Adaptive control of structures by LMS algorithm: a comparative study

By using the normalised least mean squared (NLMS) algorithm, a semi-active multi-variable adaptive controller is designed for a seismically excited structure. There is no need for a large power supply. A number of valves and battery size low-power supplies will suffice. The valves control the amount of flow of a fluid through bypass on-off orifice channels in installed energy dissipating mechanisms. Each mechanism is composed of a piston attached to a Λ-shaped chevron wind-bracing on each floor and to a cylinder attached to the upper floor. Adaptive controller parameters are estimated by the LMS optimiser, in order to search for optimal non-classical damping coefficients of the dissipating systems. They are equivalent to changing the orifice size of the bypass channels. Two versions of the LMS algorithm are used for comparative purposes: the filtered-x LMS and the classical (non-filtered) LMS. For the filtered-x version; two cases are distinguished for a more refined comparison: first, required structural transfer functions for estimating filtered-x signals are assumed to be exact and, second, these transfer functions are assumed not to be exact. Simulation results show that structural responses obtained by filtered-x LMS are more optimised than that of classical LMS, even in the case when the estimation of filtered-x signals is assumed to be poor.