PI Plus Repetitive Control Design: H-infinity Regions Approach

The paper deals with a class of plug-in type repetitive controllers intended for servo systems which follow periodic reference signals or compensate periodic exogenous disturbances. Proportional-integral (PI) feedback controller is complemented by an internal model of a generic periodic signal aiming at perfect asymptotic tracking or disturbance rejection. A novel design method is proposed allowing a simultaneous tuning of the PI controller and the repetitive control part. The design requirements can be formulated in the frequency domain as proper loop-shaping inequalities defining constraints on important closed-loop sensitivity functions. These constraints are translated directly into the parametric plane of the controller allowing to derive a complete set of admissible controllers. The proposed method is demonstrated in a case study of a flexible motion system.