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Industrial Automatic Control Systems and Controllers

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Piecewise-linear Approximation of Self-oscillations in a System of Two-position Temperature Control of the Titanium Process
V.A. Tikhonov, Yu.P. Kirin

The method of piecewise linear approximation of self-oscillations in the system of two-position temperature control of the exothermic reaction zone and heating zones of the industrial titanium reduction apparatus is proposed to solve problems of parametric identifi cation of mathematical models of zones represented by non-stationary control objects. The structures of the mathematical models of zones are assumed to be known and given by differential equations with variable coeffi cients, which consider dynamic parameters and zone perturbations. The exothermic reaction zone and adjacent heating zones of the recovery apparatus are considered as unconnected (autonomous) control objects, the common perturbation of which is the change in the heat of the exothermic reaction caused by the movement of the exothermic reaction to the heating zones. The solution of the problems of parametric identifi cation provides for splitting the working self-oscillating modes of the two-position temperature control of the named zones into a series of individual periods of temperature self-oscillations-identification intervals on which these zones are considered quasi-stationary control objects, during the recovery process at different identifi cation intervals-as a family of quasi-stationary control objects. This approach allows us to describe the dynamics of objects on the intervals of identifi cation by differential equations with constant coeffi cients. This made it possible to replace the initial models of nonstationary
objects of family control with fairly simple stationary models for which systems of fi nite equations were obtained that approximate the self-oscillating modes of on-off temperature control by linear functions on the identifi cation intervals and establish the relationship between the self-oscillation parameters and unknown coeffi cients of the differential equations. By solving systems of fi nite equations, perturbations of control objects were identified and quantitative estimates of heat released in the exothermic reaction zone and heat losses of the heating zone of the recovery apparatus were obtained. As a result of the perturbation analysis, certain regularities of the heat change in these zones are studied, which are necessary for monitoring and optimizing the technological regime of the recovery process when moving the exothermic reaction to the heating zones of the apparatus. It is noted that the proposed method of piecewise linear approximation of self-oscillations makes it possible to conduct operational identifi cation of perturbations of control objects in real time of the recovery process. This method is intended to be used to improve existing control systems and control the process of titanium reduction.
Keywords: titanium recovery; two-position control; auto-oscillations; identifi cation; piecewise linear approximation.

Contacts: E-mail: tihonov1986@yandex.ru, E-mail: klu2010@mail.ru

Pp. 16-26.

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