Cubic state observer-based modified repetitive controller for uncertain systems

Work presented in this paper modifies the conventional repetitive controller design with a cubic state observer in a state feedback setting. The new design methodology largely enhances the tracking performance of the controller subjected to a class of LTI systems with parametric uncertainty. Repetitive controller design has been modified with a cubic order polynomial state observer. Performance advantage offered by the proposed controller design compared to the existing method and inclusion of nonlinear term in the error dynamics of the observer modifies the control law. A Lyapunov-Krasovskii functional is chosen and the sufficient robust stability condition for the proposed controller is derived. A numerical example is presented to illustrate the efficacy of the proposed method and upgraded performance is observed compared to existing method. Rapid prototyping of the proposed controller is carried out using a microcontroller board.