lab., KAIST 5 5
Robust Hybrid Control System (RHCS)
Control devices
Passive control devices
• Lead rubber bearings (LRBs)
• Design procedure: Ali and Abdel-Ghaffar (1995)
• Bouc-Wen model
Passive control devices
• Lead rubber bearings (LRBs)
• Design procedure: Ali and Abdel-Ghaffar (1995)
• Bouc-Wen modelLRBF
rxyD
yF
ekpk
LRBF
rxyD
yF
ekpk
1
( , ) (1 )
1
LRB r r e r e y
n n
i r r ry
F x x k x k D y
y A x x y y x yD
Structural Dynamics & Vibration Control Lab., KAIST 6 6
Active control devices
• Hydraulic actuators (HAs)
• An actuator capacity has a capacity of 1000 kN.
• The actuator dynamics are neglected.
Active control devices
• Hydraulic actuators (HAs)
• An actuator capacity has a capacity of 1000 kN.
• The actuator dynamics are neglected.
Structural Dynamics & Vibration Control Lab., KAIST 7 7
Control algorithm: -synthesis method
where : structured singular value: transfer function of closed-loop system : perturbation
Cost function Cost function
(1)
Advantages Advantages
• Combine uncertainty in the design procedure
• Guarantee the stability and performance (robust performance)
• Combine uncertainty in the design procedure
• Guarantee the stability and performance (robust performance)
supd dy wJ j
N
d dy wN
Δ
Structural Dynamics & Vibration Control Lab., KAIST 8 8
Frequency dependent filters Frequency dependent filters
• Kanai-Tajimi filter • Kanai-Tajimi filter
(2)
10-2
100
102
104
106
10-10
10-8
10-6
10-4
10-2
100
102
Frequency (rad/sec)
Mag
init
ud
e
El Centro Mexico CityGebze K-T filter
2
0
2 2
2
2
g g g
g
g g g
S sW
s s
0 El Centro 0 ~ 10 rad/secMexico City Gebze
max mean ,
17 rad/sec,
0.3
g gx x
g
g
S S
Structural Dynamics & Vibration Control Lab., KAIST 9 9
• High-pass and low-pass filters
(3), (4)
10-2
100
102
104
106
10-1
100
Frequency (rad/sec)
Mag
nit
ud
e
Wz
Wu
10.2 1
601
1240
,u
s
Ws
11
601
130
z
s
Ws
10.2 1
601
1240
,u
s
Ws
11
601
130
z
s
Ws
Structural Dynamics & Vibration Control Lab., KAIST 10 10
• Additive uncertainty filter
(5)
10-1
100
101
102
103
104
100
101
102
103
Frequecy (rad/sec)
SV
, mag
nit
ud
e
Evaluation ModelDesign Model
10-1
100
101
102
103
104
10-4
10-3
10-2
10-1
100
101
102
Frequency (rad/sec)
SV
-dif
f, m
agn
itu
de
SV-diff-xg2yWxg2y
• Multiplicative uncertainty filter
(6)
2 2
1 2 2 2
2 2
1 1 1
2
2gx
c s sW
s s
y
1
1
42
1 2
10.32,
10,
1.71 10 ,
0.8
c
0.01W u u
Structural Dynamics & Vibration Control Lab., KAIST 11 11
LRB-installed
structure
Sensor-synthesis methodHA
Block diagram of robust hybrid control systemBlock diagram of robust hybrid control system
ey
my
syactiveu
activef
gx ey
my
syactiveu
activef
gx
Structural Dynamics & Vibration Control Lab., KAIST 12 12
Analysis model
Bridge model
• Bill Emerson Memorial Bridge
· Benchmark control problem
· Located in Cape Girardeau, MO, USA
· 16 shock transmission devices (STDs) are employed between the tower-deck connections.
Bridge model
• Bill Emerson Memorial Bridge
· Benchmark control problem
· Located in Cape Girardeau, MO, USA
· 16 shock transmission devices (STDs) are employed between the tower-deck connections.
Numerical Examples
Structural Dynamics & Vibration Control Lab., KAIST 13 13
Configuration of control devices (LRBs+HAs)
(3+2)
(3+2)
(3+4)
(3+4)
(3+4)
(3+4)
(3+2)
(3+2)
Bent 1 Pier 2 Pier 3 Pier 4
142.7 m 350.6 m 142.7 m
Structural Dynamics & Vibration Control Lab., KAIST 14 14
Bent 1
4 actuators2 actuators
Pier 2 Pier 3 Pier 4
bottom viewof bridge deck
edge girder
towerdeck
LRB
Placement of control devices
Structural Dynamics & Vibration Control Lab., KAIST 15 15
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )
-3
-2
-1
0
1
2
3
4
Acc
eler
atio
n (m
/s2 )
El C entro
PGA: 0.348gPGA: 0.348g
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )
-2
-1
0
1
2
Acc
eler
atio
n (m
/s2 )
M exico C ity
PGA: 0.143gPGA: 0.143g
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )
w/o snow, El Centrow/o snow, Mexico Cityw/o snow, Gebzew/ snow, El Centrow/ snow, Mexico Cityw/ snow, Gebze
Max. variation of evaluation criteria vs. variation of time delay
Structural Dynamics & Vibration Control Lab., KAIST 25 25
Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/o snow)
Structural Dynamics & Vibration Control Lab., KAIST 26 26
Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/ snow)
Structural Dynamics & Vibration Control Lab., KAIST 27 27
Robust hybrid control system
Control performances is superior to passive control system and slightly better than active and semiactive control systems. Has excellent robustness without loss of control performances
Control performances is superior to passive control system and slightly better than active and semiactive control systems. Has excellent robustness without loss of control performances
could be used for cable-stayed bridges containing
many uncertainties
Conclusions
Structural Dynamics & Vibration Control Lab., KAIST 28 28
Thank you for your attention!
This research is supported by the National Research Laboratory program from the Ministry of Science of Technology and the Grant for Pre-Doctoral Students from the Korea Research Foundation in Korea.