Investigation of the stability of an automatic system for regulating the flow rate of reflux in a stabilization column in the process of catalytic reforming

Authors: Dzhambekov A. M., Dmitrievskiy B. S., Terehova A. A.

Annotation: It is proposed to take into account the influence of uncontrolled disturbances on the regulation of irrigation flow into the stabilization column of the catalytic reforming unit catalyst stabilization unit by changing the coefficients of the polynomial of the denominator of the transfer function of the automatic irrigation flow control system based on a probabilistic approach to robust stability. To study the robust stability of the automatic irrigation flow control system in the stabilization column, a typical scheme of the regulation system is considered. To describe the problem, a general view of the denominator polynomial of the transfer function of an automatic irrigation flow control system in a stabilization column is obtained. For the robust stability of the automatic irrigation flow control system in the stabilization column under the influence of disturbances, the task of estimating the probability of stability of the family of polynomials of the denominator of the transfer function of the automatic control system is set. A family of polynomials of the denominator of the transfer function of an automatic irrigation flow control system in a stabilization column with uncertainty parameters varying in a cube is considered. The problem of estimating the probability of stability of a family of polynomials of the denominator of the transfer function of an automatic irrigation flow control system in a stabilization column is reduced to solving problems: sample generation and probability estimation by frequency. To assess the probability of stability of the family of polynomials of the denominator of the transfer function of the automatic irrigation flow control system in the stabilization column, four polynomials, including the nominal one, are given. Based on generating a sample of one hundred independent random variables, calculating the corresponding polynomials and checking their stability, the considered family of polynomials of the denominator of the transfer function of the automatic irrigation flow control system in the stabilization column has stability with a probability close to unity.

Keywords: catalytic reforming, catalyst stabilization, automatic control system, family of polynomials, nominal polynomial, robust stability, uncertainty set