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Article

μ-Synthesis for Fractional-Order Robust Controllers

Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
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Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: António M. Lopes
Mathematics 2021, 9(8), 911; https://doi.org/10.3390/math9080911
Received: 28 February 2021 / Revised: 12 April 2021 / Accepted: 16 April 2021 / Published: 20 April 2021
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with DK iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the DK iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this. View Full-Text
Keywords: μ-synthesis; robust control; fractional-order control; swarm optimization; artificial bee colony optimization; CNC machine; mixed sensitivity; DK iteration; Linear Matrix Inequality μ-synthesis; robust control; fractional-order control; swarm optimization; artificial bee colony optimization; CNC machine; mixed sensitivity; DK iteration; Linear Matrix Inequality
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MDPI and ACS Style

Mihaly, V.; Şuşcă, M.; Morar, D.; Stănese, M.; Dobra, P. μ-Synthesis for Fractional-Order Robust Controllers. Mathematics 2021, 9, 911. https://doi.org/10.3390/math9080911

AMA Style

Mihaly V, Şuşcă M, Morar D, Stănese M, Dobra P. μ-Synthesis for Fractional-Order Robust Controllers. Mathematics. 2021; 9(8):911. https://doi.org/10.3390/math9080911

Chicago/Turabian Style

Mihaly, Vlad, Mircea Şuşcă, Dora Morar, Mihai Stănese, and Petru Dobra. 2021. "μ-Synthesis for Fractional-Order Robust Controllers" Mathematics 9, no. 8: 911. https://doi.org/10.3390/math9080911

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