Fractional order control of unstable processes: the magnetic levitation study case

Although a considerable amount of research has been carried out in the field of fractional order controllers, the majority of the results deal with stable processes. Very little research has been reported regarding the design, analysis, and tuning of fractional order controllers for unstable processes. This paper proposes a methodology for designing and tuning fractional order controllers for a class of unstable second-order processes. The design is carried out using the stability analysis of fractional order systems, by means of Riemann surfaces and a proper mapping in the $$w{\text {-}}\hbox {plane}$$w-plane. The resulting fractional order controllers are implemented using graphical programming on industrial equipment and are validated experimentally using a laboratory scale magnetic levitation unit.

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