In this article, we present a study for the automatic adjustment of the coefficients of the adaptive fractional PID FO-PID controller using auto-tuning neurons auto-neurons . The automatic adaptation of the coefficients adaptive control is very important for robustness in practical control applications. Because parameter uncertainties and changes in the coefficients of the system from external factors can adversely affect the robustness of the controller. In order to have the adaptive feature of the fractional PID controller, the proportional, integral and derivative gain coefficients of the controller are determined online using the method proposed in this study. Auto-neurons with gradient descent optimization, adjusts the gain coefficients of the controller optimally without any prior training needs. This improves the controller's performance by reducing the error. If deterioration occurs in the parameters of the controlled system during the control process, the auto-neurons automatically adapt the controller coefficients in response to this decay. Also in this study, by using the Tustin method the discrete time domain modeling of FO-PID controller is performed. Thus, the proposed method facilitates the applicability of the FO-PID controller for practical control applications. To show the control performance and robustness of the proposed adaptive control method, first the FO-PI, FO-PD and FO-PID controllers including auto-neuron designed by using MATLAB / Simulink and then the unit step responses for two simulation examples are presented.
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