An Applicable Control-Relevant Method for Nonlinearity Assessment using Gap Metric

In this paper, an applicable control-relevant nonlinearity assessment method is proposed for nonlinear dynamic systems. In this method, nonlinear system is decomposed to a bank of linear systems using gap metric, a smart tool for measuring the distance between two linear systems. Then, the ability of each local linear model is investigated to stabilize all linear models. A criterion is proposed to measure the nonlinearity of nonlinear system based on gap metric and maximum stability margin values which bounded between 0 and 1. Unlike most of the current nonlinearity measurement, the proposed method could be used for both integrating and unstable nonlinear systems. Besides, the presented method supplies to distinguish that a single linear controller is adequate to control the nonlinear system or it is necessary to employ the multi-model based controllers design methods. Therefore, the redundancy problem could be avoided by employing the proposed method. A nonlinear Continues Stirred Reactor Tank (CSTR) process is studied that the results confirm the capability of presented nonlinearity assessment method..