Control barrier function based dynamic flexibility analysis in infinite time domain for industrial processes

Abstract

Dynamic flexibility analysis is a powerful tool for validating the operational feasibility of dynamic processes under a range of uncertainties, including model parameters and process variables. Furthermore, it indicates the maximum feasible operating space and can be utilized to enhance both process and controller design, which has the potential to be integrated for the purpose of ensuring process operational safety. However, traditional dynamic flexibility analysis relies on discretizing the differential equations of process models, rendering it unfeasible for complex processes or extended time domains. In this article, we propose a formulation of extended dynamic flexibility analysis based on control barrier functions, which is applicable to infinite time domains and capable of validating a set of initial states rather than a single initial point. We also develop a corresponding algorithm for resolution and discuss various methods for simplifying the primal problem to improve computational efficiency. Two case studies are presented to demonstrate the effectiveness of the proposed extended dynamic flexibility analysis, which indicates the maximum feasible region of uncertainties while synthesizing the corresponding safety controller, as well as the feasibility of the resolution procedure.