MULTI-CRITERIA CONTROL OF NONLINEAR THERMAL DIFFUSION PROCESSES OF TECHNOLOGICAL THERMAL PHYSICS
E.Ya. Rapoport, Yu.E. Pleshivtseva, A.V. Popov
Samara State Technical University, Samara, Russia
Keywords: systems with distributed parameters, multi-criteria optimization, optimal control, alternance method, numerical modeling
Abstract
A constructive method is proposed for the multi-criteria optimization of nonlinear objects in technological thermal physics. It involves the evaluation of the accuracy of approximation to a given temperature state in numerical modeling of thermo-diffusion fields using a uniform metric. It is clear that the structure of the program control is identical to that previously found for linear models of controlled processes. The technology developed in previous works for solving multi-criteria problems in linear systems with distributed parameters is extended to the nonlinear objects under study. This is done under conditions of selecting time-constant values of special control in the corresponding sections. This is quite simple to implement in such an approximation of program control action on digital models of the controlled variable. The capabilities of the proposed approach are illustrated by an example of independent interest: the numerical solution of the problem of optimizing the induction heating process according to three basic indicators of technical and economic efficiency using a specialized electro-thermal model of the temperature field described by nonlinear heat conduction equations.
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