Inverse problems of the dynamics of observation interpretation systems

Based on the analysis and systematization of the inverse problems of dynamics, the study of the properties and features of the types of dynamic models under consideration, an approach is proposed for the development of appropriate methods of mathematical modeling based on the use and implementation of integral models in the form of Volterra equations of the I and II kind, their functional capabilities are determined in the study of various classes of problems, and also formulated the features that affect the choice of methods for their numerical solution. Methods for obtaining integral models are proposed, which are the basis for constructing algorithms for solving inverse problems of dynamics for a fairly wide class of dynamic objects. Integral methods for the identification of dynamic objects have been developed, which make it possible to obtain stable non-optimization algorithms for calculating the parameters of mathematical models. Recurrent methods of parametric identification of transfer functions of dynamic objects with an arbitrary input action are proposed (the obtained parameters of the transfer functions are also coefficients of the corresponding differential equations, which makes it possible to obtain equivalent mathematical models in the form of integral equations). The study of algorithms that implement the proposed identification methods allows us to conclude about their efficiency in terms of the amount of computation and ease of implementation, as well as the high accuracy of calculating the model parameters.

PATH FOLLOWING PROBLEM FOR UAV CARRYING PENDULUM

The linearized dynamics of a UAV is considered along with a pendulum hanging from it. The state trajectories of the center of mass of the UAV are given. Given the trajectory of the center of mass of the UAV and the state trajectory of its yaw angle, we have to find the control actions and conditions under which the UAV would follow the path while holding the pendulum stable around its lower equilibrium point. The problem is solved using the method for solving inverse problems of dynamics. All the state trajectories of the system and all the control actions are calculated. The condition is obtained under which a solution to the path following problem exists. A specified simple trajectory is chosen as an example for visualizing the results.

On stochastic inverse problem of construction of stable program motion

One of the inverse problems of dynamics in the presence of random perturbations is considered. This is the problem of the simultaneous construction of a set of first-order Ito stochastic differential equations with a given integral manifold, and a set of comparison functions. The given manifold is stable in probability with respect to these comparison functions.

Mathematical model of the interaction of wheeled skidder with skid trail in the rotate mode

Вопросам взаимодействия колесного трелевочного трактора с пачкой древесины и волоком в режиме поворота уделяется недостаточно внимания. Разработанные математические модели не учитывают такие важные свойства объекта исследования, как упругодемпфирующие характеристики шин в продольном, поперечном направлениях и на скручивание, упруго- демпфирующие свойства механизма складывания и трелюемой пачки древесины, нелинейный характер работы элементов системы и связи их между собой. Цель исследования – разработка математической модели взаимодействия колесного трелевочного трактора с волоком в режиме поворота с учетом упруго- демпфирующих свойств шин, механизма складывания и трелюемой пачки древесины. Метод исследования – математическое моделирование. Исследование полученной системы дифференциальных управлений на ЭВМ дает возможность решить как прямую, так и обратную, задачи динамики. Проведенное исследование подтвердило адекватность разработанной математической модели взаимодействия колесного трелевочного трактора с пачкой древесины и волоком в режиме поворота. Расхождение результатов – 12–16%, что позволяет рекомендовать ее для использования в АСНИ и САПР «Колесный трелевочный трактор». The interaction of the wheeled skidder with a pack of wood and fiber in the mode of rotation is not given enough attention. The developed mathematical models do not take into account such important properties of the object of study as elastic-damping characteristics of tires in the longitudinal, transverse directions and twisting, elastic- damping properties of the mechanism with the laying and the trill packet of wood, the nonlinear nature of the system elements and their relationship to each other, etc. The purpose of this article is to develop a mathematical model of interaction wheel skidder tractor with fiber in the mode of rotation, taking into account the elastic properties of tires, folding mechanism and a trill packet of wood. Research method-mathematical modeling. The study of the obtained system of differential controls on a computer makes it possible to solve both direct and inverse problems of dynamics. Studies have confirmed the adequacy of the developed mathematical model of interaction wheel skidder with a bundle of wood and fiber in the mode of rotation, the discrepancy of results – 12–16%, which allows to recommend it for use in ASNI and CAD «Wheel skidder».

ABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMS

In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of local quadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.