Model Approximation for Dead-Time Recycling Systems

Abstract

Chemical processes with recycling commonly contain delays in both the forward and the backward paths. The characteristic equation of such systems is a quasipolynomial function, so that the corresponding transfer function contains an infinite number of poles. This feature precludes the use of classical stability analysis and control design techniques. In this work, a simple and effective methodology to derive an approximate discrete-time model for continuous-time recycling processes with delay is proposed. The method is based on the discretization, via a fictitious sampler and hold device, of the internal delayed signal, resulting in a finite-dimensional discrete-time version of the original continuous model. In this way, standard analysis methods, such as root locus and stability margin techniques, can be easily applied to the approximate model to obtain some conclusions on the stability of the original recycling process. Illustrative examples are used to show that some stability measures (e.g., stability margin) obtained with the approximate discrete-time model closely describe the behavior of the original recycling process.