Numerical Integration for Nonlinear Model Predictive Control of a Fuel Cell System

A two-stage nonlinear model predictive controller for the task of power tracking with a fuel cell system is presented. In the first stage, an economic optimization problem is solved for optimal steady states and inputs, which are tracked in the subsequent stage. For the dynamic tracking using MPC, a nonlinear, stiff ordinary differential equation must be discretized. A numerical study of different integration schemes reveals that the first order implicit Runge-Kutta integration scheme is appropriate for discretization. Compared to a high accuracy numerical integration and the standard explicit Runge-Kutta method of order four, the computation time on embedded hardware can be reduced by more than 30% and 10% respectively without loss in closed-loop cost.