1. Control of a Hybrid System using a -Synthesis Method
2004년도 학술발표회
Session B1 : 동적해석내진설계 I
-합성법을 이용한 복합시스템의 제어
Control of a Hybrid System using a -Synthesis Method
박규식, 한국과학기술원 건설 및 환경공학과 박사 후 연수과정
윤우현, 경원대학교 산업환경대학원 부교수
고만기, 공주대학교 토목공학과 교수
이인원, 한국과학기술원 건설 및 환경공학과 교수

2. Contents Introduction Robust hybrid control system Numerical examples
Conclusions
Structural Dynamics & Vibration Control Lab., KAIST

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
 The overall system robustness may be negatively impacted
by active device or active controller may cause instability
due to small margins.
Structural Dynamics & Vibration Control Lab., KAIST

4. Objective of this study
Apply a -synthesis method to improve the controller
robustness of HCS
Structural Dynamics & Vibration Control Lab., KAIST

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.
Structural Dynamics & Vibration Control Lab., KAIST

6. 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)
 Shortcomings
• Nonconvex problem
• Large controller size
Structural Dynamics & Vibration Control Lab., KAIST

7.  Frequency dependent filters
• Kanai-Tajimi filter
(2)
Structural Dynamics & Vibration Control Lab., KAIST

8. • High-pass and low-pass filters
(3), (4)
Structural Dynamics & Vibration Control Lab., KAIST

9. • Additive uncertainty filter
(5)
• Multiplicative uncertainty filter
(6)
Structural Dynamics & Vibration Control Lab., KAIST

10. Block diagram of -controller with various filtersWu
MUX Wz P
noise K
Block diagram of -controller with various filters
Structural Dynamics & Vibration Control Lab., KAIST

11. Block diagram of robust hybrid control system
LRB installed
Bridge Model
-synthesis method
HAs
Sensor
Block diagram of robust hybrid control system
Structural Dynamics & Vibration Control Lab., KAIST

12. 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.
Structural Dynamics & Vibration Control Lab., KAIST

13. Configuration of sensors
142.7 m
350.6 m
: Accelerometer
: Displacement sensor
Configuration of sensors
Structural Dynamics & Vibration Control Lab., KAIST

14. Configuration of control devices (LRBs+HAs)
Structural Dynamics & Vibration Control Lab., KAIST

15.  Historical earthquake excitations
PGA: 0.348g
PGA: 0.143g
PGA: 0.265g
Structural Dynamics & Vibration Control Lab., KAIST

16. Analysis results
 Maximum evaluation criteria for all the three earthquakes
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
0.443
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
Passive: LRB, Active: HA/, Semiactive: MRD/SMC,
Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/
Structural Dynamics & Vibration Control Lab., KAIST

17. Analysis results
 Maximum evaluation criteria for all the three earthquakes
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
0.443
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
The performance of robust hybrid control system
- better than that of passive, active, semiactive control systems
- similar to that of performance-oriented hybrid control system
Passive: LRB, Active: HA/, Semiactive: MRD/SMC,
Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/
Structural Dynamics & Vibration Control Lab., KAIST

18.  Controller robustness
• The dynamic characteristic of as-built bridge is not
identical to the numerical model.
• There are large differences at high frequencies between
full-order and reduced-order 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

19. • Stiffness matrix perturbation • Time delay of actuator
(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)
Structural Dynamics & Vibration Control Lab., KAIST

20. Max. variation of evaluation criteria vs
Max. variation of evaluation criteria vs. variation of stiffness perturbation
Structural Dynamics & Vibration Control Lab., KAIST

21. Max. variation of evaluation criteria vs. variation of time delay
Structural Dynamics & Vibration Control Lab., KAIST

22. Max. variation of evaluation criteria vs
Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/o snow)
Structural Dynamics & Vibration Control Lab., KAIST

23. Max. variation of evaluation criteria vs
Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow)
Structural Dynamics & Vibration Control Lab., KAIST

24. The hybrid system controlled by a -synthesis method
- shows good robustness w.r.t perturbation of stiffness and mass
matrices and time delay of actuator
- robustness is more affected by perturbation of stiffness matrix
than others.
Max. variation of evaluation criteria vs. variation of stiffness perturbation with time delay (w/ snow)
Structural Dynamics & Vibration Control Lab., KAIST

25. Conclusions Hybrid control system with a -synthesis method
 Has excellent robustness without loss of control
performances
 Could effectively be used to seismically excited cable-
stayed bridges which contains many uncertainties
Structural Dynamics & Vibration Control Lab., KAIST

26. Thank you for your attention!
Acknowledgements
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.
Thank you for your attention!
Structural Dynamics & Vibration Control Lab., KAIST