350 rub
Journal Information-measuring and Control Systems №12 for 2015 г.
Article in number:
Structural synthesis of Lagrangian systems of automatic control with the use of first integrals of motion
Keywords: integral of motion curve shift structural synthesis Lagrange equation of the second kind
Authors:
D.S. Andrashitov - Ph.D.(Eng.), Associate Professor, Chair of Mathematics and Computer Science, Moscow Vitte University. E-mail: dima-andrahitov@rambler.ru A.A. Kostoglotov - Dr.Sc.(Eng.), Professor, Chair of Cyber Security Information Systems, Don State Technical University (Rostov-on-Don). E-mail: kostoglotov@aaanet.ru A.A. Kuznetsov - Ph.D.(Eng.), Assjciate Professor, Military Training and Research Center of the Air Force «Air Force Academy named after Professor N.E Zhukovsky and Y.A. Gagarin» (Voronezh). E-mail: smithaa@yandex.ru S.V. Lazarenko - Ph.D.(Eng.), Don State Technical University (Rostov-on-Don). E-mail: rh3311@mail.ru
Abstract:
In the design of automatic systems as a control object is described by nonlinear differential equations, it is often difficult in the first stage - the stage of structural synthesis (select control law). It is assumed that the dynamics of the system satisfies the principle of Hamilton-Ostrogradskii. It requires finding the condition of a minimum target extended functionality comprising the integral action. It was found that a necessary condition of its minimum is the maximum of the generalized power. This allows you to set up to function structure synthesizing feedback without solving the traditional boundary value problem of the maximum principle of L.S. Pontryagin. To construct synthesis function is proposed to use the first integrals of motion. This allows you to connect it with the structure of the switching curve, which retains the stationary value of the Hamiltonian of the control system. The result is a new non-linear control as a function of the generalized coordinates. Constructiveness of the solution is confirmed by mathematical simulation test management tasks of a simple pendulum.
Pages: 12-18
References

 

  1. Bojjchuk L.M. Metod strukturnogo sinteza nelinejjnykh sistem avtomaticheskogo upravlenija. M.: EHnergija. 1971. 112 s.
  2. Flegontov A.V. Strukturnyjj sintez: metody, algoritmy, modeli, kompjuternaja podderzhka // Trudy SPIIRAN. 2002. № 1. S. 316-332.
  3. Zegzhda S.A., Tovstik P.E., JUshkov M.P. Obobshhennyjj princip Gamiltona-Ostrogradskogo i ego primenenie dlja gashenija kolebanijj // DAN. 2012. T. 447. № 3. S. 1-4.
  4. Lazarenko S.V. Metod sinteza optimalnogo upravlenija s ispolzovaniem principa Gaussa // Informacionno-izme­ritelnye i upravljajushhie sistemy. 2013. № 12. S. 37-43.
  5. Medvedev V.S., Filimonov N.A. EHnergeticheskijj podkhod v zadachakh upravlenija manipuljacionnymi robotami // Mekhatronika, avtomatizacija, upravlenie. 2003. № 4. S. 22-27.
  6. IsidoriA. NonlinearControlSystems. Vol. II. NewYork: Spinger - Verlag. 1999.
  7. Krutko P.D., Palosh V.E. Stabilizacija sostojanijj ravnovesija dvojjnogo majatnika, nagruzhennogo sledjashhejj i konservativnojj silami // Izvestija Rossijjskojj akademii nauk. Teorija i sistemy upravlenija. 2009. № 2. S. 3-17.
  8. Reshmin S.A., Ananevskijj I.M. Nepreryvnoe upravlenie mekhanicheskojj sistemojj na osnove metoda dekompozicii // Izv. RAN. Teorija i sistemy upravlenija. 2014. № 4. S. 3-17.
  9. Lure A.I. Analiticheskaja mekhanika. M.: GIFML. 1961. 824 s.
  10. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V. The combined-maximum principle in problems of estimating the motion parameters of a maneuvering aircraft // Journal of Communications Technology and Electronics. 2009. V. 54. № 4. R. 450-457.
  11. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V., SHevcova L.A. Sintez optimalnogo upravlenija na osnove obedinennogo principa maksimuma // Izvestija vysshikh uchebnykh zavedenijj. Severo-Kavkazskijj region. Tekhnicheskie nauki. 2010. № 2. S. 31-37.
  12. Andrashitov D.S., Kostoglotov A.A., Kuznecov A.A., Derjabkin I.V. Sintez algoritma avtonomnogo upravlenija matematicheskim majatnikom na osnove obedinennogo principa maksimuma // Izvestija vysshikh uchebnykh zavedenijj. Severo-Kavkazskijj region. Tekhnicheskie nauki. 2010. № 3. S. 9-14.
  13. Kostoglotov A.A., Kostoglotov A.I., Lazarenko S.V. Obedinennyjj princip maksimuma v informacionnykh tekhnologijakh analiza i sinteza. Rostov-na-Donu: RASJURGUEHS. 2010. 165 s.
  14. Kostoglotov A.A., Lazarenko S.V. Metod strukturno-parametricheskojj identifikacii Lagranzhevykh dinamicheskikh sistem v zadachakh obrabotki izmeritelnojj informacii // Izmeritelnaja tekhnika. 2014. № 2. S. 32-36.
  15. Andrashitov D.S., Kostoglotov A.I., Kostoglotov A.A., Lazarenko S.V., Cennykh B.M. Universalnyjj metod sinteza optimalnykh upravlenijj nelinejjnymi dinamicheskimi sistemami // Inzhenernyjj vestnik Dona. 2014. URL: http://www.ivdon.ru/magazine/archive/n1y2014/2251(data obrashhenija: 14.07.2015 g.).
  16. Kolesnikov A.A. Sinergeticheskaja teorija upravlenija. M.: EHnergoatomizdat. 1994. 343 s.
  17. Ajjdinjan A.R., Cvetkova O.L., Molchanov A.A. Metodika diskretnogo upravlenija ehlektrodvigatelem postojannogo toka // Vestnik DGTU. 2014. T. 14. № 3(78). S. 88-95.
  18. Konovalov A.S., JAkimovskijj D.O. Upravlenie ehlektroprivodami kosmicheskikh apparatov v osobykh rezhimakh // Informacionno-upravljajushhie sistemy. 2008. № 6. S. 26-31.