1. Implementation of Modal Control for
2002년도 한국지진공학회
추계학술발표회
Implementation of Modal Control for
Seismically Excited Structures using MR Dampers
조 상 원* : KAIST 건설 및 환경공학과, 박사과정
오 주 원 : 한남대학교 토목환경공학과, 교수
이 인 원 : KAIST 건설 및 환경공학과, 교수

2. CONTENTS Introduction Implementation of Modal Control
Numerical Examples
Conclusions
Further Study
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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 - - - -
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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
Structural Dynamics & Vibration Control Lab., KAIST, Korea

6. Objective and Scope For efficient control design,
implementation of modal control for seismically
excited structure using MR dampers and
comparison of performance with previous algorithms
Structural Dynamics & Vibration Control Lab., KAIST, Korea

7. Modal Control Scheme Modal Control Equations of motion for MDOF system
Using modal transformation
Modal equations
(1)
(2)
(3)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

8. Displacement where State space equation Control force (4) (5) (6)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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
Efficient design of weighting matrix
(7)
(8)
(9)
- Weighting matrix is reduced
Structural Dynamics & Vibration Control Lab., KAIST, Korea

10. Modal State Estimation from Various State Feedback
In reality, sensors measure not
Modal state estimator (Kalman filter) for
Using displacement feedback
Using velocity feedback
Using acceleration feedback
Modal state estimator for is required
(10)
(11)
(12)
(13)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

11. Rewrite 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
Structural Dynamics & Vibration Control Lab., KAIST, Korea

12. Numerical Examples Six-Story Building (Jansen and Dyke 2000) v2 v1
LVDT
MR Damper v1
LVDT
Control
Computer
Structural Dynamics & Vibration Control Lab., KAIST, Korea

13. 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
Structural Dynamics & Vibration Control Lab., KAIST, Korea

14. Frequency Response Analysis
Under the scaled El Centro earthquake
102
6th Floor
104
1st Floor
PSD of Displacement PSD of Velocity PSD of Acceleration
Structural Dynamics & Vibration Control Lab., KAIST, Korea

15. In frequency analysis, the first mode is dominant.
Reduced weighting matrix (22) is used in cost function.
The responses can be reduced by modal control using the lowest one mode.
(14)
Structural Dynamics & Vibration Control Lab., KAIST, Korea

16. Evaluation Criteria Spencer et al 1997
Normalized maximum displacement - Normalized maximum interstory drift - Normalized maximum peak acceleration
Structural Dynamics & Vibration Control Lab., KAIST, Korea

17. Weighting Matrix Design
Variations of evaluation criteria with weighting parameters for the acceleration feedback J1 J2
qmd
qmd
qmv
qmv J3
JT =J1+J2+J3
qmd
qmd
qmv
qmv
Structural Dynamics & Vibration Control Lab., KAIST, Korea

18. Variations of evaluation criteria with weighting parameters for the displacement feedbackJ1 J2
qmd
qmd
qmv
qmv J3
JT =J1+J2+J3
qmd
qmv
qmd
qmv
Structural Dynamics & Vibration Control Lab., KAIST, Korea

19. Variations of evaluation criteria with weighting parameters for the velocity feedbackJ1 J2
qmd
qmd
qmv
qmv J3
JT =J1+J2+J3
qmd
qmv
qmd
qmv
Structural Dynamics & Vibration Control Lab., KAIST, Korea

20. Result
Normalized Controlled Max. Responses of the acceleration feedback due to the scaled El Centro Earthquake
Jansen and Dyke 2000
Proposed
Structural Dynamics & Vibration Control Lab., KAIST, Korea

21. Normalized Controlled Max
Normalized Controlled Max. Responses of the velocity feedback due to the scaled El Centro Earthquake
Structural Dynamics & Vibration Control Lab., KAIST, Korea

22. Normalized Controlled Max
Normalized Controlled Max. Responses of the displacement feedback due to the scaled El Centro Earthquake
Structural Dynamics & Vibration Control Lab., KAIST, Korea

23. 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)
Structural Dynamics & Vibration Control Lab., KAIST, Korea