A Fractional-Order Repetitive Controller for Periodic Disturbance Rejection

A fractional-order repetitive controller is here proposed to reject a periodic disturbance acting on a time-invariant linear stable, possibly nonminimum phase, plant. The controller is designed assuming that the frequency response of the plant, in a particular range of frequencies, belongs to a generic half-plane of the complex plane. No information about the structure of the system, i.e., number and locations of zeros/poles, is required. It is shown that, if this half-plane entirely contains the frequency response of the plant, then the controller can be designed without gain constraints. In the presence of saturation nonlinearities, conditions on the system absolute stability are discussed.