1. MMC
  2. All Volumes and Issues
  3. Volume 7, Number 1, 2020
  4. The method of inverse problems of dynamics for the synthesis of a system of stabilization of the movement of a dynamic object on operatively programmable trajectories

The method of inverse problems of dynamics for the synthesis of a system of stabilization of the movement of a dynamic object on operatively programmable trajectories

MMC.
2020;
Volume 7, Number 1
: pp. 29–38
https://doi.org/10.23939/mmc2020.01.029
Received: April 01, 2019
Revised: October 01, 2019
Accepted: October 02, 2019

Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 29–38 (2020)

Authors:
  1. O. A. Mashkov
  2. V. A. Chumakevich
  3. Yu. V. Mamchur
  4. V. R. Kosenko
1
National Center for Control and Testing of Space Facilities of the State Space Agency of Ukraine
2
Lviv Polytechnic National University
3
National Center for Control and Testing of Space Facilities of the State Space Agency of Ukraine
4
National Center for Control and Testing of Space Facilities of the State Space Agency of Ukraine

The article is devoted to the analysis of the possibility of applying the method of inverse problems of dynamics for the synthesis of a system of spatial stabilization of the motion of a dynamic object on an operatively programmable trajectory.  The article proposes to apply the method of inverse problems of dynamics for the synthesis of a system for stabilizing the motion of a dynamic object on an operatively programmable trajectory.  It is concluded that the procedure for applying the method of inverse problems of dynamics provides for the sequential execution of two procedures.  The first procedure involves setting the desired trajectory of movement of a dynamic object and determining the vector of necessary control forces for the implementation of this trajectory of movement.  The second procedure involves determining the control function (control deviations) to create such forces. In the development of the concepts of the algorithmic approach (inverse problems of dynamics), an analytical expression for the governing force is obtained.  The proposed block diagram of the control algorithm can be used to synthesize control systems for complex dynamic objects, for example, remotely piloted aircraft.

control algorithm
dynamic object
control force
control function
inverse dynamics problem
operatively programmable trajectory
control system synthesis
motion stabilization
  1. Mashkov O. A.  Synthesis of multidimensional automatic systems based on the solution of inverse problems of dynamics.  KVVAIU, Kiev (1989), (in Russian).
  2. Galiullin A. C.  Methods for solving inverse problems of dynamics.  Science, Moscow (1986), (in Russian).
  3. Ermoshina O. V., Krishchenko A. P.  Synthesis of programmed control of the orientation of a spacecraft by the method of inverse problems of dynamics.  Journal of Computer and Systems Sciences International. 39 (2), 313--320 (2000).
  4. Kondratieva L. A.  Approksimacionnaja obratnaja zadacha dlja predel'nyh ciklov.  Kachestvennoe i chislennoe issledovanie matematicheskih modelej dinamicheskih sistem. Mezhvuz. sb. nauchn. trudov. 72--75 (2006), (in Russian).
  5. Kondratyeva L. A.  The Inverse Boundary-Values Problems of Dynamics on Manifolds.  Vestnik Rossijskogo universiteta druzhby narodov: Serija Matematika, informatika, fizika. 1, 34–38 (2010), (in Russian).
  6. Krutko P. D.  Inverse problems of the dynamics of controlled systems.  Mashinostroenie, Moscow (2004), (in Russian).
  7. Lavrov N. G., Strashinin E. E., Shalimov L. N.  Back dynamic concept applied to re-entry vehicle attitude control problem.  Vestnik Juzhno-Ural'skogo gosudarstvennogo universiteta. 26, 4–9 (2009), (in Russian).
  8. Artyushin L. M., Mashkov O. A., Durniak B. V., Sivov N. S.  The theory of automatic control.  UAD, Lviv (2004), (in Ukrainian).
  9. Artyushin L. M., Mashkov O. A., Sivov N. S.  The theory of automatic control.  Air Force CI, Kiev (1996), (in Russian).
  10. Velishchanskii M. A., Krishchenko A. P., Tkachev S. B.  Synthesis of spacecraft reorientation algorithms based on the concept of the inverse problem of dynamics.  Journal of Computer and Systems Sciences International. 42 (5), 811–818 (2003).
  11. Shabatura U. V., Paranchuk Ya. S., Chumakevich V. O.  Problemy stvorennia funktsionalno-stiikykh elektromekhanichnykh kompleksiv.  Bulletin of Lviv Polytechnic National University, Series of Electrical Power and Electromechanical Systems. 707, 114–119 (2011), (in Ukrainian).
  12. Chumakevych V.  Singularity of the functional-stable electromechanical complex of agricultural purpose.  Bulletin of Lviv National Agrarian University. 20, 115–128 (2016), (in Ukrainian).
  13. Mashkov V.  New approach to system level self-diagnosis.  2011 IEEE 11th International Conference on Computer and Information Technology. 579–584 (2011).
  14. Mashkov O. A., Chumakevych V. O., Sokulsky O. E., Chyrun L. B.  Features of determining controlling effects in functionally-stable systems with the recovery of a control.  Mathematical Modeling and Computing. 6 (1), 85–91 (2019).
  15. Improving the efficiency of on-board information management complexes on the basis of detecting and parrying failures in the management process.  Report on R & D No. 09026. KVVIAU, 226–264 (1990), (in Russian).
  16. Mashkov O. A.  Ocenka vremeni perehodnogo procesa v dinamicheskoj sisteme s algoritmom upravlenija na osnove reshenija obratnyh zadach dinamiki.  Otdel'nyj tematicheskij nauchno-tehnicheskij sbornik.  KVVAIU, Kiev. 65–67 (1985), (in Russian).
  17. Mashkov O. A.  Ocenka ustojchivosti dinamicheskoj sistemy s algoritmom upravlenija, poluchennym na osnove reshenija obratnyh zadach dinamiki.  Otdel'nyj tematicheskij nauchno-tehnicheskij sbornik.  KVVAIU, Kiev. 62–64 (1985), (in Russian).
  18. Mashkov O. A., Durniak B. V., Mamchur Yu. V., Timchenko O. V.  Syntez alhorytmu prohramnoho keruvannia na trenazheri dystantsiino pilotovanoho litalnoho aparata na osnovi alhorytmichnoi protsedury rishennia obernenoi zadachi dynamiky (determinovana postanovka).  Collection of scientific works "Modeling and information technologies". 82, 166–176 (2018), (in Ukrainian).
  19. Mashkov O. A., Durniak B. V., Mamchur Yu. V., Timchenko O. V.  Syntez alhorytmu prohramnoho keruvannia na trenazheri dystantsiino pilotovanoho litalnoho aparata na osnovi alhorytmichnoi protsedury rishennia zvorotnoi zadachi dynamiky (stokhastychna postanovka).  Collection of scientific works "Modeling and information technologies". 83, 146–153 (2018), (in Ukrainian).
  20. Mashkov O., Mamchur Yu.  Formalization of ecological monitoring unmanned aerial vehicle control simulator pilot training problem based on inverse dynamics problem solution.  Emerging Technologies. 2 (6), 24–30 (2018), (in Ukrainian).
  21. Artyushin L. M., Panov V. I., Shamov G. V.  Synthesis of flight control algorithms based on solving inverse problems of dynamics.  KVVAIU, Kiev (1982), (in Russian).