Linear continuous system discretization using a new general delta operator

To find the discrete mathematical model that is going to represent, by the best way, a real continuous system, is one of the problems that any control engineer will probably need to solve, since any real control system includes digital components. Up to now, the problem of finding that discrete model, was generally solved by means of the Z-transform and the shift operator but, at high sampling speed and due to numerical sensitivity problems, these methods have, in general, become not valid. For this reason, some alternatives to these discretization methods have been developed. In this paper we present on of these methods, which is based on the General Delta operator and transform. This new method offers not only a model but a set of models where each one of them depends on the value given to a certain parameter called n₂. In this article we have developed an analytical study about the optimal selection of this parameter using the sampling period for adapting the adequate parameter. We will also present an illustrative example in order to show the effect that a change in the sampling period has over the system output.