Fractional-Order PID

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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