Optimal tuning of fractional order PID controller using nelder-mead method: A case study

Abstract

For many years, the classical proportional-integral-derivative (PID) controller has been used in many control systems as this controller is easy to design. In addition, the fractional order proportional-integral-derivative (FOPID) controller has been introduced as an extended version of the classical PID controller. The optimal adjustment of the classical PID and FOPID controller in control systems is essential for achieving the desired performance of the system output. Diverse optimization strategies have also been employed to finely tune the classical PID and FOPID controller parameters. This paper describes a detailed process of deploying the FOPID controller for single-input and single-output (SISO) control systems. The Nelder-Mead approach, a derivative-free optimization technique, is employed to optimize both the classical PID and FOPID controller. Finally, a real-time simulation of a brushed DC motor is also conducted by using the Simulink, the FOMCON Toolbox for MATLAB and the Arduino Nano to demonstrate the effectiveness of the FOPID controller in comparison to the classical PID controller.