Optimal variable-order fractional PID controllers for dynamical systems. (English) Zbl 1392.49033

Summary: This paper studies the design of variable-order fractional proportional-integral-derivative (VFPID) controllers for linear dynamical systems. For this purpose, a technique to discretize fractional differential equations with variable-order operators is proposed. The resulting model and a particle swarm optimization algorithm are used to search for the optimal parameters of the VFPID controllers. Three examples illustrate the performance of the closed-loop system under the action of the VFPID and compare it with the results obtained by means of the PID and fractional PID (FPID). Furthermore, time-dependent parameters are also tested, showing that the VFPID yields a superior performance.


93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory
93B35 Sensitivity (robustness)
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
49J27 Existence theories for problems in abstract spaces
37M05 Simulation of dynamical systems
97N50 Interpolation and approximation (educational aspects)
34H05 Control problems involving ordinary differential equations


DFOC; sysdfod
Full Text: DOI


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