Empowering the Performance of Advanced NMPC by Multiparametric Programming—An Application to a PEM Fuel Cell System

Model-Predictive-Control-Based Reference Governor for Fuel Cells in Automotive Application Compared with Performance from a Real Vehicle

In this paper, a real-time capable reference governor superordinate model predictive controller (RG-MPC) is developed for fuel cell (FC) control suitable for automotive application. The RG-MPC provides reference trajectories for the subordinate proportional-integral (PI) controllers, which act directly on the FC system. Antiwindup and decoupling schemes, which are common problems in multivariable PI control, are unnecessary, given that the RG-MPC can inherently consider constraints and multivariable systems. The PI dynamics are incorporated into the prediction model used for control, ensuring the feasibility of the provided references for the PI controllers. The successive linearization technique is used in the RG-MPC to cope with the model’s nonlinear nature in real-time. The concept has been illustrated in a simulation scenario featuring efficient and safe power control of an FC stack in automotive application using real driving data obtained from an in-house-built FC vehicle. This work is the first step towards upgrading an existing, PI-based control scheme without the necessity of completely rebuilding the interface.

Multiparametric Programming in Process Systems Engineering: Recent Developments and Path Forward

The inevitable presence of uncertain parameters in critical applications of process optimization can lead to undesirable or infeasible solutions. For this reason, optimization under parametric uncertainty was, and continues to be a core area of research within Process Systems Engineering. Multiparametric programming is a strategy that offers a holistic perspective for the solution of this class of mathematical programming problems. Specifically, multiparametric programming theory enables the derivation of the optimal solution as a function of the uncertain parameters, explicitly revealing the impact of uncertainty in optimal decision-making. By taking advantage of such a relationship, new breakthroughs in the solution of challenging formulations with uncertainty have been created. Apart from that, researchers have utilized multiparametric programming techniques to solve deterministic classes of problems, by treating specific elements of the optimization program as uncertain parameters. In the past years, there has been a significant number of publications in the literature involving multiparametric programming. The present review article covers recent theoretical, algorithmic, and application developments in multiparametric programming. Additionally, several areas for potential contributions in this field are discussed, highlighting the benefits of multiparametric programming in future research efforts.