The Asian-Pacific Symposium on Structural Reliability and its ApplicationsSeoul, Korea, August 18-20, 2004
Kyu-Sik ParkKyu-Sik Park, Ph. D. Candidate, KAIST, KoreaHyung-Jo JungHyung-Jo Jung, Assistant Professor, Sejong Univ., KoreaWoon-Hak KimWoon-Hak Kim, Professor, Hankyong Nat. Univ., KoreaIn-Won LeeIn-Won Lee, Professor, KAIST, Korea
Robust Hybrid Control ofa Seismically Excited Cable-Stayed Bridge
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 22
Introduction
Robust hybrid control system Numerical examples
Conclusions
Contents
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 33
Introduction Hybrid control system (HCS)
A combination of passive and active control devices
• Passive devices: offer some degree of protection in the case of power failure • Active devices: improve the control performances
However, the robustness of HCS could be decreased by the active control devices.
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 44
Objective of this study
Apply robust control algorithms to improvethe controller robustness of HCS
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 55
Robust hybrid control system (RHCS)
Control devices Passive control devices • Lead rubber bearings (LRBs) • Design procedure: Ali and Abdel-Ghaffar (1995) • Bouc-Wen model
Active control devices • Hydraulic actuators (HAs) • An actuator has a capacity of 1000 kN. • The actuator dynamics are neglected.
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 66
Control algorithm RHCS I
• Primary control scheme · Linear quadratic Gaussian (LQG) algorithm
• Secondary control scheme
· On-off type controller according to LRB’s responses
HA,HA,
,
0,i c
i
ff
2,LRB ,LRB0.005m or 0.03m/s
otherwiser ri ix x
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 77
Bridge Model
SensorLQGOn-OffHA
LRB
MU
Xey
mysy
HA( )cu
,LRB ,LRB,r rx x
HA / 0uHA / 0f
LRBf
fgx
Block diagram of RHCS I
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RHCS II
• H2 control algorithm with frequency weighting filters
• Frequency weighting filters
20
2 2
2
2g g g
gg g g
S sW
s s
0 2.50440.3
17 rad/secg
g
S
1/ 60 11/ 30 1z
sWs
0.2(1/ 60 1)1/ 240 1u
sWs
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 99
Bridge Model
SensorH2HA
LRB
MU
X
ey
mysy
,LRB ,LRB,r rx x
HAuHAf
LRBf
fgx
Block diagram of RHCS II
DMWgkggx
R Wu
WzQzz
v
K
u
uz
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 1010
RHCS III
• H control algorithm with frequency weighting filters
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Numerical examples
Analysis model Bridge model • Bill Emerson Memorial Bridge · Benchmark control problem (Dyke et al., 2003) · Located in Cape Girardeau, MO, USA · 16 shock transmission devices (STDs) are employed
between the tower-deck connections.
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142.7 m 350.6 m 142.7 m
gx
Schematic of the Bill Emerson Memorial Bridge
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142.7 m 350.6 m 142.7 m
gx
Configuration of sensors
: Accelerometer: Displacement sensor
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142.7 m 350.6 m 142.7 m
gx
Configuration of control devices (HAs+LRBs)
2+3
2+3 4+3
4+3
4+3
4+3
2+3
2+3
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 1515
0 10 2 0 3 0 40 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 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
Historical earthquake excitations
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0 10 2 0 3 0 40 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 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
ty0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
T 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 2 3 4 5 6 7 8 9 10F re q u e n c y (H z)
0
1
2
3
4
5
6
Pow
er S
pect
ral D
ensi
ty
Historical earthquake excitations
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 1717
0 10 2 0 3 0 40 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 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
ty0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
T 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 2 3 4 5 6 7 8 9 10F 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 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 ebzePGA: 0.265gPGA: 0.265g
0 1 2 3 4 5 6 7 8 9 10F 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
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 1818
• J1/J7 : Peak/Normed base shear
• J2/J8 : Peak/Normed shear at deck level • J3/J9 : Peak/Normed overturning moment
• J4/J10 : Peak/Normed moment at deck level • J5/J11 : Peak/Normed cable tension deviation • J6: Peak Deck dis. at abutment
Evaluation criteria
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Analysis results Control performances
Displacement under El Centro earthquake
(a) Uncontrolled (b) RHCS III
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2020
Cable tension under El Centro earthquake
(a) Uncontrolled (b) RHCS III
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2121
Shear force under El Centro earthquake
(a) Uncontrolled (b) RHCS III
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2222
Evaluation criteria CHCS* RHCS I RHCS II RHCS IIIJ1. Max. base shear 0.4854 0.4607 0.5319 0.4930J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997J3. Max. base moment 0.4427 0.4395 0.5057 0.4519J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863J7. Norm base shear 0.3770 0.3762 0.3929 0.3581J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035J9. Norm base moment 0.3375 0.3378 0.3590 0.3216J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2
• Maximum evaluation criteria for all three earthquakes
*Conventional HCS controlled by LQG algorithm
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Evaluation criteria CHCS* RHCS I RHCS II RHCS IIIJ1. Max. base shear 0.4854 0.4607 0.5319 0.4930J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997J3. Max. base moment 0.4427 0.4395 0.5057 0.4519J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863J7. Norm base shear 0.3770 0.3762 0.3929 0.3581J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035J9. Norm base moment 0.3375 0.3378 0.3590 0.3216J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2
• Maximum evaluation criteria for all three earthquakes
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11
Evaluation Criteria
Val
ues
CHCS*RHCS IRHCS IIRHCS III
*Conventional HCS controlled by LQG algorithm
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Controller robustness • The dynamic characteristic of as-built bridge is not identical to the numerical model. • To verify the applicability of RHCS, the controller robustness is investigated to perturbation of stiffness parameter.
pert (1 ) K K
wherepertK
K
: nominal stiffness matrix: perturbed stiffness matrix: perturbation amount (5% ~ 20 %)
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2525
• Maximum variations of evaluation criteria for all three earthquakes (%, 5% perturbation)
Evaluation criteria RHCS I RHCS II RHCS IIIJ1. Max. base shear 14.24 9.20 6.88J2. Max. deck shear 17.78 4.42 13.49J3. Max. base moment 16.74 4.93 5.26J4. Max. deck moment 6.09 6.21 5.49J5. Max. cable deviation 13.62 13.96 14.51J6. Max. deck dis. 4.61 1.48 2.70J7. Norm base shear 6.73 6.12 5.70J8. Norm deck shear 8.09 4.93 6.44J9. Norm base moment 6.33 5.54 5.91J10. Norm deck moment 8.54 7.56 10.86J11. Norm cable deviation 16.84 13.78 17.29
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2626
• Maximum variations of evaluation criteria for all three earthquakes (%, 20% perturbation)
Evaluation criteria RHCS II RHCS IIIJ1. Max. base shear 36.51 33.02J2. Max. deck shear 22.93 34.32J3. Max. base moment 33.08 30.67J4. Max. deck moment 34.48 40.71J5. Max. cable deviation 50.07 33.27J6. Max. deck dis. 5.02 8.06J7. Norm base shear 31.78 30.19J8. Norm deck shear 39.33 35.96J9. Norm base moment 29.70 28.99J10. Norm deck moment 45.34 32.40J11. Norm cable deviation 72.35 52.74
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0
20
40
60
80
5 10 15 20
Stiffness perturbation (±, %)
Max
. var
iatio
n (%
)
RHCS IRHCS IIRHCS III
Max. variation of evaluation criteria for variations of stiffness perturbation
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Conclusions Hybrid control system with robust control algorithms
Has excellent robustness for stiffness perturbation without loss of control performances
• RHCS I obtains robustness only for 5% stiffness perturbations.
• RHCS III is more robust than RHCS II.
Robust hybrid control system could effectively be used to seismically excited cable-stayed bridge.
Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 2929
This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST) and the Grant for Pre-Doctoral Students from the Korea Research Foundation (KRF) in Korea.
Thank you for your attention!
Acknowledgements
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