Measurement of nonlinearity in chemical process control systems: The steady state map

Most chemical processes exhibit some degree of nonlinearity, and when selecting an appropriate controller design approach it is important to understand the extent of this nonlinearity. In this paper a quantitative measure of steady-state process nonlinearity is proposed. Drawing from results for nonlinear regression, the curvature is decomposed into tangential and normal components. It is shown that the tangential curvature can be reduced or eliminated by transforming the control inputs, whereas the normal curvature can be reduced or eliminated only by a combination of state feedback and transformations. The problem of scaling is addressed by identifying a ''region of interest'', and scale-independent measures of curvature are proposed. Nonlinearity is measured both as root mean squared curvature and directional curvature. The importance of curvature in the forward and inverse steady-state maps is discussed, and a transformation suggested by the curvature arrays is presented. This transformation reduces the static nonlinearity in the process, and can be used to improve the controller performance. Application of the proposed techniques is illustrated using chemical process examples.