A Novel Adaptive Gain of Optimal Sliding Mode Controller for Linear Time-Varying Systems

In this study, a new optimal control law associated with the sliding mode control is developed for the linear time-varying system based on the Bolza-Meyer criterion. The salient characteristic of the controller proposed in this work is to have adjustable gains in which the gain values can be larger than 1. This leads to the enhancement of control performances with the given cost function. It is noted here that conventional optimal control laws have a constant gain of 1 or less than 1, and hence, control performances such as the convergence speed are not satisfactory. After formulating the proposed optimal control law for linear time-varying systems, several illustrative examples are adopted and control performances were evaluated to show some benefits of the proposed controller. In particular, three crucial index values of control gain index, main input control index and the state index were investigated. Among illustrative examples, one is related to vibration control problem of the vehicle seat suspension system with magnetorheological (MR) damper. This example is specially treated to evaluate the practical applicability of the proposed optimal controller by considering the measured road profiles; two different random road excitations.