Repetitive controller for time-delay systems based on disturbance observer

A novel continuous time repetitive control design is presented for time-delay systems with periodic references and disturbances. Taking profit of the system model and an appropriate time-delay, an inner positive feedback loop is constructed to establish an internal model for periodic signals, and a simple proportional control is utilised in the outer feedback loop to stabilise the closed-loop system. Thus, the tracking capability can be guaranteed according to internal model principle. In addition, to compensate for the effect of external periodic disturbances, a disturbance observer using the system model and a model-based compensator is introduced inside the proposed internal model such that the tracking and disturbance rejection can be achieved simultaneously. Sufficient stability conditions and the robustness analysis under modelling uncertainties are all studied. Only two parameters are needed to be chosen by the designer. Numerical examples and practical experiments on a motor control system are included to illustrate the feasibility and simplicity of the proposed methods.