Measure of closed‐loop nonlinearity and interaction for nonlinear chemical processes

Abstract 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 array that leads naturally to systematic procedures for describing interaction effects of higher order and for assessing closed‐loop nonlinearity effects in nonlinear processes. Two types of nonlinear effects associated with the behavior of a process are introduced. Between‐channel nonlinearity is associated with the nonlinear dependence of an output channel on other input ‐ output pairings. Withinchannel nonlinearity is used to identify the nonlinear effects that result from the inherent nonlinearity of an individual output channel. A root‐mean‐squared measure of nonlinearity is introduced and is used to evaluate the significance of local nonlinear effects. Nonlinear interaction measures are derived that provide tools for assessing input ‐ output pairings in a nonlinear process. This new approach extends the standard techniques and provides an estimate of the effect of nonlinearity on closed‐loop interactions.