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Structural synthesis of Lagrangian systems of automatic control with the use of first integrals of motion

Keywords:

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


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.
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