Optimal Control of Nonlinear Structures

Abstract

Three optimal control algorithms are proposed for reducing oscillations of flexible nonlinear structures subjected to general stochastic dynamic loads, such as earthquakes, waves, winds, etc. The optimal control forces are determined analytically by minimizing a time-dependent quadratic performance index, and nonlinear equations of motion are solved using the Wilson-θ numerical procedures. The optimal control algorithms developed for applications to nonlinear structures are referred to as the instantaneous optimal control algorithms, including the instantaneous optimal open-loop control algorithm, instantaneous optimal closed-loop control algorithm, and instantaneous optimal closed-open-loop control algorithm. These optimal algorithms are computationally efficient and suitable for on-line implementation of active control systems to realistic nonlinear structures. Numerical examples are worked out to demonstrate the applications of these optimal control algorithms to nonlinear structures. In particular, control of structures undergoing inelastic deformations under strong earthquake excitations are illustrated. The advantage of using combined passive/active control systems is also demonstrated.