Disturbance Observer Based Repetitive Control System with Non-minimal State Space Realization and Anti-windup Mechanism

Abstract This paper develops a disturbance observer-based repetitive control system using a non-minimal state-space realization in which all state variables are chosen to correspond to the system’s input and output variables and their past values. To enable the repetitive control system to follow a periodic reference signal or reject a disturbance signal of the same nature, a disturbance observer is used to estimate an input disturbance that contains the same frequency characteristics. This new approach differs from previously published design in repetitive control because it separates the design procedure into two simple tasks: first, stabilization by the design of a non-minimal state feedback control; and second, to independently incorporate the periodic modes via the estimation of the disturbance. Moreover, because this design ensures the stability of the disturbance observer, its implementation contains an anti-windup mechanism when the control signal reaches its maximum or minimum value. Without the complication of an observer for the state variables, the detection of a disturbance occurs earlier and the repetitive controller acts much faster than in the case of minimal state controller incorporating an observer. This leads to considerable performance improvement, with excellent disturbance rejection achieved with smaller control signal variations.