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Stability analysis of digital repetitive control systems under time-varying sampling period

Stability analysis of digital repetitive control systems under time-varying sampling period

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  • Author(s): J.M. Olm 1 ; G.A. Ramos 2 ; R. Costa-Castelló 3
    • View affiliations
    • Affiliations: 1: Department of Applied Mathematics IV, Universitat Politècnica de Catalunya, Vilanova i la Geltrú, Spain
      2: Department of Electrical and Electronic Engineering, Universidad Nacional de Colombia, Bogotá, Colombia
      3: Institute of Industrial and Control Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain
  • Source: Volume 5, Issue 1, 6 January 2011, p. 29 – 37
    DOI:  10.1049/iet-cta.2009.0308 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.

Inspec keywords: time-varying systems; discrete time systems; robust control; closed loop systems; digital control

Other keywords: stability analysis; closed-loop stability; time-varying sampling period; reference-disturbance period variation; internal model principle-based technique; digital repetitive control systems; discrete-time dynamic controller; robust control approach

Subjects: Discrete control systems; Time-varying control systems; Stability in control theory

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