Methodology for applying control theory in modeling the processes of centrifugal enrichment of mineral raw materials

ABSTRACT

The article discusses an approach aimed at the formation of a methodology for applying the principles and models used in the automatic control theory in relation to the processes of enrichment of mineral raw materials. The problem solved in the article is posed as follows, try to represent the process of gravitational enrichment, namely centrifugal concentration, in the form of a transfer function and try to find its parameters. The paper proposes an approach to modeling centrifugal concentrators based on transfer functions, using averaged values of output characteristics. Proposal of a mechanism for determining the parameters of transfer functions and their calculation based on experimental data. To check the presented calculations, the MatLAB software tool with the Simulink package was used. As a result, the transfer function of the KC-CVD6 apparatus used in the gold deposit was found and satisfactory results were obtained. The work uses methods of identification of automatic systems, methods of system analysis, as well as methods of mathematical modeling, namely the numerical solution of differential equations, implemented in the MatLAB environment with the Simulink package. A comparison with the classical regression model was made; as a result, the modeling error was reduced by two times. The simulation error for the concentrate yield was less than 1%.

KEYWORDS:

• Gravity beneficiation
• gold centrifugal concentration
• knelson concentrator
• control theory
• transfer function
• differential equations

Disclosure statement

No potential conflict of interest was reported by the author(s).

List of symbols

α - content of the valuable component in the feed;

β - content of the valuable component in the concentrate;

γ - content of the valuable component in the tail;

δ_in - productivity of the apparatus for solid (input);

δ_con - productivity of the apparatus for concentrate (output);

ε(t) - input feed flow;

x_con(t) - concentrate output;

x_tl(t) - tailings output;

G_con(p) - transfer function;

$k$, $k_{ob},k_{con},k_{tl}$ - gain;

$T_1$, $T_{ob},T_{con},T_{tl}$ - time constant;

T – test duration;

q - custom parameter vector;

$\omega (t)$ - weight function;

$m_{x_{con}}(t)$, $m_{\epsilon }(t)$ - mathematical expectations;

$q_1$ - fluidizing water consumption;

$q_2$ - valve opening time.