Nonlinear Measure for Nonlinear Dynamic Processes Using Convergence Area: Typical Case Studies

Abstract

Several industrial chemical processes exhibit severe nonlinearity. This paper addresses the computational and nonlinear issues occurring in many typical industrial problems in aspects of its stability, strength of nonlinearity, and input output dynamics. In this article, initially, a prospective investigation is conducted on various nonlinear processes through phase portrait analysis to understand their stability status at different initial conditions about the vicinity of the operating point of the process. To estimate the degree of nonlinearity, for input perturbations from its nominal value, a novel nonlinear measure Δ0 is put forward that anticipates on the converging area between the nonlinear and their linearized responses. The nonlinearity strength is fixed between 0 and 1 to classify processes to be mild, medium, or highly nonlinear. The most suitable operating point, for which the system remains asymptotically stable, is clearly identified from the phase portrait. The metric Δ0 can be contemplated as a promising tool to measure the nonlinearity of Industrial case studies at different linear approximations. Numerical simulations are executed in matlab to compute Δ0, which conveys that the nonlinear dynamics of each industrial example is very sensitive to input perturbations at different linear approximations. In addition to the identified metric, nonlinear lemmas are framed to select appropriate control schemes for the processes based on its numerical value of nonlinearity.