1. Modal Control for Seismically Excited Structures using MR Damper
CJK-OSM2, Busan, Korea
November 3-9, 2002
Modal Control for Seismically Excited Structures using MR Damper
Sang-Won Cho* : Ph.D. Candidate, KAIST
Kyu-Sik Park : Ph.D. Candidate, KAIST
Woon-Hak Kim : Professor, Hankyoung National University
In-Won Lee : Professor, KAIST

2. CONTENTS Introduction Implementation of Modal Control
Numerical Examples
Conclusions
Further Study

3. Introduction Backgrounds Semi-active control device has
reliability of passive and adaptability of active system.
MR dampers are quite promising semi-active device for
small power requirement, reliability, and inexpensive to manufacture.
It is not possible to directly control the MR damper.
Control Force of MR Damper = ,
Input voltage
Structural Response

4. Previous Studies 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 - - - -

5. Difficulties in designing phase of controller
Inaudi (1997)
Modulated homogeneous friction algorithm for a variable friction device
Dyke, Spencer, Sain and Carlson (1996)
Clipped optimal controller for semi-active devices
Jansen and Dyke (2000) - -
- Formulate previous algorithms for use with MR dampers
- Compare the performance of each algorithm -
Difficulties in designing phase of controller -
Efficient control design method is required

6. Objective and Scope Implementation of modal control for seismically
excited structure using MR dampers and
comparison of performance with previous algorithms

7. Modal Control Scheme Modal Control Equations of motion for MDOF system
Using modal transformation
Modal equations
(1)
(2)
(3)

8. Modal control is desirable for civil engineering structure
Displacement
where
State space equation
Control force
Modal control is desirable for civil engineering structure
(4)
(5)
(6)
- Involve hundred or thousand DOFs - Vibration is dominated by the first few modes

9. Design of Optimal Controller
Design of is based on optimal control theory
Clipped-optimal algorithm is adopted for MR damper
General cost function
Cost function for modal control
(7)
(8)

10. Comparing design efficiency of weighting matrix
(9)
- Weighting matrix is reduced - Control force is focus on reducing responses of the selected modes

11. Modal State Estimation from Various State Feedback
In reality, sensors measure not
Modal state estimator (Kalman filter) for
and is changeable depending on the feedback
Modal state estimator for is required
(10)

12. Various feedback cases for better performance
- Displacement feedback - Velocity feedback - Acceleration feedback - Performance of each feedback is compared
(11)
(12)
(13)

13. Rewrite the state space equations
Observation spillover problem by
Control spillover problem by
- Produce instability in the residual modes - Terminated by the low-pass filter
- Cannot destabilize the closed-loop system

14. Numerical Examples Six-Story Building (Jansen and Dyke 2000) v2 v1
LVDT
MR Damper v1
LVDT
Control
Computer

15. System Data Mass of each floor : 0.277 N/(cm/sec2)
Stiffness : 297 N/cm
Damping ratio : each mode of 0.5%
MR damper
Type : Shear mode - Capacity : Max. 29N

16. Frequency Response Analysis
Under the scaled El Centro earthquake
102
6th Floor
104
1st Floor
PSD of Displacement PSD of Velocity PSD of Acceleration

17. In frequency analysis, the first mode is dominant.
Reduced weighting matrix (22) is chosen in cost function.
The responses can be reduced by modal control using the lowest one mode.
(14)
: for modal displacement - : for modal velocity

18. Evaluation Criteria Spencer et al 1997
Normalized maximum displacement - Normalized maximum interstory drift - Normalized maximum peak acceleration

19. Weighting Matrix Design
Variations of evaluation criteria
All 12 weighting matrixes are designed
with weighting parameters
for each feedback case
Acceleration feedback
Displacement feedback
Velocity feedback
J1 - J2 - J3 - J4 = J1 + J2 + J3

20. Weighting matrix design for the acceleration feedback
AJ1
AJ2 J1 J2
qmd
qmd
qmv
qmv
AJ3
AJT J3
JT =J1+J2+J3
qmd
qmd
qmv
qmv

21. Weighting matrix design for the displacement feedback
DJ1
DJ2 J1 J2
qmd
qmd
qmv
qmv
DJ3
DJT J3
JT =J1+J2+J3
qmd
qmv
qmd
qmv

22. Weighting matrix design for the velocity feedback
VJ1
VJ2 J1 J2
qmd
qmd
qmv
qmv
VJ3
VJT J3
JT =J1+J2+J3
qmd
qmv
qmd
qmv

23. Result Controlled max. responses
Under the scaled El Centro earthquake,
For all 12 designed weighting matrixes,
Compared with previous 6 algorithms
(Jansen and Dyke 2000)

24. Normalized controlled max. responses of the acceleration feedback
Jansen and Dyke 2000
Proposed

25. Normalized controlled max. responses of the displacement
feedback

26. Normalized Controlled Max. Responses of the velocity feedback

27. Conclusions Modal control scheme is implemented to seismically
excited structures using MR dampers
Kalman filter for state estimation and low-pass filter
for spillover problem is included in modal control scheme
Weighting matrix in design phase is reduced
Modal controller achieve reductions resulting in the
lowest value of all cases considered here
Controller AJT, VJT fail to achieve any lowest value, however
have competitive performance in all evaluation criteria
Controller AJ1 : 39% (in J1) - Controller AJ2 : 30% (in J2) - Controller VJ3 : 30% (in J3)

28. Future Work Examine the influence of the number of controlled mode
Further improvement of design efficiency and
performance of modal control scheme

29. Thank you for your attention.