|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|
|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.|
|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. Metodika rascheta optimal'nogo kolichestva nagrevatel'nykh elementov v zavisimosti ot znacheniy temperaturnogo polya izotropnogo sterzhnya [Method of calculating the optimal number of heating elements depending on the values of the temperature field of an isotropic rod], Nauchno tekhnicheskie vedomosti SPbGPU. Ser. Informatika. Telekommunikatsii. Upravlenie [Scientific technical statements SPbGPU. Ser. Computer science. Telecommunications. Control. Vol. 2], 2011, No. 6-2 (138), pp. 48-53.
4. Il'yushin Yu.V. Stabilizatsiya temperaturnogo polya tunnel'nykh pechey konveyernogo tipa [Stabilization of the temperature field of conveyor-type tunnel furnaces], Nauchno tekhnicheskie vedomosti SPbGPU. Ser. Informatika. Telekommunikatsii. Upravlenie [Scientific technical statements SPbGPU. Ser. Computer science. Telecommunications. Control], 2011, No. 3 (126), pp. 67-72.
5. Chernyshev A.B. Modifitsirovannyy kriteriy absolyutnoy ustoychivosti nelineynykh raspredelennykh sistem upravleniya [Modified criterion of absolute stability of nonlinear distributed control systems], Izvestiya vuzov. Sev.-Kavk. region. Tekhnicheskie nauki [University News. North-Caucasian Region. Technical Sciences Series], 2009, No. 3 (151), pp. 38-41.
6. Ilyushin Y.V., Pershin I. M., Pervukhin D.A., Afanaseva О.V. Design of distributed systems of hydrolithosphere processes management. A synthesis of distributed management systems, IOP Conference Series: Earth and Environmental Science. Power supply of mining companies, Vol. 87.
7. Ilyushin Y.V., Pershin I. M., Pervukhin D.A., Afanaseva О.V. Design of distributed systems of hydrolithospere processes management. Selection of optimal number of extracting wells, IOP Conference Series: Earth and Environmental Science. Power supply of mining companies, Vol. 87.
8. Pershin I.M., Veselov G.E., Pershin M.I. Sistemy peredachi i obrabotki raspredelennoy informatsii [Systems for the transmission and processing of distributed information], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2015, No. 5 (166),
9. Malkov A.V., Pershin I.M., Pomelyayko I.S. Matematicheskaya model' kislovodskogo mestorozhdeniya uglekislykh mineral'nykh vod [Mathematical model of the Kislovodsk carbonate mineral water field], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2015, No. 7 (168), pp. 116-125.
10. Pershin I.M., Veselov G.E., Pershin M.I. Approksimatsionnye modeli peredatochnykh funktsiy raspredelennykh ob"ektov [Approximation models of transfer functions of distributed objects], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2015, No. 7 (168), pp. 126-138.
11. Pershin I.M., Veselov G.E., Pershin M.I. Sintez raspredelennykh sistem upravleniya gidrolitosfernymi protsessami mestorozhdeniy mineral'nykh vod [Synthesis of distributed control systems for hydrolithospheric processes of mineral water deposits], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2014, No. 8 (157), pp. 123-137.
12. Kolesnikov A., Zarembo Ya., Puchkov L., & Zarembo V. Zinc Electrochemical Reduction on a Steel Cathode in a Weak Electromagnetic Field, Russian Journal of Physical Chemistry A, 2007, Vol. 8 (10), pp. 1715-1717. Retrieved January 22, 2014, from http://dx.doi.org/10.1134/ s0036024407100330.
13. Pershin I. Analysis and synthesis of systems with distributed parameters. Pyatigorsk: RIA-KMV, 2007.
14. Pleshivtseva Y., & Rapoport E. The Successive Parameterization Method of Control Actions in Boundary Value Optimal Control Problems for Distributed Parameter Systems, Journal of Computer and Systems Sciences International, 2009, Vol. 48 (3), pp. 351-362. Retrieved January 22, 2014, from http://dx.doi.org/10.1134/S1064230709030034.
15. Rapoport E. Alternance Properties of Optimal Solutions and Computational Algorithms in Problems of Semi-Infinite Optimization of Controlled Systems, Journal of Computer and Systems Sciences International, 1996, Vol. 35 (4), pp. 581-591.
16. Rapoport E. Structural Parametric Synthesis of Automatic Control Systems with Distributed Parameters, Journal of Computer and Systems Sciences International, 2006, Vol. 45 (4),
pp. 553-566. Retrieved January 22, 2014, from http://dx.doi.org/10.1134/S1064230706040071.
17. Rapoport E., & Pleshivtseva Y. Combined Optimization of Metal Hot Forming Line with Induction Pre-Heating, IEEE 26th Convention of Electrical and Electronics Engineers, Israel, Eilat, 2010.
18. Rapoport E., & Pleshivtseva Yu. Models and Methods of Semi-Infinite Optimization Inverse Heat-Conduction Problems, Heat Transfer Research, 2006, Vol. 37 (3), pp. 221-231.
19. Tikhonov А., & Samarsky А. Equations of mathematical physics. Moscow: Science, 1965.
20. Zarembo V., & Kolesnikov A. Background Resonant Acoustic Control of Heterophase Processes, Theoretical Foundations of Chemical Engineering, 2006, Vol. 40 (5), pp. 483-495. Retrieved January 22, 2014, from http://dx.doi.org/10.1134/s0040579506050058.
21. Zarembo V., Kolesnikov A., & Ivanov E. Background Electromagnetic-Acoustic Control of Structural And Plastic Properties of Metals, Bulletin of the Russian Academy of Sciences: Physics, 2006, Vol. 70 (8), pp. 1239-1243.
22. Zаrembo V., Kiseleva O., Kolesnikov A., Burnos N., & Suvorov K. Structuring of Inorganic Materials in Weak Rf Electromagnetic Fields, Inorganic Materials, 2004, Vol. 40 (1), pp. 86-91. Retrieved January 22, 2014, from http://dx.doi.org/10.1023/B:INMA.0000012184.66606.59.