One estimation of the stability defect of sets in an approach game problem

A game problem of the approach to a compact target set at a fixed termination time is studied. We investigate the question of estimating the stability defect of a set in the space of game positions, which is weakly invariant with respect to a finite set of unification differential inclusions. © 2015, IFAC Hosting by Elsevier Ltd.Russian Science Foundation, RSF15-11-1001

STATISTICAL ANALYSIS OF DYNAMIC CHARACTERISTICS ASYNCHRONOUS ELECTRIC MOTOR WITH CHANGING LOAD PARAMETERS

Abstract: Research of operation electrical machines in transitional mode is an actual task. Modeling dynamic processes with changing load parameters and probabilistic assessment of simulation results allows taking into account the degree of influence of these changes on transient response. An approach to the study of the dynamics of an asynchronous electrical motor under external and parametric perturbations shown. Recommendations was given on the use of this method in solving the problem of identifying the parameters of electric machines

Features of application of sensitivity theory for analysis of influence of parametric disturbances on dynamic properties electromechanical converters

At the design and testing stage of electromechanical converters, the analysis of the influence of parametric perturbations on the dynamic properties of an object using sensitivity theory, which allows to evaluate the quality of operation of electrical machines depending on operating conditions, is relevant. Based on the system of differential equations of a DC motor, the sensitivity equations of the corresponding coordinates were obtained in three parameters. A vector structural scheme of the sensitivity model has been formed, as well as the Simulink-model, with the help of which sensitivity function plots were obtained, which determine the additional motion of the object of study when parameters change within specified limits. It is shown that the largest steady-state values of the sensitivity functions correspond to changes in the moment of inertia. It is revealed that the influence of the moment of inertia on the coordinates of the object of study is the most significant. Where in the coordinate most sensitive to variations in parameters is the rotation speed of the electromechanical converter. The problem of statistical analysis of errors of the output coordinates of a DC motor under the assumption of normal distribution of parametric disturbances was also solved. Simulations were carried out and dispersions and relative estimates of the influence of variable parameters were calculated, and graphs were obtained to estimate the degree of influence of parametric disturbances

An estimate of the stability defect for a positional absorption set subjected to discriminant transformations

We study bordering "paths," i. e., sets in the position space of an approach-evasion differential game that contain the positional absorption set. The positional absorption set provides an exact (classical) solution of the game. At the same time, its boundary is nonsmooth, which complicates the construction of this set. On the contrary, a set different from the positional absorption set may not provide an exact solution of the game but can be constructed with relative ease, for example, with the help of analytical formulas. There may be other reasons for using "paths" in solving a game. For example, the smoothness of the boundary of a chosen "path" allows one to efficiently form the players' control procedures guaranteeing the solution of a game problem in a "soft" setting by taking the motion of a conflict-control system to a neighborhood of the target set. In this paper, we propose a procedure for smoothing a set in a part of variables; the procedure is based on discriminant transformations. We study the stability defect caused by replacing the positional absorption set of a differential game by a set-"path" with boundary that is smooth in the space variables. An estimate for the stability defect of the constructed set is presented. The results are illustrated by the example of a known differential game. © 2012 Pleiades Publishing, Ltd

Q-tables formation method for automated monitoring of electromechanical converters parameters with application of linear integral criterion

In the process of functioning working sets with electromechanical converters included in their composition, it is necessary to take into account the influence of endogenous and exogenous disturbances that cause deviations of the parameters of electric machines from the nominal values given by the manufacturer in the appropriate documentation. These deviations of the parameters, even those within the permissible range of changes, have a noticeable effect on the quality of functioning of electromechanical converters and working sets as a whole. During the life cycle of the work of electromechanical converters, their parameters change as a result of natural wear and senescence, which necessitates continuous or periodic analysis and monitoring of the state objects under study. The paper considers a method based on the calculation of the linear integral criterion Q and the formation of Q – tables, which allows monitoring the functioning of electromechanical converters with unstable parameters during operation as part of working sets. Simulink – models of linear integral criterion calculation system and system of automated monitoring of electromechanical DC converter parameters are presented, which allow estimating unstable parameters. In these models static characteristics are implemented in tabular form reflecting the dependencies between the parameters of the electromechanical converters and the linear integral criterion. The results of the study allow us to obtain estimates of changes in the unstable parameters of electromechanical DC converters with the required accuracy

Experimentalanalytical identification of a mathematical model of a dc motor using the least squares method

The urgency of the problem lies in the formation of mathematical models of electromechanical converters corresponding to the objects of study with high accuracy. An experimental-analytical assessment of transient modes of a DC motor based on an installation for the study of electrical machines has been carried out. Based on the results obtained, an approximation of transient process graphs was carried out using the least squares method and an approximate polynomial of the corresponding order was selected with the closest imminence to the dynamic properties of the object under study

Comparative analysis of hardware and software of the monitoring method of fun ctioning electromechanical DC converters

THE PURPOSE. The task of analysis and monitoring of the functioning of electromechanical converters in transient and static modes is relevant at the design and operation stages. Software products for recording and processing measurement information, as well as for performing the necessary technical calculations, such as LabView, MatLab Simulink and others, offer great opportunities for solving the task and allow obtaining reliable results. METHODS. The study of electromechanical DC converters with built-in tachogenerators carried out, the measurement and fixing of the output coordinates of which is provided by experimental sets of various configuration with subsequent processing of the results of functional monitoring using application programs. RESULTS. The developed experimental sets differ in the composition and cost of hardware, the need to use one or another software support, the form of presenting the results of monitoring the functioning of research objects and the accuracy of the results. CONCLUSION. The present study aimed at a comparative analysis of two experimental sets. These sets allow obtaining mathematical models of electromechanical DC converters necessary for the implementation of the monitoring method of the function ing. The analysis performed from the point of view of material costs for hardware and software, the processing time of the experimental results and the correspondence of the obtained results to the required accuracy of the formation of mathematical models

Method of analysis and monitoring of the electromechanical converters parameters based on a linear integral criterion using sensitivity models

During the electromechanical converters operation in the composition of the working sets, objects parameters can change both under the influence of external factors, such as changes in the environmental characteristics, and due to parametric disturbances caused by changes of the physical characteristics of electromechanical converters elements. In this regard, the analysis and monitoring of electromechanical converters parameters is an important task. The article deals with a method that allows to ensure control over the operation of electromechanical converters during operation as part of working sets, based on variations analysis of the object parameters. The article provides a linear integral criterion computational scheme using the reference and sensitivity models to the parameters to be analyzed. The results provide a good way to estimate changes of the electromechanical converters parameters with the required accuracy