Modified Method of State Variables

Abstract

Formal mathematical model development of an object with lumped parameters is an integral part of CAE systems. The computer-aided design (CAD) system functionality largely depends on the formation method used. The article proposes to modify a method of state variables, which is a pioneer in formal mathematical models development of technical objects whose behaviour is described by a system of ordinary differential equations.The classical method of state variables uses a graph-based representation of the object structure and allows development of its mathematical model in the normal Cauchy form without incorrect locations. The incorrect locations mean situations when capacitance-type branches fall in the graph chords or inductance-type branches fall in the graph tree branches. If there are incorrect locations in the object’s scheme then, to have a model of correct development, additional elements are included to eliminate them. Such an approach is possible if the object description is performed at the level of the basic two-poles, but it is assumed that in all modern CAD systems there is a pre-processor in which it is possible (and as a rule) to use multi-pole components. In this case, it is challenging for an unsophisticated user to make scheme correction.The modified method of state variables proposed in the article is free from this drawback and allows us to obtain a mathematical model in the normal Cauchy form and with incorrect locations available. This will allow us to use both explicit and implicit integration methods, conduct modal analysis, and simply have a model version in the FMI standard.