Analytical Synthesis of Quasi-Optimal Regulators for Linear Objects Based on Conditionally Adequate Low-Order Models. Part 2

Abstract

For linear high-order plants (n l 4), analytical (exact) control algorithms in the form of feedback that are optimal in terms of the rapid response criterion are practically unknown, and for them the problem of synthesizing approximately rapid response control laws remains relevant. In this part of the work, an approach to the synthesis of rapid response highorder systems is developed, proposed in its first part, using the idea of transforming the original rapid response problem to a similar problem of controlling objects described by models of the first or second order, for which the optimal control algorithms in terms of rapid response are known. These algorithms underlie the investigated approach to the synthesis of rapid response control systems, which involves finding special functions that describe the relationship between the phase coordinates of models of a low-order object (by analogy with the works of A. A. Kolesnikov, they are called aggregated or macro-variables) with the phase coordinates of the original high-order object as well as the calculation of the parameters of the low-order models used, which in a certain sense ensure their adequacy to the original object and, accordingly, the rapid response of the synthesized systems. In this part of the work, in contrast to its first part, the synthesis uses two models of an object, not of the first, but of the second order, which are characterized by conditional and approximate adequacy in relation to the original model of a high-order object. In the case of conditional adequacy, the parameters of the low-order model are found exactly using the eigenvalues and vectors of the original object, and with approximate adequacy, using the least squares method. On the basis of these two second-order models, two methods for the synthesis of quasi-optimal controllers are developed, which differ in the use of nonlinear feedbacks that provide an increased rapid response of the designed control system that is sufficiently close to the limiting values. In particular, by the example of modeling, it is shown that Accordingly, the main content of the work is devoted to the results of a comparative analysis of the properties of these rapid response controllers, as well as the analysis of the features and conditions of applicability of the proposed synthesis methods