Nonlinearity measures: definition, computation and applications

This paper is the ®rst of two papers treating the quanti®cation of open loop nonlinearity of dynamic systems. A generic de®nition of a nonlinearity measure is presented on the basis of the ``bestʹʹ linear approximation of a nonlinear system. Generalizing an earlier approach of AllgoÈ wer, 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 in®nite dimensional nested optimization problem into a convex ®nite 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 com- putationally ecient lower bound approximation of the proposed nonlinearity measure. The additional diculties associated with a trajectory rather than an operating point dependent analysis will be discussed in the forthcoming second part of this communi- cation treating transient reaction processes.