Nonlinearity measures: definition, computation and applications

Abstract 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.

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