Obtaining the output function of an electromechanical system model by a numerical method and fractional-order controller design

The aim of this study is to present a method for controlling a mass-spring-damper system, whose output function is calculated through a numerical method, using a Fractional Order PID controller. Calculating the output function of some systems can be difficult or complex. Many numerical methods have been developed for this purpose. In this study, the output function is numerically calculated using the Hermite collocation method. For the control of a closed-loop system containing this output function, different fractional-order derivative and integral parameter values were employed. These fractional-order derivative and integral parameter values were used in the Fractional Order PID controller. Then, it compared wtih the conventional PID controller to determine the optimal values. This study distinguishes itself from the existing literature through the innovative approaches brought by the fractional-order PID controller in enhancing system performance and the applicability of the Hermite collocation method as a numerical solution technique. It has been demonstrated that the fractional-order PID controller provides superior performance compared to the conventional PID controller. Simulation results were utilized to verify the effectiveness of the controller. The obtained results indicate the potential of the fractional-order PID controller to enhance control precision in dynamic systems.