Synthesis and Stability Analysis of Repetitive Controllers

A class of repetitive controllers for tracking control of dynamical systems subject to repetitive desired trajectories is presented. Within the framework of periodic functions, the necessary and sufficient conditions along with an explicit procedure for. stability inverting a linear time-invariant plant is formulated. Next, the stability of a repetitive control system, which is a distributed parameter system, is analysed and the necessary and sufficient conditions for its asymptotic convergence are postulated. An extended Nyquist criteria for the stability analysis and synthesis of this controller is subsequently proposed. Finally, a modified repetitive controller is introduced, which expands the domain of applicability of the original controller to a wider class of plants, including nonminimum phase system. The main stability results pertaining to the orignal controller are then extended to those of the modified controller. Several simulation and design examples are also presented.