MEASURE OF CLOSED-LOOP NONLINEARITY AND INTERACTION FOR NONLINEAR CHEMICAL PROCESSES

A new approach for assessing nonlinear interaction effects and closed- loop nonlinearity in multivariable processes is presented. It is based on a differential geometric interpretation of the relative gain away that leads naturally to systematic procedures for describing interacti on effects of higher order and for assessing closed-loop nonlinearity effects in nonlinear processes. Two types of nonlinear effects associa ted with the behavior of a process are introduced. Between-channel non linearity is associated with the nonlinear dependence of an output cha nnel on other input-output pairings. Within channel nonlinearity is us ed to identify the nonlinear effects that result from the inherent non linearity of an individual output channel. A root-mean-squared measure of nonlinearity is introduced and is used to evaluate the significanc e of local nonlinear effects. Nonlinear interaction measures are deriv ed that provide tools for assessing input-output pairings in a nonline ar process. This new approach extends the standard techniques and prov ides an estimate of the effect of nonlinearity on closed-loop interact ions.