Nonlinear Reduced-Order Models for Staged Processes with Discrete Legendre Orthogonal Polynomials

Rigorous dynamic tray-by-tray models for multi-stage separation processes are not widely used in industrial practice because of two major difficulties: the high order and the complex nonlinear thermodynamic equations. Especially in areas of identification, control and optimization, there is a definite need for reduced-order models. A new order reduction method, based on Discrete Legendre Orthogonal Polynomials (DLOP´s), is described and applied to a simple distillation column. The DLOP´s are well adapted to the approximation of the concentration profiles, functions of a discrete variable (stage number), and using the GALERKIN weighed residual method yields a uniform approximation error. Both the number of differential equations and the number of nonlinearities to be computed are drastically reduced, the original model structure is preserved and the accuracy is adjustable. The DLOP method compares favourably with other methods, especially concerning the stiffness of the reduced model.