MEASUREMENT OF NONLINEARITY IN CHEMICAL PROCESS CONTROL By

A framework for the assessment of nonlinearity in controlled processes is developed. Assuming that the process can be represented by a twice differentiable process map, the extent of nonlinearity is measured by evaluating the induced local curvature of the process response. The magnitude of this curvature is assessed with respect to an appropriately chosen scaling region. This approach provides an effective methodology for the development of dimensionless curvature measures that can be used to characterize and quantify the nonlinear behaviour of steady-state and dynamic controlled processes. The impact of steady-state curvature on controller performance is studied using a bioreactor example. A potential application of the measure of dynamic nonlinearity to chemical processes is demonstrated. First and second order sensitivity equations of the output with respect to the inputs are used to evaluate the nonlinearity measures for continuous and batch chemical processes. Using classical differential geometrical tools, a set of second order identities related to the invertibility of the nonlinear process are developed. Their geometrical interpretation provides a fundamental definition and a new interpretation of the RGA. Application of the identities to the assessment of higher order interaction is shown to be very similar to the analysis of the linear RGA. Higher interaction tables are constructed to measure the contributions of the nonlinear terms to interaction in a closed-loop process. An analysis of exact linearization of control systems by state-feedback and coordinate transformations is presented. The Gardner and Shadwick (GS) algorithm is used to uncover obstructions to linearizability of classes of models. This provides a systematic way of choosing