Repetitive dynamic matrix control for systems with periodic specifications

This paper proposes a Repetitive Dynamic Matrix Control (RDMC) for systems with periodic specifications. The new algorithm is able to track periodic references and reject repetitive disturbances with a known period based on a modified prediction error. A repetitive version of the Generalized DMC (GDMC) is also proposed such that it can be applied to control open-loop unstable systems. Only the step-response coefficients are required to describe the dynamical system such that the RDMC preserves the modeling simplicity of the Dynamic Matrix Control (DMC). The proposed solution can be interpreted as an extension of the DMC for repetitive control applications. A data-driven filter design is proposed in order to ensure null prediction steady-state error in the presence of periodic disturbances even for unstable open-loop systems. Two case studies are presented to show the usefulness of the proposed strategy for control systems with periodic specification and to illustrate the typical advantages and drawbacks of the proposed repetitive control extension of the DMC algorithm.