1. KAIST-Kyoto Univ. Joint Seminar
Daejeon, Korea
February 25, 2002
Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers
Sang-Won Cho* : Ph.D. Student, KAIST
Ji-Sung Jo : Ph.D. Student, KAIST
In-Won Lee : Professor, KAIST

2. CONTENTS Introduction Semi-Active Control Proposed Control Algorithm
Numerical Example
Conclusions and Further Studies
Structural Dynamics & Vibration Control Lab., KAIST, Korea

3. Introduction Recent Earthquakes Kobe, Japan (1995)
5,400 of death and 1.5 trillion won of damage
Gebze, Turkey (1999)
14,491 of death and 13 trillion won of damage
Chi-Chi, Taiwan (1999)
2,161 of death and 9.2 trillion won of damage
 To increase the safety and reliability, structural control is required
Structural Dynamics & Vibration Control Lab., KAIST, Korea

4. Structural Control Strategies
Active control
Use external control force to reduce the responses
Large external power
The problem of reliability under earthquake
Active Mass Damper (AMD)
Passive control
Increase the capacity of energy dissipation of structure
No external power
No adaptability to various external load
Lead Rubber Bearing (LRB)
능동제어기법은 외부제어력으로 구조물의 응답을 감소시키는 ‘방식’이다.
따라서 대규모의 외부 전력이 필요하다
그러므로 지진시에 전력차단과 같은 신뢰성에 문제가 있다.
이에 비해서 수동제어 방식은 구조물의 에너지 소산능력을 증가시키는 방식이다.
따라서 외부입력전원이 필요가 없다.
Structural Dynamics & Vibration Control Lab., KAIST, Korea

5. Change the characteristics of control devices Small external power
Semi-active control
Change the characteristics of control devices
Small external power
Reliability of passive system with adaptability of
active system
Variable-orifice damper, MR/ER damper
Structural Dynamics & Vibration Control Lab., KAIST, Korea

6. Semi-Active Control Devices
Variable-orifice damper
Feng and Shinozuka (1990), Kawashima et al. (1992)
Variable-friction damper
Akbay and Aktan (1990), Kannan et al. (1995)
Semi-active impact damper
Masri and Yang (1973), Papalou and Masri(1996)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

7. Controllable fluid damper Electrorheorogical fluid damper (ER damper)
Ergott and Masri(1992)
Magnetorheorogical fluid damper (MR damper)
Carlson et al. (1994)
Table 1 Properties of MR and ER Fluids
Property
MR Fluids
ER Fluids
Response Time
milliseconds
Operable Temp. Range
-40 to 150°C
+10 to 90°C
Stability
Unaffected by most impurities
Cannot tolerate impurities
Structural Dynamics & Vibration Control Lab., KAIST, Korea

8. Without Magnetic Fields
MR Damper
Characteristics of MR fluid
With Magnetic Fields
Without Magnetic Fields
Wires to
Electromgnet
Diaphragm
MR Fluid
Voltage dependence 강조
Coil
Accumulator
Bearing &
Seal
Structural Dynamics & Vibration Control Lab., KAIST, Korea

9. Model of the parallel-plate MR damper (Jansen et al. 2000)
Modeling of MR damper
Model of the parallel-plate MR damper (Jansen et al. 2000) x
(1) f c0
Voltage dependence of the damper parameters
(2)
v : commanded voltage
Indirect control command is used
Structural Dynamics & Vibration Control Lab., KAIST, Korea

10. Objective and Scope
To develop an efficient semi-active control strategies
considering the characteristics of MR damper
Structural Dynamics & Vibration Control Lab., KAIST, Korea

11. Semi-Active Control Semi-Active Control Algorithms
Karnopp et al. (1974)
“Skyhook” damper control algorithm
Feng and Shinozukah (1990)
Bang-Bang controller for a hybrid controller on
bridge
Brogan (1991), Leitmann (1994)
Lyapunov stability theory for ER dampers
McClamroch and Gavin (1995)
Decentralized Bang-Bang controller
Structural Dynamics & Vibration Control Lab., KAIST, Korea

12. Modulated homogeneous friction algorithm for a
Inaudi (1997) :
Modulated homogeneous friction algorithm for a
variable friction device
Sack et al. (1994), Dyke (1996) :
Clipped optimal controllers for semi-active devices
Structural Dynamics & Vibration Control Lab., KAIST, Korea

13. Clipped-Optimal Control (Dyke et al. 1996)
Optimal control with clipped algorithm
Optimal control
State-space equation
Cost function
(3)
(4)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

14. Optimal control algorithm K : solution of Ricatti equation
(5)
(6)
Control force is linear to the state of structure - No consideration of saturation
Structural Dynamics & Vibration Control Lab., KAIST, Korea

15. Indirect control command to MR damper
Clipped algorithm
Indirect control command to MR damper
Control voltage v , instead of control force
(7)
fc : calculated optimal control force
fi : control force of MR damper
H : Heaviside step function
vi : control voltage
Structural Dynamics & Vibration Control Lab., KAIST, Korea

16. Proposed Control Strategy :
Clipped Decentralized Bang-Bang Control (CDBBC)
Decentralized Bang-Bang Control
To use full capacity of MR damper
To consider the saturation of MR damper
High speed switching control command
Clipped algorithm
Indirect control command
Structural Dynamics & Vibration Control Lab., KAIST, Korea

17. Decentralized Bang-Bang Control (McClamroch and Gavin, 1995)
Based on Lyapunov stability theory
Lyapunov function V(z)
Derivative of Lyapunov function
(8)
(9)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

18. Control law which minimize Eq.(9)
Approximate sign function
Modified decentralized bang-bang control
(10)
(11)
(12)
where
Structural Dynamics & Vibration Control Lab., KAIST, Korea

19. Indirect control command to MR damper
Clipped algorithm
Indirect control command to MR damper
Control voltage v , instead of control force
(13)
fc : calculated CMBB Control force
fi : control force of MR damper (nonlinear)
H : Heaviside step function
vi : control voltage
Structural Dynamics & Vibration Control Lab., KAIST, Korea

20. ` Block diagram of proposed control algorithm
Structure
MR Damper `
Clipped
Algorithm
Modified
DBB
Control
Clipped Modified Decentralized Bang-Bang Control (CMDBBC)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

21. Numerical Examples Three-Story Building (Dyke at al. 1996) v f Control
Computer
Structural Dynamics & Vibration Control Lab., KAIST, Korea

22. System matrices
Structural Dynamics & Vibration Control Lab., KAIST, Korea

23. Modified Bouc-Wen Model
Damper modeling and parameters
Value
coa
21.0 Nsec/cm a
140 N/cm
cob
3.50 Nsec/cmV b
695 N/cmV ko
46.9 N/cm 
363 cm-2
c1a
283 Nsec/cm 
c1b
2.95 Nsec/cmV A
301 k1
5.00 N/cm n 2 xo
14.3 cm 
190 sec-1
Bouc-Wen c0 c0 k1 k1 c1 c1 k0 k0
Modified Bouc-Wen Model
Structural Dynamics & Vibration Control Lab., KAIST, Korea

24. 3 Modes of MR damper Passive-off : input Voltage = 0 V
Passive-on : input Voltage = 2.5 V
Semi-Active : switching on and off according
to control algorithm
Structural Dynamics & Vibration Control Lab., KAIST, Korea

25. Structural responses by CMDBBC
(Under El Centro Earthquake, at 3rd floor)
Uncontrolled
CMDBBC
Structural Dynamics & Vibration Control Lab., KAIST, Korea

26. Peak responses under El Centro Earthquake
Control
Strategy
Uncont.
Passive-
Off On
Clip.-Opt.
CMBBC xi
(cm)
0.538
0.820
0.962
0.211
0.357
0.455
0.076
0.196
0.306
0.114
0.185
0.212
0.080 di
0.319
0.201
0.153
0.103
0.158
0.110
0.090
0.101
0.111
(cm/sec2)
856
1030
1400
420
480
717
281
494
767
696
739
703
310
507
772 F
(N) -
258
979
941
982
Structural Dynamics & Vibration Control Lab., KAIST, Korea

27. Discussions Performance of CMDBBC Measured control forces
Capacity of MR damper : 3000N (104% of total weight)
Unsaturated condition !!
Control
Strategy
Uncont.
Passive-
Off On
Clip.-Opt.
CMBBC
F(N) -
258
979
941
982
Structural Dynamics & Vibration Control Lab., KAIST, Korea

28. Peak responses under scaled El Centro earthquake
Control
Strategy
Uncont.
Passive-
Off On
Clip.-Opt.
CMDBBC xi
(cm)
2.742
4.179
4.863
3.209
4.211
4.869
0.859
1.474
1.862
1.321
2.223
2.818
0.864
1.503
1.876 di
1.591
1.014
1.935
1.632
0.646
0.394
1.035
0.805
0.642
0.373
4399
5342
7053
14276
9321
11354
2235
2574
2741
5986
4711
5599
2126
2532
2598 f
(N) -
1500
Structural Dynamics & Vibration Control Lab., KAIST, Korea

29. Conclusions Proposed Clipped modified decentralized bang-bang
control reduce the structural responses from the
uncontrolled value
Performance of proposed is not better than clipped
optimal control under unsaturated condition
For the strong earthquake (i.e. saturated condition),
proposed control is superior in reducing the responses
Structural Dynamics & Vibration Control Lab., KAIST, Korea

30. Further Studies Clipped Modified Decentralized Bang-Bang Control
Improve the performance
Apply to full-scale MR damper
Experimental Studies
Shaking table test
Full-scale MR damper test
Structural Dynamics & Vibration Control Lab., KAIST, Korea