Repetitive learning control for linear periodic plants

In manufacturing and industrial applications that perform repetitive tasks, exploiting the periodic properties of the design problem is an important part of maximizing performance. In these applications, we can often model the behavior of the plant as a linear periodic (LP) system. Repetitive learning control has been proposed as a method for the repetitive control of linear periodic plants. A repetitive learning controller uses the tracking error and control input in the previous period to compute the control input for the present period. We relax the earlier conditions for the existence of a controller that guarantees the convergence of the tracking error to zero. We propose several methods of designing a repetitive learning controller, based on eigenvalue assignment and matrix inequality techniques. The latter includes fixed P, P-K iterations, and C-C iterations. C-C iterations is a novel method for designing static output feedback gains to satisfy both asymptotic and transient performance specifications