Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

Abstract

Interest in chemical processes that perform well in dynamic environments has led to the development of design methodologies that account for operational aspects of processes, including flexibility, operability, and controllability. In this article, we address the problem of identifying process designs that optimize an economic objective function and are guaranteed to be stable under parametric uncertainties. The underlying mathematical problem is difficult to solve as it involves infinitely many constraints, nonconvexities and multiple local optima. We develop a methodology that embeds robust stability constraints to steady-state process optimization formulations without any a priori bifurcation analysis. We propose a successive row and column generation algorithm to solve the resulting generalized semi-infinite programming problem to global optimality. The proposed methodology allows modeling different levels of robustness, handles uncertainty regions without overestimating them, and works for both unique and multiple steady states. We apply the proposed approach to a number of steady-state optimization problems and obtain the least conservative solutions that guarantee robust stability.

Conservativeness and stability properties in the optimal design of dynamical systems under uncertainty

“…Process systems engineering has recognized the disadvantages of this two-stage approach, including the extensive time it requires and the potential need for redesign, at an early stage. This observation has spurred research efforts aimed at simultaneously designing the process system and its control scheme [5], [6], [7].…”

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

“…On the basis of the ideas of Chang and Sahinidis and Harney et al, we developed a new method to addresses the robust steady-state optimization of index-2 DAE systems under parametric uncertainty. Because the Lyapunov linearization theorem cannot be applied to DAE systems, the matrix pencil and Routh–Hurwitz test are used to formulate the stability constraints.…”

“…Because the Lyapunov linearization theorem cannot be applied to DAE systems, the matrix pencil and Routh–Hurwitz test are used to formulate the stability constraints. Furthermore, Chang and Sahinidis used a bound of states under parametric uncertainty to handle the multiplicity with different stability trends. Since the bound was simply based on the assumption according to the authors’ knowledge, the optimization result may lead to designs that are overly conservative or less robustly stable.…”

“…Particle swarm optimization was used to solve the resulting nonconvex, nondifferentiable optimization problem. Chang and Sahinidis 14 considered parametric uncertainty for the optimal steady state system design ensuring robust stability. They solved the steadystate optimization problems to global optimality as semi-infinite optimization problems, where stability constraints were addressed with Hurwitz's criterion.…”

Robust optimization of periodically operated nonlinear uncertain processes

“…When robustness is addressed with the pseudo-spectral radius or with the smoothed spectral radius it is difficult to consider parametric uncertainty. Chang and Sahinidis (2011) consider parametric uncertainty for optimal steady state solutions and possible extension of the proposed method to oscillating processes. The authors solve semi-infinite programs, where stability constraints are addressed with the Routh-Hurwitz criterion.…”