Stability of the program manifold of automatic indirect control systems taking into account the external load

Year 2023, Volume: 7 Issue: 2, 405 - 412, 23.07.2023

Sailaubay Zhumatov Sandugash Mynbayeva

https://doi.org/10.31197/atnaa.1200890

Abstract

The problems of stability system that arises in the construction of different automatic systems of indirect control are considered. It is known that a given program is not always exactly performed, since there are always initial, constantly acting perturbations.
Therefore, it is also reasonable to require the stability of the program manifold itself with respect to some function. In the first part, the stability being investigated of automatic indirect control systems with rigid and tachometric feedback. Necessary and sufficient conditions for the absolute stability of a program manifold are established separately. In the second part, the automatic systems of indirect control taking into account the external load are considered. The equations of the hydraulic actuator, taking into account the action of an external load, are presented in a convenient form for research. Then it reduces to studying the stability of the system of equations with respect to a given program manifold. By constructing LyapunovВ’s functions for the system in canonical form, sufficient conditions are obtained for the absolute stability of the program manifold. The results obtained can be used in the construction of stable automatic indirect control systems.

Keywords

program manifold, indirect control system, external load, rigid and tachometric feedback, Lyapunov function

Supporting Institution

Institute of Mathematics and Mathematical modelling, Almaty, Kazakhstan

Project Number

AP 09258966

Thanks

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan

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