Hybrid feedback-least mean square algorithm for structural control

Classical control algorithms such as the linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) algorithms have been used for structural control problems over the past three decades. These algorithms suffer from a number of fundamental shortcomings. They are susceptible to parameter uncertainty and modeling error. They present optimum solutions in a narrow sense only because the external excitation term is ignored in their formulation and solution. These algorithms achieve a significant level of attenuation in the vicinity of the natural frequencies of the structure. But, they fail to suppress the vibrations when frequency of the external disturbance differs even slightly from the natural frequencies of the structure. In this paper, a hybrid feedback-least mean square (LMS) algorithm is presented for control of structures through integration of a feedback control algorithm such as the LQR or LQG algorithm and the filtered-x LMS algorithm. The algorithm is applied to the active tuned mass damper system. It is shown that the hybrid feedback-LMS algorithm minimizes vibrations over the entire frequency range and thus is less susceptible to modeling error and inherently more stable.