Wavelet-hybrid feedback-least mean square algorithm for robust control of structures

In a companion article, the writers presented a hybrid feedback-least mean square (LMS) algorithm for control of structures through integration of a feedback control algorithm such as the linear quadratic regulator and linear quadratic Gaussian algorithms and the filtered-x LMS algorithm. Low-pass filtering of dynamic environmental disturbance signals due to winds and earthquakes is required when the hybrid feedback-LMS algorithm is used for control of civil structures, because the frequency bandwidths of such environmental signals are much wider than those of common structural systems. In this paper, it is shown that the wavelet transform can be used as an effective filtering scheme for control problems. A wavelet-hybrid feedback-LMS algorithm is presented for robust control of civil structures. The effectiveness of the proposed control model is demonstrated by application to an active tuned mass damper system and an active mass driver benchmark problem. Simulation results demonstrate that the proposed model is effective for control of both steady and transient vibrations without any significant additional computational burden, and can be used readily to enhance the performance of existing feedback control algorithms.