1. Robust Hybrid Control System
2003년도 대한토목학회 정기 학술대회
Robust Hybrid Control System
for a Seismically-Excited Cable-Stayed Bridge
박규식, 한국과학기술원 건설 및 환경공학과 박사과정
정형조, 세종대학교 토목환경공학과 조교수
김운학, 한경대학교 토목공학과 교수
이인원, 한국과학기술원 건설 및 환경공학과 교수

2. CONTENTS
Introduction
Robust hybrid control system
Numerical examples
Conclusions

3. 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.

4. Objective of this study
Apply robust control algorithms to improve
the controller robustness of HCS

5. ROBUST HYBRID CONTROL SYSTEM
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)
• actuator capacity: 1000 kN
• The actuator dynamics are neglected.

6. Robust hybrid control system
Control algorithm
 RHCS I
• Primary control scheme
· Linear quadratic Gaussian (LQG) algorithm
• Secondary control scheme
· On-off type controller according to LRB’s responses

7. Robust hybrid control system
Bridge Model
LRB
MUX HA
On/Off
LQG
Sensor
Block diagram of RHCS I

8. Robust hybrid control system
 RHCS II
• H2 control algorithm with frequency weighting filters
• Frequency weighting filters

9. Robust hybrid control system Block diagram of RHCS II
Bridge Model R Wu kg Wg Q Wz DM
LRB
MUX HA H2
Sensor K
Block diagram of RHCS II
 RHCS III
• H control algorithm with frequency weighting filters

10. NUMERICAL EXAMPLES Analysis model  Bridge model
• Bill Emerson Memorial Bridge
· Benchmark control problem
· Under construction in Cape Girardeau, MO, USA
· 16 Shock transmission devices (STDs) are employed
between the tower-deck connections.

11. Configuration of control devices (HAs+LRBs)
Numerical examples
142.7 m
350.6 m
2+3
4+3
Configuration of control devices (HAs+LRBs)

12.  Historical earthquake excitations
Numerical examples
 Historical earthquake excitations
PGA: 0.348g
PGA: 0.143g
PGA: 0.265g

13. Analysis results  Control performances Numerical examples El Centro
Mexico City
Gebze
Max.

14.  Controller robustness
Numerical examples
 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.
where
: nominal stiffness matrix
: perturbed stiffness matrix
: perturbation amount

15. Numerical examples
Max. variation of evaluation criteria for variations of stiffness perturbation

16. • Maximum variations of evaluation criteria for all three
Numerical examples
• Maximum variations of evaluation criteria for all three
earthquake (%, 5% perturbation)
Evaluation criteria
CHCS
RHCS I
RHCS II
RHCS III
J1. Max. base shear
9.75
10.34
9.20
7.69
J2. Max. deck shear
16.62
16.26
4.42
14.34
J3. Max. base moment
16.68
15.97
4.93
5.01
J4. Max. deck moment
4.46
5.37
6.21
8.91
J5. Max. cable deviation
13.08
14.22
13.96
15.68
J6. Max. deck dis.
7.51
4.06
1.48
3.52
J7. Norm base shear
50.00
6.54
6.12
7.02
J8. Norm deck shear
139.17
7.94
10.68
J9. Norm base moment
39.94
5.98
5.54
10.36
J10. Norm deck moment
42.15
10.37
7.56
21.82
J11. Norm cable deviation
41.32
18.65
13.78
30.31

17. • Maximum variations of evaluation criteria for all three
Numerical examples
• Maximum variations of evaluation criteria for all three
earthquake (%, 20% perturbation)
Evaluation criteria
RHCS II
RHCS III
J1. Max. base shear
36.51
27.33
J2. Max. deck shear
22.93
38.66
J3. Max. base moment
33.08
30.86
J4. Max. deck moment
34.48
40.75
J5. Max. cable deviation
50.07
31.97
J6. Max. deck dis.
5.02
18.86
J7. Norm base shear
31.78
29.98
J8. Norm deck shear
39.33
35.21
J9. Norm base moment
29.70
32.17
J10. Norm deck moment
45.34
33.66
J11. Norm cable deviation
72.35
47.83

18. CONCLUSIONS Hybrid control system with robust control algorithms
 has excellent robustness for stiffness perturbation without
loss of control performances
 could be used to seismically excited cable-stayed bridges
This research is supported by the National Research Laboratory (NRL) program
(Grant No.: 2000-N-NL-01-C-251) from the Ministry of Science of Technology
(MOST) and grant for pre-doctoral students (Grant No.: KRF D00050)
from the Korea Research Foundation (KRF) in Korea.