Optimal Sliding Mode Output Tracking Control for Linear Systems with Uncertainties Based on Observers

The problem of optimal sliding mode tracking control for a class of uncertain systems with tracking signal generated by an exosystem is considered in this paper. Firstly, making use of the original system and the reference exosystem, an augmented system is constructed, and the optimal tracking problem for the original system is transformed into the optimal regulating problem for the augmented system. Secondly, considering the uncertainty of the system, based on the optimal feedback control law of nominal system, an optimal sliding surface is designed to make the sliding mode minimize the given performance index and have a complete robustness to uncertainties. Thirdly, a reduced-order reference input observer is designed in order to guarantee the control law physically realizable. At last, the method is applied to a class of flight simulator servo systems with low speed friction phenomenon. Simulation results show the effectiveness and superiority of the proposed method.