First Order Type Models for Multivariable Process Control

It is well known in classical feedback control that many high order linear time-invariant systems can be approximated, for the purpose of feedback design, by a low order state-space model due to the presence of approximately cancelling poles and zeros in the system transfer function. The paper presents an equivalent technique in the case of a multi-variable system described by a strictly proper mxm, minimum-phase and invertible transfer function matrix G (s) by the application of the contraction mapping theorem. It is shown that, in many cases of practical interest, a multi-variable first-order type model is adequate for the purposes of control system design and that such a model can be determined directly from transient response data or, equivalently, by the analysis of the high and low frequency characteristics of the system. The application of the technique is illustrated by the analysis of a high order binary distillation column model and the dynamics of a counter-flow heat exchanger.