Fractional Order Transfer Function for Modeling an Electrohydraulic System

This paper presents the analysis and synthesis of the fractional-order model of an electrohydraulic system expressed by fractional-order transfer functions of the servo valve and the double-acting cylinder by applying Caputo’s definition. From the analysis of the differential equations of the system dynamics, it is possible to obtain the fractional order expression that relates the output signal with respect to the input signal, of each of the analyzed elements. Then, these transfer functions are put in a block diagram to perform numerical simulations that allow comparing the performance of the proposed approach with respect to the modeling given in integer order. The results of the simulations have shown that the variation of the fractional exponent can reduce the settling time and rise time of the system response to a step input, however, it also shows the need to correctly understand the physical operation of the system to avoid a performance that does not correspond to real scenarios.