1st-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 multivariable system described by a strictly proper m × m, 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 multivariable 1st-order-type model is adequate for the purpose 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.