Design and implement of neural network based fractional order PI<sup>α</sup> controller

Abstract

Traditional Ractional-order 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 is more flexible and gives an opportunity to better adjust the dynamical properties of a fractional-order control system than the traditional PID controller. However, the selection of controller parameters is more difficult for fractional-order 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 which introduces additional two parameters λ and μ. For better adaptive capacity of system uncertainty without generality loss, a fractional-order PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> controller with self-tuning parameters is presented based on neural network. The discretization method used and the material design method of fractional-order PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> controller are described, and the architecture of back-propagat ion neural networks and parameters self-tuning algorithm of the controller are discussed indetail. The experiment results show that the controller presented can maintain the performance of the normal fractional-order controller, while possesses better flexibility and parameters self-tuning ability.