Stability of the program manifold of automatic indirect control systems taking into account the external load
- 23 July 2023
- journal article
- Published by Erdal Karapinar in Advances in the Theory of Nonlinear Analysis and its Application
- Vol. 7 (2), 405-412
- 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
Funding Information
- Institute of Mathematics and Mathematical modelling, Almaty, Kazakhstan (AP 09258966)
This publication has 10 references indexed in Scilit:
- On the Stability of a Program Manifold of Control Systems with Variable CoefficientsUkrainian Mathematical Journal, 2019
- ABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMSNEWS OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN, 2018
- On a program manifold’s stability of one contour automatic control systemsOpen Engineering, 2017
- Solution of the Problem of Stochastic Stability of an Integral Manifold by the Second Lyapunov MethodUkrainian Mathematical Journal, 2016
- Inverse Problems in Ordinary Differential Equations and ApplicationsPublished by Springer Science and Business Media LLC ,2016
- Simulation of control processes, stability and stabilization of systems with program constraintsJournal of Computer and Systems Sciences International, 2015
- On the inverse stochastic reconstruction problemDifferential Equations, 2014
- Exponential stability of a program manifold of indirect control systemsUkrainian Mathematical Journal, 2010
- Stability of a program manifold of control systems with locally quadratic relationsUkrainian Mathematical Journal, 2009
- Stability in Nonlinear Control SystemsPublished by Walter de Gruyter GmbH ,1961