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Journal Nanotechnology : the development , application - XXI Century №1 for 2020 г.
Article in number:
Solution of the problem for the dynamic optimization of the technological process of finishing of precision parts with the use of the pontryagin-s maximum principle
DOI: 10.18127/j22250980-202001-02
UDC: 621.923
Keywords: Dynamic optimization technological process process of finishing precision parts the Pontryagin-s maximum principle
Authors:

A.I. Psareva – Student, Bauman Moscow State Technical University

V.V. Nazarov – Ph.D. (Eng.), Associate Professor, Bauman Moscow State Technical University

N.R. Rudenko – Ph.D. (Eng.), Associate Professor, Bauman Moscow State Technical University

A.V. Barinov – Senior Research Scientist, JSC “Russian Space Systems” (Moscow)

Abstract:

Statement of the problem. The article discusses the methodology and the sample solution for the dynamic optimization of the technological process of finishing of precision parts, for example, the plane-parallel substrate for microelectronics, with the use of the Pontryagin maximum principle.

Aim of the of work. To improve the efficiency of the finishing process, it is necessary to solve the problems of stabilizing the quality of processing and indicators of optimal automatic control.

Since the basic requirements for finishing processes are presented in the form of restrictions on the input and output indicators of the processed workpieces, the task of optimizing the finishing process consists in achieving the specified output indicators while ensuring the specified optimization criterion.

Results. The use of dynamic optimization methods involves setting a mathematical model of the optimized refinement process in the form of a system of differential equations describing the change in the process state variables depending on the factors that influence it.

Application of the Pontryagin maximum principle allows you to find a solution with simpler actions and in a more convenient form. After setting the task of optimizing the technological process of fine-tuning, we determine the system of differential equations describing the process, write down the optimization criterion. We compose the Hamilton function and solve the optimization problem.

Practical significance. The result of the solution is to find the process control variables in the form of time functions.

Pages: 13-21
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Date of receipt: 20 января 2020 г.