Gaussian process repetitive control: Beyond periodic internal models through kernels

Noud Mooren (Corresponding author), Gert Witvoet, Tom Oomen

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Abstract

Repetitive control enables the exact compensation of periodic disturbances if the internal model is appropriately selected. The aim of this paper is to develop a novel synthesis technique for repetitive control (RC) based on a new more general internal model. By employing a Gaussian process internal model, asymptotic rejection is obtained for a wide range of disturbances through an appropriate selection of a kernel. The implementation is a simple linear time-invariant (LTI) filter that is automatically synthesized through this kernel. The result is a user-friendly design approach based on a limited number of intuitive design variables, such as smoothness and periodicity. The approach naturally extends to reject multi-period and non-periodic disturbances, exiting approaches are recovered as special cases, and a case study shows that it outperforms traditional RC in both convergence speed and steady-state error.

Original languageEnglish
Article number110273
Number of pages13
JournalAutomatica
Volume140
DOIs
Publication statusPublished - Jun 2022

Bibliographical note

Funding Information:
The research leading to these results has received funding from the European Union H2020 program ECSEL-2016-1 under grant no. 737453 (I-MECH) , and the ECSEL Joint Undertaking under n. 101007311 (IMOCO4.E) . This work is also part of the research programme VIDI with project number 15698, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO) . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.

Keywords

  • Disturbance rejection
  • Gaussian processes
  • Internal model control
  • Repetitive control

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