On globally linearising control about singular points

Globally linearising control (GLC) was first proposed by Kravaris-Chung (1987) and is the method upon which this paper is focused. It uses explicit differential geometric techniques to produce a linear relationship between the process output and manipulated input. The linearising transformation of GLC involves inherent process model inversion. Thus, in common with other model based control schemes, its stability depends on the existence of a well defined and stable inverse. Hirschom (1979) gave necessary and sufficient conditions for the existence of such an inverse, and introduced the concept of relative order which can be used to characterise nonlinear system structure. The stability of the process inverse, and hence the success of the GLC technique, requires globally defined relative order and stable zero dynamics, which many real chemical processes do not possess. Where local anomalies in the relative order occur, a singular point will arise. In this paper, the problem of singularities is examined: how the GLC behaves at such points and whether a practical solution to the problem exists