1. a Bang-Bang Type Controller
2003년도 한국전산구조공학회 봄 학술발표회
Hybrid Control with
a Bang-Bang Type Controller
박규식, 한국과학기술원 건설 및 환경공학과 박사과정
정형조, 세종대학교 토목환경공학과 조교수
조상원, 한국과학기술원 건설 및 환경공학과 박사과정
이인원, 한국과학기술원 건설 및 환경공학과 교수

2. Contents Introduction HCS with a bang-bang type controller
Numerical examples
Conclusions

3. Introduction Hybrid control system (HCS) Cable-stayed bridge
 A combination of passive and active devices
 Higher level of performance
 Reliable and robust
Cable-stayed bridge
 Aesthetic shape, structural efficiency and economical
construction
 Very flexible due to low structural damping
 Vibration control is needed to protect the bridge.

4. Objective of this study
Apply robust hybrid control system for seismic protection
of a cable-stayed bridge

5. HCS with a bang-bang type controller
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  Primary control scheme
• Linear quadratic Gaussian (LQG) algorithm
• Optimal weighting matrix: Maximum response approach
 Secondary control scheme
• Bang-Bang type controller according to LRB’s responses

7. Block diagram of hybrid control system
Bridge Model
HCS
Block diagram of hybrid control system

8. Hybrid control with a bang-bang type controller
Bridge Model
Sensor
LQG
On/Off HA
LRB
MUX
Hybrid control with a bang-bang type controller

9. 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.

10. Schematic of the Bill Emerson Memorial Bridge

11. : Accelerometer : Displacement sensor Location of sensor 142.7 m

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

13.  Historical earthquake excitations
PGA: 0.348g

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

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

16.  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:

17. Analysis results  Control performances (a) Time-history response
(b) Frequency response
Base shear force record at pier 2
under El Centro earthquake

18. Restoring force record of LRB at pier 2

19. • Maximum evaluation criteria for all the three earthquakes
Passive
Active
Hybrid
J1. Max. base shear
0.5459
0.4898
0.5125
J2. Max. deck shear
1.4616
1.1706
0.9510
J3. Max. base moment
0.6188
0.4562
0.4439
J4. Max. deck moment
1.2656
0.8803
0.6737
J5. Max. cable deviation
0.2077
0.1469
0.1479
J6. Max. deck dis.
3.8289
1.8079
1.6787
J7. Norm base shear
0.4211
0.3820
0.3824
J8. Norm deck shear
1.5502
0.9737
0.9366
J9. Norm base moment
0.4815
0.3591
0.3435
J10. Norm deck moment
1.4429
0.7659
0.8196
J11. Norm cable deviation
2.233e-2
1.622e-2
1.718e-2

20. • Actuator requirements
Earthquake
Max.
Active
Hybrid
1940
El Centro NS
Force(kN)
1000
Stroke(m)
0.0984
0.0740
Vel. (m/s)
0.5502
0.5480
1985
Mexico City
649.37
332.13
0.0403
0.0278
0.2452
0.2003
1990
Gebze NS
924.57
0.1300
0.1207
0.4197
0.4226
Actuator requirement constraints
Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

21.  Controller robustness
• The dynamic characteristic of as-built bridge is not
identical to the numerical model.
• To verify the applicability of HCS, the controller
robustness is investigated to perturbation of stiffness
parameter.
where
: nominal stiffness matrix
: perturbed stiffness matrix
: perturbation amount

22. *: Active control system using 32 HAs (-synthesis)
• Maximum variations of evaluation criteria for the ±7%
stiffness perturbation systems under El Centro earthquake (%)
Evaluation criteria
Turan
(2001)*
Active
Hybrid
J1. Max. base shear
36.9
9.1
J2. Max. deck shear
52.0
68.0
21.8
J3. Max. base moment
22.5
50.1
6.2
J4. Max. deck moment
31.0
27.3
5.1
J5. Max. cable deviation
9.2
7.0
5.6
J6. Max. deck dis.
19.0
16.3
2.3
J7. Norm base shear
47.4
196.4
7.2
J8. Norm deck shear
35.3
335.2
5.3
J9. Norm base moment
28.5
138.1
7.4
J10. Norm deck moment
18.7
84.5
13.3
J11. Norm cable deviation
31.3
71.0
17.1
*: Active control system using 32 HAs (-synthesis)

23. (a) Time-history response (b) Frequency response
Base shear force record at pier 2 in the 7% stiffness perturbed bridge model under El Centro earthquake 23

24.  Could be used to seismically excited cable-stayed bridges
Conclusions
HCS with a bang-bang type controller
 More effective than passive or active control system in
reducing structural responses
 Robust for stiffness matrix perturbation due to the passive
control part and bang-bang type controller
 Could be used to seismically excited cable-stayed bridges

25. Thank you for your attention!
Acknowledgements
This research is supported by the National Research Laboratory and Smart Infra-Structure Technology Center.
Thank you for your attention!