Bilinear approximations of a nonlinear distributed fixed-bed reactor model

Abstract

Abstract In studies on control of fixed-bed reactors little attention has been given to the problem of controlling a reactor subject to large input disturbances. This paper proposes a new idea for modelling fixed-bed reactors, which is based on a bilinear model instead of a linear one. Two bilinear modelling approaches for fixed-bed reactors are presented, with a typical laboratory-scale plant as an example. The first approach is bilinearization by a systematic method. By lumping via orthogonal collocation and by direct bilinearization around a specified operating state, the detailed highly nonlinear distributed model of the reactor is simplified to a singularly perturbed bilinear model if the input variable occurs multiplicatively. The other approach is bilinearization via a parameter estimation technique. Based on the lumped reactor model with or without multiplicative input low-order bilinear state models are structured, whose states are selected as temperature variables at axial orthogonal collocation points only. The coefficient matrices are determined by means of the recursive parameter estimation algorithm based on block-pulse functions. The reduced bilinear models developed in this paper are shown to be able to approximate the actual reactor transients more accurately than linear ones over a much wider range around the operating state, and thus are very helpful for developing efficient control laws for fixed-bed reactors.