Analysis of local robustness of a positional electric drive using Hermite- Biehler polynomials

THE RELEVANCE of this work lies in the analysis of the local robustness of a controlled electric drive, which is a key task in the case of operation under conditions of uncertainty, when one of the most important requirements for the system is to maintain the ability of the object of study to maintain stability and the required quality of control processes under the influence of destabilizing factors of various physical natures. PURPOSE. The paper studies the system properties of a positional electric drive with the definition of quantitative estimates of permissible variations in the parameters of the mathematical model of the system. The target setting of this analysis is to evaluate direct and indirect indicators of the quality of the positional electric drive operation based on the interval polynomial formed as a result of the study using computer modeling methods. Analysis of local robustness allows us to estimate the boundaries of asymptotic stability of the system under study under parametric disturbances. Formation of an interval polynomial based on the apparatus of Hermite-Bieler polynomials and computer modeling of the positional electric drive under study in the range of calculated boundaries of parameter variations is an important and urgent task. METHODS. When solving the research problem, methods of mathematical analysis, stability theory and theory of automatic control systems, vector-matrix equations in the form of state spaces and differential equations in operator form, the mathematical apparatus of Hermite-Biehler polynomials, as well as modeling of the dynamics equations of the electric drive under study in a software environment were used MatLab. RESULTS. In this work, the problem of analyzing the local robustness of a positional electric drive is solved and an interval polynomial with lower and upper bounds of the coefficients is obtained that accompanies the characteristic polynomial of the system under research. Based on the results of the analysis, computer modeling was carried out and quantitative estimates of the quality indicators of the functioning of the electric drive under research were obtained in the time and frequency domains. Graphs of additional motion are presented, which allow, when forming control objects of this class with sensors and coordinate controllers, to carry out a comparative analysis of the configuration of the system under research for the potential stability of performance indicators under conditions of parametric disturbances. CONCLUSION. The research of the system properties of a positional electric drive according to the output coordinate of its mathematical model from the point of view of local robustness analysis allows us to evaluate the range of parameter variations according to the degree of achievability of the required indicators of the quality of functioning of the object using the characteristic features of various control algorithms. The results of the analysis provide the opportunity to rationally distribute control resources based on classical algorithms and evaluate the effect of introducing output coordinate controllers into the system under conditions of parametric disturbances. It is also possible to compare options for the formation of correction algorithms using classical methods with an adaptive approach of search or analytical (non-search) types, based on the use of reference models of the research object with identification or direct types of control.

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