A Computer Aided Design Approach to the Development of Simplified Control Models for Non-Linear Distributed Parameter Processes

Abstract

A method is presented for the generation of simplified models useful in process control applications. The process may comprise e.g. distributed heat and mass transfer phenomena as well as lumped parameter subsystems. Non-linearities represented by continuously differentiable functions of the dependent variables are allowed.The distributed phenomena are approximated by truncated power series in the space variables with time dependant coefficients. These will be used as state variables in the resulting simplified model. The partial differential equations are integrated over a finite number of space regions, meaning that the mass and energy balances are satisfied in average in each region. The procedure will result in a system of ordinary differential equations with time as independent variable. If the original partial differential equations are non-linear (linear) then the simplified system will be non-linear (linear).The method as such has been tested recently in various applications. However, a considerable amount of algebraic work is required, except in very simple applications. A computerized procedure has therefore been developed to generate the coefficient matrices of the ordinary differential equations in a standard format. The basic subroutines can be organized to fit various partial differential equations for arbitrary polynomial degrees.The method is applied to a packed distillation column, a process that is fundamentally non-linear. A low order control model is worked out and examined. Conclusions are drawn regarding the use of the model, e.g. in control system design and for measuring point selection.