Mohammad Ali Vali - Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Mahdi Mashayekhi Esfichar - Department of Mathematics, Payame, Noor University (PNU), P.O. BOX ۱۹۳۹۵-۴۶۹۷. Tehran, Iran
Shahriar Farahmand Rad - Department of Mathematics‎, ‎Payame Noor University (PNU), ‎P.O‎. ‎BOX ۱۹۳۹۵-۴۶۹۷‎, ‎Tehran‎, ‎Iran

Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model‎. ‎The IFT algorithm is performed iteratively with the aim of optimizing the control coefficients at each stage via an objective function‎. ‎In this research‎, ‎for the first time‎, ‎the IFT algorithm is used to adjust all the coefficients of the fractional order PID controllers‎, ‎i.e.‎, ‎PI^α D^β controllers to have optimal performance‎. ‎For this purpose‎, ‎fractional order calculations and the integer-order version of the IFT algorithm are firstly presented‎, ‎and the novel IFT algorithm is then used to adjust coefficients of the PI^α D^β controller‎. ‎Finally‎, ‎the performance of the proposed method is illustrated and verified through some examples.

Fractional order PID‎, ‎Iterative feedback tuning‎, ‎PID controller‎, ‎PI^α D^β controller‎, ‎Fractional order calculus‎, ‎Fractional order systems