Optimal variable-order fractional PID controllers for dynamical systems

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Abstract

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.

MSC

26A33
49J25
37M05
97N50
34H05

Keywords

Variable-order fractional calculus
Variable-order PID controller
Robust control
Optimal control
Particle swarm optimization

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