The Auxiliary Parametric Sensitivity Method as a Means of Improving Project Management Analysis and Synthesis of Executive Elements

Abstract

To write differential state equations of investigated actuating devices in the needed Cauchy’s normal form, we must abandon the traditional theory of electrical circuits for the theory of electromagnetic circuits. In this work, the known and developed new mathematical models for the analysis of special states have been involved. For solving this problem, it is necessary, at first, to construct a mathematical model of the actuating device. This model is based on the construction of a monodromy matrix, and simulation of transient and steady-state processes at the same time. To make the numerical analysis more convenient, differential equations for models of electromechanical state are written down in Cauchy's normal form. The algorithm involves the study of transient and stationary processes by decomposing them into constituent parts using the mathematical apparatus of the classical theory of nonlinear differential equations, which are calculated in a relatively simple way. The transitional process is obtained as a result of the differentiation of state equations for given initial conditions. We obtain a steady-state process by the initial conditions that exclude transient response. Such conditions we receive by the iterative Newton method. The proposed method of auxiliary variation equations allowed bypass procedure of differentiation of matrix coefficients over the argument that ensured the possibility of the algorithm application of the method of parametric sensitivity. The method of analysis can be spread to more complex nonlinear systems, such as electric motors.