A comparative study between fractionalized and fractional order PID controllers for control of a stable system based on particle swarm optimization algorithm

Abstract

Most industrial applications use integer-order proportional integral derivative (IOPID) controllers due to well-known characteristics such as simplicity and ease of implementation. However, because of their nonlinear nature and the underlying iso-damping feature of fractional-order operators, fractional-order PID (FOPID) and fractionalized-order PID (FrOPID) controllers outperform the IOPID controllers. In this study, three different controllers based on particle swarm optimization are used to regulate a stable system. While a FrOPID controller only has to optimize four parameters and a normal PID controller only needs to optimize three parameters, a FOPID controller requires the optimization of five parameters. Set-point tracking, and better disturbance rejection are obtained with the fractional PID controller, whereas fractionalized PID outperforms the other controllers in terms of noise attenuation