An Efficient Measure for Quantification of Nonlinearity in Chemical Engineering Processes Based on I/O Steady-State Loci

Abstract

Nonlinearity is virtually ubiquitous in chemical engineering plants, and assessing the degree of nonlinearity involved in a process is of special interest for process control purposes. In this paper, we introduce a simple nonlinearity measure to quantify the extent of nonlinearity in a dynamic system based on its normalized steady-state input/output loci. Our nonlinearity measure obviates the limitations of previous metrics in terms of computational effort and correct identification of highly nonlinear relationships. The measure is satisfactorily applicable to various I/O relationships—from truly linear to sinusoidal, for instance. In order to illustrate the efficiency of the proposed measure, four numerical examples concerning a double-effect evaporator, a jacketed continuously stirred tank reactor (CSTR) with an irreversible reaction, a CSTR involving van de Vusse reactions, and the Henson–Seborg–Pottmann CSTR are presented.

Keywords:

• Continuously stirred tank reactor (CSTR)
• Linear process control
• Nonlinearity measure
• System analysis

Acknowledgments

We are obliged to the editor and reviewers of the CECJ for their valuable comments. Also, we sincerely thank Prof. Randolph Rach of the George Adomian Center for Applied Mathematics in Hartford, Michigan, who helped us improve English language usage in the article.