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

CONTENTS Introduction Implementation of Modal Control Numerical Examples Conclusions Further Study

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

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 - - - -

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

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

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

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

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)

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

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)

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

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

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

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

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

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

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

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

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

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

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)

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

Normalized controlled max. responses of the displacement feedback

Normalized Controlled Max. Responses of the velocity feedback

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)

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

Thank you for your attention.