Implementation of modal control for seismically excited structures using magnetorheological dampers

Abstract

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings.