Discrete-time Observer Repetitive Control System Based on a Two-dimensional Model

To implement less conservative than those that ignore the difference between the control and learning actions, an observer using discrete-time repetitive control (RC) design schema was presented, based on the two-dimensional (2D) system theory for linear systems with uncertainty. First, to describe both the learning process occurring between two cycles and the control behavior during a repetitive cycle, a two dimensional discrete-time model was established accordingly. Furthermore, by rebuilding the state variables, the repetitive controller designing was transformed to the feedback gain design problem. Thus, through linear matrix inequality (LMI), the stability conditions that also gained quotient of repetitive system were obtained. By comparison, the applicability of the proposal is stronger, significantly improving the robustness and tracking speed. Test numerical simulation results show that the method can achieve high control accuracy within only a few learning cycles, and the two-dimensional system theory has broad application prospects in repetitive control design and analysis.