A design method of fractional order PI<sup>λ</sup>D<sup>μ</sup> controller for higher order systems

Abstract

A model reduction method and an explicit fractional order (FO) PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller tuning rule are proposed for higher order systems. In this paper, at first, Cuckoo Search (CS) algorithm is used for approximating higher order system to obtain a desired fractional order plus time-delay (FOPTD) model. Then, a kind of fractional PID controller is derived, which is based on the internal model control (IMC) principle by approximating the time-delay term of the system model with the first order Padé series. Finally, the analytical expression for robust tuning of the controller parameter is developed according to the maximum sensitivity index. Simulation studies are carried out on various types of process dynamics and the results show that the proposed model reduction method and FO PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller tuning rule could provide a better dynamic performance of both the set-point tracking and disturbance rejection and robustness against parameters perturbation.