1. Robust Hybrid Control System
2003년도 한국지진공학회 추계 학술발표회
Robust Hybrid Control System
박규식, 한국과학기술원 건설 및 환경공학과 박사과정
정형조, 세종대학교 토목환경공학과 조교수
오주원, 한남대학교 토목환경공학과 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 (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 capacity has a capacity of 1000 kN.
• The actuator dynamics are neglected.

6. 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. Bridge Model
Sensor
LQG
On/Off HA
LRB
MUX
Block diagram of RHCS I

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

9. Block diagram of RHCS II
Bridge Model
Sensor H2 HA
LRB
MUX DM Wg kg R Wu Wz Q K
Block diagram of RHCS II

10.  RHCS III
• H control algorithm with frequency weighting filters

11. 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.

12. Schematic of the Bill Emerson Memorial Bridge

13. Configuration of sensors
142.7 m
350.6 m
: Accelerometer
: Displacement sensor
Configuration of sensors

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

15.  Historical earthquake excitations
PGA: 0.348g

16.  Historical earthquake excitations
PGA: 0.348g
PGA: 0.143g

17.  Historical earthquake excitations
PGA: 0.348g
PGA: 0.143g
PGA: 0.265g

18.  Evaluation criteria
• Structural response
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: Deck dis. at abutment
• Control strategy
J12: Peak control force, J13: Device stroke
J14: Peak power, J15: Total power
J16: No. of control devices, J17: No. of sensors
J18:

19. Displacement under El Centro earthquake
Analysis results
 Control performances
(a) Uncontrolled
(b) RHCS III
Displacement under El Centro earthquake

20. Cable tension under El Centro earthquake
(a) Uncontrolled
(b) RHCS III
Cable tension under El Centro earthquake

21. Base shear force under El Centro earthquake
(a) Uncontrolled
(b) RHCS III
Base shear force under El Centro earthquake

22. • Maximum evaluation criteria for all the three earthquakes
CHCS*
RHCS I
RHCS II
RHCS III
J1. Max. base shear
0.4841
0.4810
0.5319
0.4808
J2. Max. deck shear
0.9476
0.9508
0.9607
0.9579
J3. Max. base moment
0.4444
0.4426
0.5057
0.4380
J4. Max. deck moment
0.6750
0.6739
0.6441
0.5750
J5. Max. cable deviation
0.1468
0.1469
0.1252
0.1473
J6. Max. deck dis.
1.6702
1.6787
1.0652
1.1923
J7. Norm base shear
0.3744
0.3749
0.3929
0.3514
J8. Norm deck shear
0.9261
0.9352
0.7868
0.9301
J9. Norm base moment
0.3345
0.3389
0.3590
0.3132
J10. Norm deck moment
0.7806
0.8055
0.5404
0.7458
J11. Norm cable deviation
1.819e-2
1.769e-2
1.275e-2
1.782e-2
*Conventional HCS (HCS with LQG)

23.  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

24. Max. variation of evaluation criteria for variations of stiffness perturbation

25. • 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

26. • 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

27. 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

28. Thank you for your attention!
Acknowledgements
This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST).
Thank you for your attention!