MATHEMATICAL AND SIMULATION MODEL FOR THE PROBLEMS OF PROCESSES OPTIMAL CONTROL USING PROGRAM SYSTEMS

ŠEBEJ, P.; HRUBINA, K.

Abstract

The heat conduction equation ranks among the most important equations used in various technological disciplines (electric engineering, mechanical engineering, metallurgy, etc). The methods used for solving the equation can be broadly classified into the following three groups: a) Analytical methods (which are not suitable for consideration for the class of general problems encountered in practice). b) Analogue methods (the network methods closely connected with numerical methods appear to be the most suitable) c) Numerical methods which in present undergo the most intensive development paralleling the development of computers. Among the most generally used we may mention the network method, the finite difference method – the collocation and approximation methods [Lions 1978, Ramirez 1994]. Results of numerous papers indicate that it is possible to create a very efficient tool for the solution of the heat conduction equation by uniting the variational principles with the finite element method. The finite element method is known to be closely connected with the network method and to be basically a variational method. [Hrubina 1993, Hulko 1998, Zienkiewicz 1979]. The paper deals with the possible solution of the defined problem of optimum control with distributed parameters and non-stationary heat distribution by the use of simulations in the system MS EXCEL. Owing to a general formulation of mathematical model of the investigated thermal process that is expressed by bidimensional partial differential equation with boundary conditions is the area of the simulations usability within the system MS-Excel rather wide.

Coresponding author e-mail: sebej[at]fvt[dot]sk

Session: Modelling, Simulation, and Identification of Processes