? -Synthesis for Fractional-Order Robust Controllers

Vlad Mihaly, Mircea Şuşcă, Dora Morar, Mihai Stănese and Petru Dobra
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Vlad Mihaly: Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
Mircea Şuşcă: Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
Dora Morar: Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
Mihai Stănese: Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
Petru Dobra: Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania

Mathematics, 2021, vol. 9, issue 8, 1-21

Abstract: The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a ? -synthesis design procedure with D – K iteration. ? -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 D – K 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 ? -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 ? -synthesis approach in MATLAB does not offer this.

Keywords: ? -synthesis; robust control; fractional-order control; swarm optimization; artificial bee colony optimization; CNC machine; mixed sensitivity; D – K iteration; Linear Matrix Inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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