Institute of mechanics and seismic stability of structures named after. M.T. Urazbaev Uzbekistan Academy of Sciences

The paper proposes mathematical model of stabilizing a hydraulic distributor with hydraulic control. It determines the Lyapunov function ensuring the system stability. The Bellman equation is obtained to find the optimal stabilizing function for the hydraulic system using the dynamic programming method. The optimal stabilizing function for the hydraulic distributor is established. Based on the proposed hydraulic distributor stabilization model, implemented in the MATLAB/Simulink environment, the paper provides data on alterations in pressure in the system, hydraulic distributor piston and slide valve displacements obtained with and without the stabilizing function, which adequately describes working process of the hydraulic system.
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References

[1] Malkin I.G. Teoriya ustoychivosti dvizheniya [Theory of motion stability]. Moscow, Nauka Publ., 1966. 530 p. (In Russ.).

[2] Shcherbakov V.S., Zhdanov A.V., Menkov V.V. Structure and algorithm of automated designing system of steering hydrodrive mechanism. Vestnik SibADI [The Russian Automobile and Highway Industry Journal], 2008, no. 3, pp. 89–92. (In Russ.).

[3] Annakulova G.K., Lebedev O.V. Dinamicheskie rezhimy i khaoticheskie dvizheniya elementov privodov mashin [Dynamic modes and chaotic motions of machine drive elements]. Tashkent, IM i SS AN RUz Publ., 2010. 141 p. (In Russ.).

[4] Lyapunov A.M. Izbrannye trudy. Raboty po teorii ustoychivosti [Selected works. Works on the theory of stability]. Moscow, Nauka Publ., 2007. 572 p. (In Russ.).

[5] Kuntsevich V.M. Sintez sistem avtomaticheskogo upravleniya s pomoshchyu funktsiy Lyapunova [Synthesis of automatic control systems using Lyapunov functions]. Moscow, Nauka Publ., 1977. 400 p. (In Russ.).

[6] Pyatnitskiy E.S. Automated subsystems of analysis and synthesis of nonlinear motion control systems. Problemy mashinostroeniya i nadezhnosti mashin, 1990, no. 5, pp. 74–81. (In Russ.).

[7] Pyatnitskiy E.S. Design of systems for the stabilization of programmed motions of nonlinear control plants. Avtomatika i telemekhanika. 1993, no. 7, pp. 19–37. (In Russ.). (Eng. version: Autom. Remote Control, 1993, vol. 54, no. 7, pp. 1046–1062.)

[8] Pupkov K.A., Egupov N.D., red. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya. T. 4: Teoriya optimizatsii sistem avtomaticheskogo upravleniya. Moscow, Bauman MSTU Publ., 2004. 744 p. (In Russ.).

[9] Bellman R.E., Glickberg, Gross O.A. Some aspects of the mathematical theory of control processes. Rand Corp., 1958. 244 p.

[10] Lewis E.E., Stern H. Design of hjdraulic contorl sjstems. McGraw-Hill, 1962. 360 p. (Russ. ed.: Gidravlicheskie sistemy upravleniya. Moscow, Mir Publ., 1966. 203 p.)

[11] Gamynin N.S. Osnovy sledyashchego gidravlicheskogo privoda [Fundamentals of tracking hydraulic drive]. Moscow, Oborongiz Publ., 1962. 293 p. (In Russ.).

[12] Gamynin N.S. Gidravlicheskiy privod sistem upravleniya [Hydraulic drive of control systems]. Moscow, Mashinostroenie Publ., 1972. 376 p. (In Russ.).

[13] Pugatin D.R., Zedgenizov V.G. [Mathematical model of a spool hydraulic distributor with hydraulic control]. Aviamashinostroenie i transport Sibiri. Sb. st. XV Vseros. nauch.-tekhn. konf. [Aviation Machine Building and Transport of Siberia. Proc. XV Russ. Sci.-Tech. Conf.]. Irkutsk, Izd-vo IRNITU Publ., 2021, pp. 185–189. (In Russ.).

[14] Vasilyev V.V., Simak L.A., Rybnikova A.M. Matematicheskoe i kompyuternoe modelirovanie protsessov i sistem v srede MATLAB/Simulink [Mathematical and computer modeling of processes and systems in MATLAB/Simulink environment]. Kiev, NAN Ukrainy Publ., 2008. 91 p. (In Russ.).

[15] Ruppel A.A., Sagandykov A.A., Korytov M.S. Modelirovanie gidravlicheskikh sistem v MATLAB [Modeling of hydraulic systems in MATLAB]. Omsk, SibADI Publ., 2009. 171 p. (In Russ.).

[16] Darsht Ya.A. Simulation models of hydraulic apparatuses. Avtomatizatsiya i sovremennye tekhnologii [Automation. Modern Technologies], 2005, no. 3, pp. 28–30. (In Russ.).