Lyapunov based control algorithm for seismically excited buildings

Abstract

Several different seismic active control algorithms have been proposed in the last decades, most of these studies are based on the applications of the traditional linear quadratic regulator control (LQR). This paper develops a new control algorithm for SDOF structures based in Lyapunov method. This algorithm uses Lyapunov’s direct approach for stability analysis in design of feedback controller. The approach requires the use of Lyapunov function candidate, which must be a positive definite function of the states of the system. The controller is designed so as to make the derivative of the Lyapunov function negative semidefinite. Numerical simulations using one story frame structure modeled as shear building structure subjected to earthquake excitations have been performed to evaluate the effectiveness of the proposed algorithm.