Nonlinearity measures:: definition, computation and applications

This paper is the first of two papers treating the quantification of open loop nonlinearity of dynamic systems. A generic definition of a nonlinearity measure is presented on the basis of the "best" linear approximation of a nonlinear system. Generalizing an earlier approach of Allgower, the measure can be applied both to the analysis of steady state operating points of continuously operated processes as well as to a trajectory dependent analysis of batch or other transient processes. An approximative computational strategy transferring the original infinite dimensional nested optimization problem into a convex finite dimensional minimization problem is discussed. The applications in this paper focus on operating point dependent analysis. Three continuously operated stirred tank reactor (CSTR) examples are investigated including a benchmark CSTR. The latter is also used to illustrate a computationally efficient lower bound approximation of the proposed nonlinearity measure. The additional difficulties associated with a trajectory rather than an operating point dependent analysis will be discussed in the forthcoming second part of this communication treating transient reaction processes. (C) 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved.