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Fractional-Order PID

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PID Control in the Third Millennium

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

Thinking of Laplace and frequency domains, it should not be hard for the feedback control community to understand that, by considering more general control actions of the form s α,α∈ℝ, we could achieve more satisfactory compromises between the positive and negative effects of the basic control actions (proportional, derivative, and integral ones) on the controlled system behavior, and that we could develop more powerful design methods to satisfy the controlled system specifications by combining these actions. The characteristic operators of these actions in the Laplace domain are equivalent to fractional-order derivatives and integrals in the time domain. This leads us to the so-called Fractional Calculus (FC), the generalization of the classical calculus to orders of integration and differentiation not necessarily integer. The application of the fractional-order operators to the PID algorithm gives us the Fractional-order PID (FoPID), one of the subjects deserving more attention in Fractional-order Control (FOC). In this chapter, after introducing the above mentioned generalized control actions, the FoPID will be studied, and the tuning rules and ways for its implementation will be reviewed and discussed, as well as its practical applications.

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Authors and Affiliations

  1. University of Extremadura, Campus Universitario, 06006, Badajoz, Spain

    Blas M. Vinagre

  2. University Carlos III of Madrid, Avenida Universidad 30, 28911, Leganés, Madrid, Spain

    Concepción A. Monje

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  1. Blas M. Vinagre
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  2. Concepción A. Monje
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Correspondence to Blas M. Vinagre .

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  1. Dept of Telecommunic. & Systems Engin., School of Engineering, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, 08193, Spain

    Ramon Vilanova

  2. Facoltà di Ingegneria, Dipto. Elettronica per l'Automazione, Università Brescia, Via Branze 38, Brescia, 25123, Italy

    Antonio Visioli

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Vinagre, B.M., Monje, C.A. (2012). Fractional-Order PID. In: Vilanova, R., Visioli, A. (eds) PID Control in the Third Millennium. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2425-2_15

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