Generalised repetitive control: relaxing the period-delay-based structure

Most current repetitive controllers apply the internal model principle by embedding one or multiple period delays into the control scheme. While being simple and often effective, this structure involves a number of disadvantages: (i) in many applications, large memory buffers are needed; (ii) information about the spectrum of the periodic input cannot be fully exploited; and (iii) accounting for period-time uncertainty results in controllers that are overly robust for lower harmonic frequencies. In order to overcome these disadvantages, the present study proposes a novel repetitive controller structure that sacrifices the simplicity of the period-delay-based structure for the benefit of more design freedom. The resulting generalised repetitive controller encompasses the period-delay-based structure as a special case and is designed based on semi-definite programming. Numerical results reveal that a generalised repetitive controller yields significantly better performance with the same amount of memory or, conversely, requires substantially less memory to achieve equivalent performance.