Online Fractional order PID Controller tuning Based on Bode’s Ideal Transfer Function, FRIT and RLS

This paper presents a new strategy for digital control and parameters identification of robust fractional order controllers based on fractional reference model. The model consists on an ideal closed-loop system whose open-loop is given by the Bode’s ideal transfer function with the suitable parameters. This technique suggests an online parameters tuning of fractional order PID controller (FPID) using the Fictitious Reference Iterative Tuning method (FRIT) that’s enabling us to obtain the desired parameters with only one-shot experimental data without any plant model identification. After having set the optimal non-integer orders α and β, the gains of the FPID are then estimated in a recursive manner using the so-called Recursive Least Squares (RLS) algorithm with forgetting factor, which can cope with variation of plant characteristics adaptively. Simulation examples have been proposed to illustrate and validate the effectiveness of the introduced conception strategy, and compared it with other results already existing in the literature. Keywords—fractional order PID control; fictitious reference iterative tuning; recursive least squares algorithm; online tuning; fractional reference model; Bode’s ideal loop.