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This paper presents the design and robustness analysis of fractional andinteger order PID controllers for the control of a non-linear industrialprocess in the presence of parametric uncertainness and external disturbances.The nonlinear system is linearized using an input-output linearizationtechnique. Three controllers were designed for the linearized system, aninteger order PID controller, a fractional PID controller, and a SIMC PIDcontroller. The robustness analysis of the proposed controllers is based on afactorial experimental design. The input factors for the experiment are theuncertainty in gains of the plant, the presence of random noise in the feedbackloop, and the existence of external perturbations. The outputs of theexperiment measure the performance of each controller through the time stepresponse and the control action of each controller using the mean value and thestandard deviation. The obtained results show that the fractional order PIDcontroller has better performance in the presence of the analyzed experimentalfactors, especially in the control action indicating greater robustness andlower energy consumption.

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