Self Playing Show

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International Symposium on Earthquake
Engineering Commemorating 10th Anniversary of the
1995 Kobe Earthquake
HYBRID SYSTEM CONTROLLEDBY A ?-SYNTHESIS METHOD
Kyu-Sik Park, Post-Doctoral Researcher, KAIST,
Korea Namihiko Inoue, Senior Researcher, BRI,
Japan Hyung-Jo Jung, Assistant Professor, Sejong
Univ., Korea In-Won Lee, Professor, KAIST, Korea
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Contents

• Introduction
• Robust hybrid control system
• Numerical examples
• Conclusions

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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.
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• Objective

? Apply a hybrid control system for vibration
control of a seismically excited cable-stayed
bridge ? Apply a ?-synthesis method to improve
the controller robustness
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Robust Hybrid Control System (RHCS)

• Control devices

? Passive control devices Lead rubber
bearings (LRBs) Design procedure Ali and
Abdel-Ghaffar (1995) Bouc-Wen model
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? Active control devices Hydraulic actuators
(HAs) An actuator capacity has a capacity of
1000 kN. The actuator dynamics are neglected.
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• Control algorithm ?-synthesis method

? Cost function
(1)
where
structured singular value transfer function
of closed-loop system perturbation
? Advantages
Combine uncertainty in the design procedure
Guarantee the stability and performance (robust
performance)
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? Frequency dependent filters
Kanai-Tajimi filter
(2)
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High-pass and low-pass filters
(3), (4)
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Additive uncertainty filter
(5)
Multiplicative uncertainty filter
(6)
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LRB-installed structure
?-synthesis method
Sensor
HA
Block diagram of robust hybrid control system
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Numerical Examples

• 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.
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142.7 m
350.6 m
142.7 m
Configuration of control devices (LRBsHAs)
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tower
deck
LRB
Placement of control devices
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? Historical earthquake excitations
PGA 0.348g
PGA 0.143g
PGA 0.265g
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? Evaluation criteria
- 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
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• Analysis results

? Control performances
(a) STDs
(b) RHCS
Displacement under El Centro earthquake
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(a) STDs
(b) RHCS
Cable tension under El Centro earthquake
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(a) STDs
(b) RHCS
Base shear force under El Centro earthquake
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Important responses of bridge and the peak
and normed control forces for all the three
earthquakes
Passive Active Semiactive Hybrid I Hybrid II
Max. dis (cm) 0.2745 0.1054 0.1091 0.1117 0.0804
Max. deck shear (kN) 5533 4344 5206 3375 4408
Max. base moment (kN?m) 349754 249586 267714 244316 244582
Max. (Tmax/Tf) 0.4773 0.4561 0.4611 0.4586 0.4556
Min. (Tmin/Tf) 0.2705 0.2822 0.2774 0.2853 0.2821
Max. (?T) 784 453 527 453 438
Max. control force (kN) 1102 1000 1000 1338 1493
Normed control force (kN) 110 141 121 120 93
Tf failure tension of cable Passive LRB,
Active HA/?, Semiactive MRD/ ?, Hybrid I
LRBHA/LQG, Hybrid II LRBHA/?
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? 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.
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Stiffness matrix perturbation
(7)
where
nominal stiffness matrix perturbed stiffness
matrix perturbation amount
Mass matrix perturbation Additional snow
loads (97.7 kg/m2, UBC) are added to the
deck.
Time delay of actuator
(8)
where
time delay time delay amount sampling time
(0.02 sec)
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Max. variation of evaluation criteria vs.
variation of stiffness perturbation
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Max. variation of evaluation criteria vs.
variation of time delay
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Max. variation of evaluation criteria vs.
variation of stiffness perturbation and time
delay (w/o snow)
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Max. variation of evaluation criteria vs.
variation of stiffness perturbation and time
delay (w/ snow)
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Conclusions

• Robust hybrid control system

? Control performance is improved consuming
similar control forces. ? Has excellent
robustness without loss of control performances
? could be used for cable-stayed bridges
containing many uncertainties
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Acknowledgements

• This presentation is supported by the Japan
  Association for Earthquake Engineering (JAEE).

Thank you for your attention!