Sang-Won Cho* : Ph.D. Candidate, KAIST Sang-Won Cho* : Ph.D. Candidate, KAIST Byoung-Wan : Ph.D. Candidate, KAIST Byoung-Wan : Ph.D. Candidate, KAIST Hyung-Jo Jung : Research Assistant Professor, KAIST Hyung-Jo Jung : Research Assistant Professor, KAIST In-Won Lee : Professor, KAIST In-Won Lee : Professor, KAIST Implementation of Modal Control for Seismically Excited Structures using MR Dampers ICANCEER2002 Hong Kong August 19-20, 2002

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

2 Structural Dynamics & Vibration Control Lab., KAIST, Korea Background Background Introduction Introduction Semi-active control device hasSemi-active control device has reliability of passive and adaptability of active system. MR dampers are quite promising semi-active device forMR 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 damperIt is not possible to directly control the MR damper Control Force of MR Damper Control Force of MR Damper Input voltage Structural Response =,

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

4 Structural Dynamics & Vibration Control Lab., KAIST, Korea Inaudi (1997)Inaudi (1997) Modulated homogeneous friction algorithm for a variable friction device Dyke, Spencer, Sain and Carlson (1996)Dyke, Spencer, Sain and Carlson (1996) Clipped optimal controllers for semi-active devices Jansen and Dyke (2000)Jansen and Dyke (2000) - Formulate previous algorithms for use with MR dampers - Compare the performance of each algorithm - - There is no application of modal control scheme to MR damper Efficient controller to design is required - -

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

6 Structural Dynamics & Vibration Control Lab., KAIST, Korea Modal Control Modal Control Scheme Equation of MDOF systemEquation of MDOF system Using modal transformationUsing modal transformation DisplacementDisplacementwhere

7 Structural Dynamics & Vibration Control Lab., KAIST, Korea Feedback controllerFeedback controller State space equationState space equationwhere Control forceControl force However, sensors measure notHowever, sensors measure not - Modal state estimator for

8 Structural Dynamics & Vibration Control Lab., KAIST, Korea Based on optimal control theoryBased on optimal control theory General cost functionGeneral cost function Cost function for modal controlCost function for modal control Design efficiencyDesign efficiency Clipped-optimal algorithm is adopted for MR damperClipped-optimal algorithm is adopted for MR damper Design of Optimal Controller

9 Structural Dynamics & Vibration Control Lab., KAIST, Korea Modal state estimator (Kalman filter) forModal state estimator (Kalman filter) for Using displacement feedbackUsing displacement feedback Using velocity feedbackUsing velocity feedback Using acceleration feedbackUsing acceleration feedback Modal State Estimation from Various State Feedback (8) (11) (9) (10)

10 Structural Dynamics & Vibration Control Lab., KAIST, Korea Control forceControl force State space equation with modal estimatorState space equation with modal estimator State space equation by residual modesState space equation by residual modes Define errorDefine error

11 Structural Dynamics & Vibration Control Lab., KAIST, Korea Rewrite state space equationsRewrite state space equations Observation spillover problem byObservation spillover problem by Control spillover problem byControl spillover problem by - Produce instability in the residual modes - Terminated by the low-pass filter - Cannot destabilize the closed-loop system

12 Structural Dynamics & Vibration Control Lab., KAIST, Korea Numerical Examples Numerical Examples Six-Story Building (Jansen and Dyke 200) Control Computer LVDT v1v1 v2v2 MR Damper

13 Structural Dynamics & Vibration Control Lab., KAIST, Korea System Data Mass of each floor : N/(cm/sec2)Mass of each floor : N/(cm/sec2) Stiffness : 297 N/cmStiffness : 297 N/cm Damping ratio: each mode of 0.5%Damping ratio: each mode of 0.5% MR damperMR damper - Type: Shear mode - Capacity: Max. 29N

14 Structural Dynamics & Vibration Control Lab., KAIST, Korea Frequency Response Analysis Under the scaled El Centro earthquakeUnder the scaled El Centro earthquake  10 2  10 4 PSD of Displacement PSD of Velocity PSD of Acceleration 1 st Floor 6 th Floor

15 Structural Dynamics & Vibration Control Lab., KAIST, Korea In frequency analysis, the first mode is dominantIn frequency analysis, the first mode is dominant Weighting matrix(2  2) in cost functionWeighting matrix(2  2) in cost function - reduce the responses by modal control using the lowest one or two modes

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

17 Structural Dynamics & Vibration Control Lab., KAIST, Korea Weighting Matrix Design Variations of evaluation criteria with weighting parameters for the acceleration feedbackVariations of evaluation criteria with weighting parameters for the acceleration feedback q md q mv J1J1J1J1 q md q mv J2J2J2J2 q md q mv J3J3J3J3 q md q mv J T =J 1 +J 2 +J 3

18 Structural Dynamics & Vibration Control Lab., KAIST, Korea q md q mv J1J1J1J1 q md q mv J2J2J2J2 q md q mv J3J3J3J3 q md q mv J T =J 1 +J 2 +J 3 Variations of evaluation criteria with weighting parameters for the velocity feedbackVariations of evaluation criteria with weighting parameters for the velocity feedback

19 Structural Dynamics & Vibration Control Lab., KAIST, Korea q md q mv J1J1J1J1 q md q mv J2J2J2J2 q md q mv J3J3J3J3 q md q mv J T =J 1 +J 2 +J 3 Variations of evaluation criteria with weighting parameters for the displacement feedbackVariations of evaluation criteria with weighting parameters for the displacement feedback

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

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

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

23 Structural Dynamics & Vibration Control Lab., KAIST, Korea Conclusions Conclusions Modal control scheme is implemented to seismically Modal control scheme is implemented to seismically excited structures using MR dampers excited structures using MR dampers Kalman filter for state estimation and low-pass filter Kalman filter for state estimation and low-pass filter for spillover problem is included in modal control scheme for spillover problem is included in modal control scheme Weighting matrix in design phase is reduced Weighting matrix in design phase is reduced Modal controller achieve reductions resulting in the Modal controller achieve reductions resulting in the lowest value of all cases considered here lowest value of all cases considered here Controller A JT, V JT fail to achieve any lowest value, however Controller A JT, V JT fail to achieve any lowest value, however have competitive performance in all evaluation criteria have competitive performance in all evaluation criteria - Controller A J2 : 30% (in J1) - Controller V J1 : 41% (in J2) - Controller V J3 : 30% (in J3)

24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Future Work Further improvement design efficiency and Further improvement design efficiency and performance of modal control scheme performance of modal control scheme

25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Thank you for your attention.