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

Abstract

In the past few years and in many applications, linear feedback control has proved to be adequate for the control of various nonlinear systems. Therefore, before attempting the controller design phase, it is natural to ask, “When is a linear controller adequate for a nonlinear system?” This article provides a new nonlinearity analysis method based on the gap metric and the stability margin that is able to quantify the nonlinearity degree of a system once it has an internal model control controller. The internal model control strategy is used since it provides a direct measure of the discrepancy between outputs from the nonlinear system and its internal model when both are subject to the same controller. It is shown that a feedback loop may exhibit much lower nonlinearity than an open-loop nonlinear system by a careful design of a single linear internal model control controller via the gap metric and stability margin, used as model-based analysis tools for linear time-invariant systems. Both simulations and an experimental validation on a semibatch reactor prove the effectiveness of the proposed method.