Modeling of chemical reactor dynamics by nonlinear principal components

The modelling of nonisothermal continuous stirred chemical reactor dynamics by linear and nonlinear principal components methods is investigated. The derived models are analysed with respect of their ability to predict the existence of the reactor multiple steady states and their use for adaptive on-line process control. The time evolution of the state variables is approximated by a single-step finite difference prediction equation. Nonlinear principal components are determined by a feedforward neural network with a single hidden layer. Input and output patterns are jointly projected to a two dimensional surface yielding an implicit process model. The ability of implicit models to predict controlled and manipulative variables without the need for separate model development for the direct and inverse models makes them ideally applicable in adaptive internal model control loops. The model correctly predicts the existence of three steady states and provides an excellent fit to untrained samples of patterns under various dynamic conditions. The linear models based on a partial least squares algorithm can correctly model behaviour under unsteady conditions, but they fail to predict multiple steady states in chemical reacting systems. Since accurate model of steady-state properties is essential for process control, linear principal component models are inadequate when multiple steady states exist.