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This work focuses on the application and simulation of fractional order \(PI^{\gamma }D^{\mu }\) controller to the position control for a highly nonlinear electrohydraulic system consisting of a 4/3 servo valve and a double-acting asymmetric hydraulic cylinder, using MATLAB®’s fminsearch function with the time-weighted absolute error (ITAE) as the objective function for tuning the five parameters of the fractional controller based on the classical PID controller simulation reported in the literature. Numerical simulations were developed in MATLAB®/Simulink® without external perturbation and with two different types of inputs to the system to compare the behavior of both controllers through the minimum ITAE value. The results obtained show an advantage in the rise time of the fractional order controller and a significant reduction of the ITAE value.

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On the Fractional Calculus Applied to the Control of an Electrohydraulic System to Compare the Behavior in Relation to Classical PID

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  • 发表日期：

    2025年

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  • Edgar H. Robles,
  • Felipe J. Torres,
  • Antonio Balvantin

摘要

This work focuses on the application and simulation of fractional order \(PI^{\gamma }D^{\mu }\) controller to the position control for a highly nonlinear electrohydraulic system consisting of a 4/3 servo valve and a double-acting asymmetric hydraulic cylinder, using MATLAB®’s fminsearch function with the time-weighted absolute error (ITAE) as the objective function for tuning the five parameters of the fractional controller based on the classical PID controller simulation reported in the literature. Numerical simulations were developed in MATLAB®/Simulink® without external perturbation and with two different types of inputs to the system to compare the behavior of both controllers through the minimum ITAE value. The results obtained show an advantage in the rise time of the fractional order controller and a significant reduction of the ITAE value.