An Efficient Algorithm for Nonlinear Model Predictive Control of Large-Scale Systems Part I: Description of the Method Ein effizienter Algorithmus für die nichtlineare prädiktive Regelung großer Systeme Teil I: Methodenbeschreibung

The work at hand consists of two parts: In Part I appearing in this issue, we present an efficient state-of-the-art algorithm for online optimization in nonlinear model predictive control (NMPC), the so called real-time iteration scheme; in Part II, which will appear in the next issue, we give an experimental proof-of-concept of the method, by presenting results obtained at a pilot-scale distillation column, where reoptimized controls are delivered every 20 seconds, employing a stiff differential-algebraic optimization model with more than 200 system states. The efficiency of the approach that is based on the direct multiple shooting method is due to a special initialization technique, the so called initial value embedding, which enables an optimal transition from one optimization problem to the next one. This allows to intertwine the optimization iterations with the process development in a way that only one iteration needs to be performed per sampling time, and the iterates nevertheless stay close to the respective optimal nonlinear solutions. A main advantage of the algorithm lies in the fact that nonlinear first principle system models – which are often developed anyway for process analysis and design – can be reused in a straightforward way for control purposes, even if they are large-scale.