Pressure blast melting and blow enrichment with oxygen – process intensifiers or an unfounded tribute to traditions

Abstract

In the paper well-known equations for a Doubly-Fed Machine (DFM) speed observer are taken. The equations are composed for rotor-side control, similar to an adaptive speed observer with a reference model for squirrel-cage induction machines (IM) with stator-side control. In this case, however, the rotor model is taken as the reference model and the stator model serves as the adaptive one. The structure of the adaptation algorithm is determined based on the conditions of Lyapunov’s second stability theorem. The adaptation function is formed using the stator flux linkage vector and is defined as the vector cross product of the stator flux linkage vector estimates obtained from the reference and adaptive systems. To solve the problem of parametric synthesis of the DFM speed observer, an original method is proposed based on the stability analysis of the linearized observer model via its characteristic equation. The parameters of the PI controller derived from the adaptation function are determined based on the stability analysis of the nonlinear observer, using the coefficients of the first-order approximation characteristic equation. An analytical expression for the stability boundary is obtained in the PI controller parameter plane from the algebraic Hurwitz stability criterion, expressed as an inequality for fixed rotor speeds. Asymptotes of the characteristic equation roots are identified as the integral component tends to infinity. Reasonable lower and upper bounds for these parameters are determined based on the rate at which the real parts of the characteristic roots approach the identified asymptotes. The speed observer is proposed to be used together with a rotor angular position identifier, which acts as a calculator based on corresponding formulas. The functionality of the resulting sensorless relay-vector control system for the DFM is verified through mathematical modeling