Optimal fractional‐order controller design using direct synthesis method

Abstract

In this study, an optimal fractional‐order controller is proposed for a type of fractional‐order model utilising the direct synthesis method. In that respect, the fractional counterpart of the second‐order integer transfer function is selected as a closed‐loop reference transfer function. The stability region of the fractional‐order closed‐loop reference transfer function is given via a theorem and related lemmas. Considering that a unity feedback loop is used, the parameters of the fractional‐order closed‐loop reference transfer function are specified based on the integral square error performance index within the specified stability region using a genetic algorithm. The time‐domain characteristics of the optimal fractional‐order closed‐loop reference transfer function are compared with those of the optimal second‐order integer closed‐loop reference transfer function. The fractional‐ and integer‐order controllers that are designed based on optimal closed‐loop reference transfer functions are implemented on a real‐time system. The performance of the fractional‐order controller outperforms that of the integer counterpart on the integral square error criterion. Moreover, the simulation and practical results are consistent with each other.