Comparison of Euler’s Backward Difference and Bilinear Transform Discretization Methods for Modeling and Simulation of a DC Motor

Abstract

AbstractThe modelling and simulation of mechatronics systems are becoming more important with the appearance of the concept of cyberphysical systems. Virtual axes of motion can be simulated with simple DC motor models which require discretization methods. Bilinear transform method is commonly used as a precise discretization method. This study compares the Euler’s backwards differences method and the bilinear transform method in both time and frequency domains for the discretization of a model of a DC motor. For the backward differences method two design criteria are used: one is the computation of the discrete pole in terms of the time constant and the sampling time, and the second is choosing a sample time corresponding to one fifteenth of the time constant. The Euler’s backwards differences method is found suitable and even better than bilinear transform method for this type of application. This study shows that Euler’s Backwards Discretization using a sampling time of \(\tau /15\) is good to reproduce a first order dynamic response of a conventional DC motor.KeywordsEuler backward differencesBilinear transformDC motor modeling