# Article

 Article title METHODOLOGY FOR THE DETERMINATION OF THE STABILITY IN A SPATIALLY DISTRIBUTED CONTROL OBJECT WITH IMPULSE INPUT IMPACT Authors Yu. V. Ilyushin, I. M. Pershin Section SECTION III. AUTOMATION AND CONTROL Month, Year 05, 2018 @en Index UDC 681.5 DOI Abstract The emergence and development of the theory of systems with distributed parameters (DPS) is due to the complexity and non-standard methods of research, analysis and synthesis. Thus, the problems of the theory of systems with distributed parameters are much more complex than concentrated. This is due to the need for a spatially distributed analysis of the current state of the control object, including variable in time. Which in turn expands the class of possible impacts on the control object (for example, space-time controls). For the analysis of such systems, the application of the theory of systems with distributed parameters becomes unacceptable. A feature of the study of systems with distributed parameters is the development of a mathematical apparatus and methods of their study. It is worth noting that among nonlinear systems, there is a class of systems with one nonlinear element, for which the developed apparatus is applicable with minor modifications. For example, pulse systems with distributed parameters. In such systems, one represented as a group of elements can form a multidimensional, multilevel system. Then the main task of the synthesis of such systems becomes the search for possible solutions, based on the search for possible states of the system that ensure the stable operation of the system. There are a huge number of such possible solutions, depending on the different initial and boundary conditions, the type of reaction to deviations from the specified mode, etc. The characteristic of non-linear links is described with indication of logical conditions. Due to the nonlinear characteristic, the output variable will not be proportional to the input variable. Based on this, the response of a closed system, for example, to a pulse signal will depend on the power of this signal. In the case of analysis of dynamic oscillatory systems, pay attention to the attenuation of the transition process, which appears due to changes in the oscillation period. Thus, due to the lack of a single method for solving nonlinear distributed systems, it is necessary to carry out the synthesis of a particular method for solving a problem. The article builds a mathematical model of a two-dimensional spatial control object. The transfer function of the multidimensional system is constructed. A method for determining the stability of a spatially distributed control object with a pulse input is proposed. The analysis of the results is carried out. The conclusion is made about the generalization of the results of research on a class of systems with distributed parameters whose input action is a pulsed signal. Download PDF Keywords Distributed systems; thermal field; impulse input effect. References 1. Il'yushin Yu.V., Chernyshev A.B. Ustoychivost' raspredelennykh sistem s diskretnymi upravlyayushchimi vozdeystviyami [Stability of distributed systems with discrete control actions], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2010, No. 12 (113), pp. 166-171. 2. Il'yushin Yu.V., Chernyshev A.B. Opredelenie shaga diskretizatsii dlya rascheta teplovogo polya trekhmernogo ob"ekta upravleniya [Determining the discretization step for calculating the thermal field of a three-dimensional control object], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2011, No. 6 (119), pp. 192-200. 3. Il'yushin Yu.V. 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