Fractional controller based on a robust PIα observer for uncertain fractional systems

Iván Trejo-Zúñiga, Sergio M. Delfín-Prieto and Rafael Martínez-Guerra

International Journal of Systems Science, 2019, vol. 50, issue 4, 829-842

Abstract: In this paper, we present a fractional sliding mode controller based on a robust $ PI^{\alpha } $ PIα observer for fractional systems with bounded disturbances. This controller is introduced to achieve closed-loop Mittag–Leffler stability for uncertain fractional systems; meanwhile, the robust $ PI^{\alpha } $ PIα observer is designed such that a $ \mathcal {L}_{2} $ L2 stability is obtained via quadratic Lyapunov functions and the tuning is achieved with linear matrix inequality approach. The performance and stability of the proposed controller are analysed and demonstrated through a generalised $ n\alpha $ nα-differentiator. Finally, to illustrate the effectiveness of the proposed approach a comparative analysis against the fractional Super-Twisting is carried out.

Date: 2019
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DOI: 10.1080/00207721.2019.1574043

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