GRAPHICAL INTERPRETATIONS OF STEADY-STATE INTERACTION MEASURES

The relative gain, the relative disturbance gain, and the singular val ue decomposition are commonly used methods to analyze multivariable li near processes. In this paper, graphical interpretations of these inte raction measures are described, and additional graphical techniques fo r visualizing steady-state process interactions are proposed. For syst ems with two inputs and two outputs, these interaction measures are di rectly related to the angle of intersection and degree of rotation of constant output contours, or, in the case of singular value decomposit ion, constant sums of squares contours. Extensions to larger systems a nd the relative disturbance gain are identified in terms of projection s between one-dimensional subspaces. The relationship between these in teraction measures and measures of association in multivariate statist ical analysis is established. The impact of process nonlinearities on interaction measures is identified graphically as deformations of the constant output norm contours. The use of graphical methods is demonst rated for mixing and high-purity distillation examples.