μ-Synthesis for Fractional-Order Robust Controllers

Mathematics

Vlad Mihaly¹  Mircea Şuşcă¹  Dora Morar¹  Petru Dobra¹  Mihai Stănese¹ 

[1] Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania;

关键词: μ-synthesis;    robust control;    fractional-order control;    swarm optimization;    artificial bee colony optimization;    CNC machine;   

DOI  :  10.3390/math9080911

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown