Control quality enhancement using fractional PIλDμcontroller

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Abstract
The proportional–integral–derivative (PID) controllers have remained, by far, the most commonly and practically used in all industrial feedback control applications; therefore, there is a continuous effort to improve the system control quality performances. More recently Podlubny has proposed the fractional PIλDμ controller, a generalisation of the classical PID controller, involving an integration action of order λ and differentiation action of order μ. Since then, many researchers have been interested in the use and tuning of this type of controller. In this article, a new conception method of this fractional PIλDμ controller is considered. The basic ideas of this new tuning method are based, in the first place, on the classical Ziegler–Nichols tuning method for setting the parameters of the fractional PIλDμ controller for λ = μ = 1, which means setting the parameters of the classical PID controller, and on the minimum integral squared error criterion by using the Hall–Sartorius method for setting the fractional integration action order λ and the fractional differentiation action order μ. Illustrative examples and simulation results are presented to show the control quality enhancement of this proposed fractional PIλDμ controller conception method compared to the PID controller conception using Ziegler–Nichols tuning method.

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