Tuning Method for Parameters in Fractional-Order PID Controllers Based on Neural Networks with Improved Borges Derivative

This paper investigates the turning method of fractional-order PID (FOPID) controllers based on neural networks with Borges derivative. The Borges derivative is applied to the controller structure and the turning of parameters in FOPID controllers. To ensure the Borges derivative can be applied for the negative real number as the independent variable, the improved Borges derivative is defined in this paper. Borges derivative is also used to update the coefficients and the orders of a novel type of FOPID controllers with the Borges difference and the Borges sum. In this paper, the selections of the orders in Borges derivative are discussed, and FOPID controllers based on neural networks are improved to gain the higher optimization speed and accuracy than that via the integer-order PID controllers. Finally, we give an example to verify the effeteness of turning method.