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 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 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 , 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..

Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

“…The above discussion reveals that there are indigenous number of articles that discuss the concepts of system identification and measurement of nonlinear metric [21] in separate attempts. There exist enumerable identification methods and methods for quantification of nonlinearity.…”

“…Nevertheless, there are several nonlinear indices to mark the value of nonlinearity in the dynamic systems [18][19][20]. The concept of Convergence-area-based-nonlinearity measure (CANM) has been endorsed in the current study [21].…”

Linear controller design approach for nonlinear systems by integrating gap metric and stability margin

“…Therefore, before any attempts at the use of a nonlinear controller, it is often beneficial to verify the adequacy of classical linear control techniques, especially since they have proved to be sufficient for the control of various nonlinear systems. [1][2][3][4] Consequently, there is a need to check the restrictions of linear control performance and quantify the nonlinearity level of a process to determine whether linear control could be sufficient or nonlinear control would be indispensable.…”