V.F. Shishlakov1, N.V. Reshetnikova2, E.Yu. Vataeva3, D.V. Shishlakov4

1–4 Saint-Petersburg State University of Aerospace Instrumentation (St. Petersburg, Russia)

Non-stationary automatic control systems (ACS) are systems whose parameters change over time. This type of system has a mathematical model described by differential equations with variable parameters. As a rule, the parameters of the elements and devices included in the ACS, to one degree or another, depend on time, in other words, the system in the general case is non-stationary. This dependence may be due to the presence of elements in the system, the operation of which directly depends on time or is the cause of heating or operational wear of the elements that make up the ACS. The presence of nonstationarity in systems complicates the methods of their analysis, synthesis and modeling. The real characteristics of most elements of automatic control systems have nonlinear static and dynamic characteristics, therefore, the complexity of the synthesis of nonlinear nonstationary control systems is due to the fact that there are no unified approaches to solving this problem. The time dependence of the system parameters limits the possibility of a one-time solution of the controller synthesis problem, since the ACS operation modes determined by its nonstationarity, as a rule, do not make it possible to ensure the specified quality indicators of its operation for all modes. In this connection, below we consider the solution to the problem of synthesizing the control laws of the controller for nonlinear non-stationary ACS. As a mathematical apparatus for solving the synthesis problem, it is proposed to use the inversion of the direct variational analysis method – the generalized Galerkin method – to solve the problem. This makes it possible to completely algebraize the solution of the problem for the investigated class of ACS. Thus, the paper offers options for obtaining the parameters of the controller applicable to systems with the property of nonstationarity.

Shishlakov V.F., Reshetnikova N.V., Vataeva E.Yu., Shishlakov D.V. Synthesis of non-stationary continuous nonlinear control systems by the generalized Galerkin method. Science Intensive Technologies. 2021. V. 22. № 8. P. 75−79. DOI: https://doi.org/10.18127/j19998465-202108-11 (in Russian)

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