Statistical robustness analysis of fractional and integer order PID controllers for the control of a nonlinear system

TL;DR

This paper compares the robustness of fractional and integer order PID controllers for nonlinear systems, demonstrating fractional controllers' superior performance under uncertainties and disturbances.

Contribution

It introduces a robustness analysis framework for fractional and integer PID controllers using factorial experimental design on a linearized nonlinear system.

Findings

Fractional PID controllers show better robustness against uncertainties.

Fractional controllers have lower energy consumption.

Performance metrics favor fractional PID in disturbed environments.

Abstract

This paper presents the design and robustness analysis of fractional and integer order PID controllers for the control of a non-linear industrial process in the presence of parametric uncertainness and external disturbances. The nonlinear system is linearized using an input-output linearization technique. Three controllers were designed for the linearized system, an integer order PID controller, a fractional PID controller, and a SIMC PID controller. The robustness analysis of the proposed controllers is based on a factorial experimental design. The input factors for the experiment are the uncertainty in gains of the plant, the presence of random noise in the feedback loop, and the existence of external perturbations. The outputs of the experiment measure the performance of each controller through the time step response and the control action of each controller using the mean value and the standard deviation. The obtained results show that the fractional order PID controller has better performance in the presence of the analyzed experimental factors, especially in the control action indicating greater robustness and lower energy consumption.