Design of an active compliant liquid column damper by LQR and wavelet linear quadratic regulator control strategies

Abstract

A new active tuned liquid column damper is developed for seismic vibration control of structures by employing the configuration of the compliant liquid column damper (CLCD). This control system is referred to as the active CLCD or ACLCD. The theoretical model of the proposed ACLCD is presented, in which the controller is designed first by the linear quadratic regulator (LQR) algorithm. The design procedure developed for the ACLCD is illustrated both for an example flexible structure and for an example stiff structure, subjected to a recorded accelerogram input. The optimal design of the passive CLCDs is also presented, to provide the basis for the choice of the damper parameters of the ACLCD. The optimum control parameters of the ACLCD are evaluated with the objective of minimizing the displacement response of the structure while maintaining the stability of response reduction and satisfying the constraints on peak liquid and whole damper displacements. A multiresolution‐based wavelet controller (WLQR) is also designed for the ACLCD, achieving structural displacement response reductions comparable to that obtained from the conventional LQR controller but with the application of comparatively lower control forces. The enhanced effectiveness of the ACLCD over that of the passive CLCD is demonstrated through a time domain study. The performances of the LQR‐ and WLQR‐based control strategies are compared, in terms of both structural response reduction and requirement of peak control force magnitudes, for the design input as well as under excitation variability.