Abstract

The main purpose of this publication is the proper determination of the fractional order at the Zener viscoelastic models and the analysis of the implications derived from the accuracy in obtaining this. The procedure is performed using the numerical method of Levenberg-Marquardt from values reported in the literature. The parameters used are obtained from an artery segment using a stress relaxation test. After determining the fractional order is proceeded to find the model solution using, the function of Mittag-Leffler with two parameters and the convolution operation in order to compare the behavior of the fractional model vs the integer order and identify their key differences. The displacements present on the artery are obtained, under the stimulus of a normal blood pulse and two dissimilar, simulating the effect in blood flow caused by an arrhythmia and by mechanical ventilation process. Finally the dynamic response from the pulses is analyzed using the convolution operation and Gauss Kronrod numeric method, where the solutions accuracy obtained by the fractional model is observed, an compared with the integer order model.

Abstract

This paper presents a novel modeling technique for a VTOL electromechanical nonlinear dynamical system, based on fractional order derivatives. The proposed method evaluates the possible fractional differential equations of the electromechanical system model by a comparison against actual measurements and in order to estimate the optimal fractional parameters for the differential operators of the model, an extended Kalman filter was implemented. The main advantages of the fractional model over the classical model are the simultaneous representation of the nonlinear slow dynamics of the system due to the mechanical components and the nonlinear fast dynamics of the electrical components.