Analysis of Dynamic Characteristics of an Unregulated Object

Abstract

The article studies an unregulated object and analyzes the dynamic structure of the object based on a steady-state signal. The first stage of the analysis is associated with general questions: based on a priori data on the object under study, one must first select one of the operator types, choosing functional, differential (ordinary, with a lagging argument with partial derivatives), integral or integro-differential operators. Then we limit the selected operator type. Taking into account more detailed a priori information, we limit ourselves to considering linear or weakly nonlinear operators with constant coefficients. Under such conditions, it is necessary to take into account not only the a priori properties of the analyzed object, but also the preliminary information obtained from the signal. Regularities in the behavior of the signal make it possible to ignore any class of operators as clearly not corresponding to the observed manifestations of the object. The development of methods for finding in a certain class an equation that has a given function as its solution relates to inverse problems of analysis. The direct scheme – to find the movement of an object of known structure under given conditions – has a narrower technical area of direct applications. In the work, a general and fairly simple principle for describing a signal was formulated and, to some extent, substantiated. According to this basic position, the quantitatively significant and regularly manifested properties of a signal under given observation conditions are linked to each other by a certain dynamic structure of the object. The role of the object's movements, which are less significant under these conditions, as well as the role of the external environment, is reflected in this description by the forceF(t), which fluctuates in time and disturbs the dynamic system. The task of analyzing the dynamic structure of an object is reduced to assessing the numerical values of the coefficientsA_0^((k)),A_m^((k)). A priori ideas about the dynamic structure of the analyzed object allow us to represent these coefficients in the form of unambiguous expansions, which are described in detail in the article. Based on the numerical processing of the signal U(t;x), the dynamic characteristics of the unregulated object were analyzed.