Optimal variable order fractional PID controllers for dynamical systems
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.
J. Comput. Appl. Math.