robust hybrid control of a seismically excited cable-stayed bridge
DESCRIPTION
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 PresentationTRANSCRIPT
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 )
-2
-1
0
1
2
3
Acc
eler
atio
n (m
/s2 )
G ebze
PGA: 0.265gPGA: 0.265g
0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )
0
1
2
3
4
5
6
7
8
Pow
er S
pect
ral D
ensi
ty
0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )
0
1
2
3
4
5
6
Pow
er S
pect
ral D
ensi
ty
0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )
0
1
2
3
4
5
6
7
8
9
Pow
er S
pect
ral D
ensi
ty
Historical earthquake excitations Historical earthquake excitations
Structural Dynamics & Vibration Control Lab., KAIST 16 16
- Max. responses J1: Base shear J2: Shear at deck level J3: Base moment J4: Moment at deck level J5: Cable deviation J6: Deck dis.
- Normed responses J7: Base shear J8: Shear at deck level J9: Base moment J10: Moment at deck level J11: Cable deviation
Evaluation criteria Evaluation criteria
Structural Dynamics & Vibration Control Lab., KAIST 17 17
Analysis results
Control performances Control performances
Displacement under El Centro earthquake
(a) STDs (b) RHCS
Structural Dynamics & Vibration Control Lab., KAIST 18 18
Cable tension under El Centro earthquake
(a) STDs (b) RHCS
Structural Dynamics & Vibration Control Lab., KAIST 19 19
Base shear force under El Centro earthquake
(a) STDs (b) RHCS
Structural Dynamics & Vibration Control Lab., KAIST 20 20
Evaluation criteria Passive Active Semiactive Hybrid I Hybrid II
J1. Max. base shear 0.546 0.523 0.468 0.485 0.497
J2. Max. deck shear 1.462 1.146 1.283 0.921 1.170
J3. Max. base moment 0.619 0.416 0.485 0.443 0.454
J4. Max. deck moment 1.266 0.821 1.184 0.656 0.752
J5. Max. cable deviation 0.208 0.154 0.219 0.143 0.144
J6. Max. deck dis. 3.830 1.465 3.338 1.553 1.117
J7. Norm base shear 0.421 0.368 0.370 0.377 0.360
J8. Norm deck shear 1.550 1.005 1.351 0.899 0.976
J9. Norm base moment 0.482 0.316 0.404 0.338 0.307
J10. Norm deck moment 1.443 0.682 1.607 0.728 0.617
J11. Norm cable deviation 0.022 0.016 0.019 0.017 0.015
• Maximum evaluation criteria for all the three earthquakes • Maximum evaluation criteria for all the three earthquakes
Passive: LRB, Active: HA/, Semiactive: MRD/SMC,
Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11
Passive
Active
Semiactive
Hybrid I
Hybrid II
Structural Dynamics & Vibration Control Lab., KAIST 21 21
Controller robustness
• The dynamic characteristic of as-built bridge is not identical to the numerical model.
• There are large differences at high frequencies between evaluation and design models.
• There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.
Controller robustness
• The dynamic characteristic of as-built bridge is not identical to the numerical model.
• There are large differences at high frequencies between evaluation and design models.
• There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.
Robust analysis should be performed to verify the applicability of the control system.
Structural Dynamics & Vibration Control Lab., KAIST 22 22
where : nominal stiffness matrix: perturbed stiffness matrix: perturbation amount
• Stiffness matrix perturbation
• Mass matrix perturbation
· Additional snow loads (97.7 kg/m2, UBC) are added to the deck.
where : time delay: time delay amount: sampling time (0.02 sec)
• Time delay of actuator
(7)
(8)
pert (1 ) K K
pertKK
sT
sT
pert (1 ) K K
pertKK
sT
sT
Structural Dynamics & Vibration Control Lab., KAIST 23 23
0
10
20
30
40
50
60
70
80
90
±5% ±10% ±15% ±20%
Stiffness Perturbation (%)
Max
. Var
iati
on (
%)
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 stiffness perturbation
Structural Dynamics & Vibration Control Lab., KAIST 24 24
0
5
10
15
20
25
30
35
40
0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020
Time Delay (sec)
Max
. Var
iati
on (
%)
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.
Acknowledgements