Parametric synthesis of a nonlinear automatic control system with distributed parameters

Аuthors

Goncharova V. I.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia

e-mail: goncharova_31kaf@bk.ru

Abstract

The development of an automatic control system for any fairly complex technical object is a long, multifaceted process; one of the main stages is the construction of an adequate mathematical model of the control object. The choice of a mathematical model of an object is in one way or another connected with the idealization of its mathematical description, which involves highlighting the main patterns in the behavior of the object and neglecting secondary connections and effects, taking into account the expected conditions of its physics of functioning in a real system. In this work, we will consider an example related to temperature control in a furnace. Since in such a system it is necessary to take into account several variables, when constructing a mathematical model, the automatic control system is distributed. If, in a system for regulating the heating of a rod in a furnace, we implement the transition from partial differential equations inherent in systems with distributed parameters to ordinary differential equations, then it is most advisable to consider the system as a linear system with a retarded argument.

It should be noted that such a procedure is very useful, since algorithms for efficiently solving ordinary differential equations are much better developed compared to algorithms for directly solving partial differential equations.

The paper presents a possible implementation of the transition from partial differential equations to ordinary differential equations for solving the problem of parametric synthesis using the generalized Galerkin method for automatic control systems with distributed parameters. As a mathematical apparatus, the method of separation of variables (Fourier) is used, as well as obtaining state space matrices in order to obtain the transfer function of an automatic control system with distributed parameters.

Keywords:

automatic control system (ACS), ACS with distributed parameters, method of separation of variables (Fourier), partial differential equations, generalized Galerkin method

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