Lime Recovery Process Mathematical Model and Synthesis of Automatic Control System

Abstract

Lime required for the liquor causticizing process is obtained by way of recovering the lime sludge in rotary furnaces. By analysing the physical and chemical processes that come about in a lime recovery furnace a mathematical model of the object was developed comprising a system of non-linear differential equations in partial derivatives of the 1st order. To ensure steady-state operational conditions for the furnace a boundary-value problem algorithm for the system of conventional non-linear differential equations had been worked out to be solved by the application of a digital computer. Static characteristics of the object were studied and the linearization of the equations was carried out. The linear differential equations of the partial derivatives were reduced to a system of conventional differential equation combining the variables at the integration interval boundaries. This has been achieved by the approximated length integration and with the help of the Ermit interpolation polynomicals. The dynamics of the object is investigated by the series development of the transition functions with reference to the moments of the impulse transfer function. Therewith an algorithm was suggested for obtaining the impulse transfer function moments directly from the system of differential equations without the application of complicated transfer function. The synthesis of the open and closed part of the combined automatic control system is accomplished with regard to the impulse transfer function moments of the multiple-bound object.