Yu.P. Korniushin1, A.V. Maksimov2, A.V. Finoshin3, V.O. Miloserdov4

1–4 Moscow state technical University n. a. N. Uh. Bauman (national research University) (Kaluga, Russia)

The problem of studying the robust properties of nonlinear tracking systems with regulators operating at sliding intervals using the apparatus of matrix operators is considered. The problem is caused by the fact that it was traditionally believed that optimal systems synthesized according to the quadratic quality criterion are sensitive to the parametric uncertainty of the object model. This was determined by the fact that «once» found from the solution of the Riccati equation, the parameters of the regulator are unchanged. And, the built system is not «rough», and sometimes they lose not only optimality, but also efficiency. Systems are considered when a priori information about an object is not known exactly, but only with some confidence, given by the intervals of belonging of its parameters to a certain interval.

Purpose. To develop a method and algorithm for the synthesis of optimal regulators that ensure robust properties of the system in relation to the parametric uncertainty of the control object. The only requirement is to belong to the mathematical model of the control object, to have nonlinear characteristics of an analytical type, or reduced to them.

A new synthesis method is proposed that allows the construction of regulators that deliver robust properties to nonlinear control objects with the above properties with respect to the parametric uncertainty of the object. The matrix operator apparatus is used, which allows parameterizing the synthesis task. There are no restrictions on controls. Nevertheless, with simulated constraints on the control in magnitude, the robust properties of the control system were preserved.

The proposed algorithm for the synthesis of regulators providing robust properties to nonlinear control systems in relation to their mathematical models can be used in the design of electromechanical complexes and systems of various functional purposes.

Korniushin Yu.P., Maksimov A.V., Finoshin A.V., Miloserdov V.O. A method for studying the robustness of one class of nonlinear control systems. Achievements of modern radioelectronics. 2024. V. 78. № 11. P. 50–59. DOI: https://doi.org/10.18127/j20700784-202411-06 [in Russian]

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