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Method for designing PIλDμ stabilisers for minimum-phase fractional-order systems

Merrikh Bayat, F ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1049/iet-cta.2008.0062
  3. Publisher: 2010
  4. Abstract:
  5. This paper deals with the problem of designing the PI λDμ-type controllers for minimum-phase fractional systems of rational order. In such systems, the powers of the Laplace variable, s, are limited to rational numbers. Unlike many existing methods that use numerical optimisation algorithms, the proposed method is based on an analytic approach and avoids complicated numerical calculations. The method presented in this paper is based on the asymptotic behaviour of fractional algebraic equations and applies a delicate property of the root loci of the systems under consideration. In many cases, the resulted controller is conveniently in the form of P, Iλ, PDμ or PIλDμ. Four design examples are explained and the results are compared with existing fractional-order PIDs. These results confirm the usefulness of the proposed method
  6. Keywords:
  7. Algebraic equations ; Analytic approach ; Asymptotic behaviour ; Existing method ; Fractional systems ; Fractional-order systems ; Minimum phase ; Numerical calculation ; Optimisations ; Rational numbers ; Asymptotic analysis ; Numerical methods ; Root loci
  8. Source: IET Control Theory and Applications ; Volume 4, Issue 1 , January , 2010 , Pages 61-70 ; 17518644 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/5385522/?reload=true&arnumber=5385522