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On Modeling the controlled mechanical systems with digital controllers

A. S. Andreev1, E. A. Kudashova2

AnnotationSynthesis of discrete-time control which solves the problem of stabilization of holonomic mechanical systems’ program motion is considered. Such systems are described by Lagrange equations of the second kind. Digital control signals are used in computer-containing control systems for continuous processes. Development of models for such controlled processes leads to investigation of continuous-discrete systems with state described by a continuous function and discrete control functions. This paper proposes an approach for constructing of controller taking into account non-linearity of the system and non-stationarity of program motion. By means of Lyapunov vector function and the comparison system sufficient conditions of given program motion’s stabilization are obtained. A feature of the article is in solving of the problem by use of Lyapunov vector function with components that explicitly depend on time, and are nonlinear with respect to the generalized coordinates. It allows to solve the stabilization problem in general having the possibility to select the most suitable control parameters for each particular system.
Keywordsstabilization, control, discrete-time control, synthesis of control for mechanical systems, Lyapunov vector-function, comparison systems, nonstationary nonlinear dynamical systems

1Dean of Faculty of Mathematics and Information and Aviation Technology, Prof., D.Sc., Head of Information Security and Control Theory Department, Ulyanovsk State University, Ulyanovsk; andreevas@sv.ulsu.ru

2Programmer of Information Security and Control Theory Department, Faculty of Mathematics, Information and Aviation Technology, Ulyanovsk State University, Ulyanovsk; katherine.kudashova@yandex.ru

Citation: A. S. Andreev, E. A. Kudashova, "[On Modeling the controlled mechanical systems with digital controllers]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:3 (2016) 107–116 (In Russian)