Robust Optimization of Index-2 Differential Algebraic Equations with Guaranteed Stability under Parametric Uncertainty: Application to a Reactor–Separator–Recycle Process

Abstract

In this article, we propose a method for steady-state optimal design of index-2 differential algebraic systems under parametric uncertainty. We use the matrix pencil to evaluate directly the stability of index-2 differential algebraic equations and formulate stability constraints using the Routh–Hurwitz test. The underlying mathematical problem is difficult to solve because it involves infinite stability constraints. We developed an algorithm where an infinite number of constraints can be implemented as several relaxation problems that are solved iteratively. Additionally, the simulation result under parametric uncertainty is used to estimate the bound of the state perturbations rather than assumptions based on experience that may lead to overly conservative or not implementable designs. To illustrate the method, we apply it to a reactor–separator–recycle process and obtain the robustly stable design.