Response Variance Reduction of a Nonlinear Mechanical System via Sliding Mode Control

Abstract

An analysis of a target tracking mechanical system subject to random base excitations is presented in this paper. Sliding mode controls are proposed to minimize the random error of target tracking. Two special cases are studied. In the first case, it is assumed that all the system parameters are known and the state variables are measurable. A sliding mode control is then determined. This highly idealized example reveals the effect of sliding mode control parameters on the reduction of response variance and provides a benchmark for designing a robust controller that deals with systems with unknown parameters. The second case deals with a robust sliding mode control where some parameters of the system are assumed to fall in a known range of values. The proposed controls are proven stable in the mean square sense. The statistical aspects of the controlled system are studied by considering the first and second order moments of the state variables. The equations for these moments are derived and solved by using the method of Gaussian closure in order to investigate the variance reduction performance of the controls.