Continuous Fractional‐Order Sliding PI Control for Nonlinear Systems Subject to Non‐Differentiable Disturbances

Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Hölder type, a continuous and chattering‐free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differin...

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Bibliographic Details
Published inAsian journal of control Vol. 19; no. 1; pp. 279 - 288
Main Authors Muñoz‐Vázquez, A. J., Parra‐Vega, V., Sánchez‐Orta, A.
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.01.2017
Subjects
disturbance rejection
fractional calculus
Fractional sliding mode control
Hölder continuity
Nonlinear systems
robustness
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Summary:Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Hölder type, a continuous and chattering‐free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differintegral operators to show that a sliding mode is induced, and sustained, in finite‐time, to guarantee asymptotic tracking. The closed‐loop system achieves exact rejection of Hölder disturbances even in case of uncertain flow, but assuming certain knowledge of the input matrix. Furthermore, it is shown that our methodology generalizes continuous high‐oder sliding mode schemes by using an integral action of fractional‐order. A representative simulation study is discussed to show the feasibility of the proposal.
Bibliography:The authors acknowledge partial support from Conacyt Basic Research Grants 133346 and 133544, as well as Grant for PhD Scholarship 243206.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.1370