Understanding Model Predictive Control part1
- Learning-Based Model Predictive Control for the Energy Management of Hybrid Electric Vehicles Including Driving Mode Decisions(arXiv)
Author : David Theodor Machacek, Stijn van Dooren, Thomas Huber, Christopher Onder
Abstract : This paper presents an online-capable controller for the energy management system of a parallel hybrid electric vehicle based on model predictive control. Its task is to minimize the vehicle’s fuel consumption along a predicted driving mission by calculating the distribution of the driver’s power request between the electrical and the combustive part of the powertrain, and by choosing the driving mode, which depends on the vehicle’s clutch state. The inclusion of the clutch state in a model predictive control structure is not trivial because the underlying optimization problem becomes a mixed-integer program as a consequence. Using Pontryagin’s Minimum Principle and a simplified vehicle model, it is possible to prove that a drive cycle-dependent critical power request Pcrit exists, which uniquely separates the optimal driving mode. Based on this result, a learning algorithm is proposed to determine Pcrit during the operation of the vehicle. The learning algorithm is incorporated into a multi-level controller structure and the working principle of the resulting multi-level learning-based model predictive controller is analyzed in detail using two realistic driving missions. A comparison to the solution obtained by Dynamic Programming reveals that the proposed controller achieves close-to-optimal performance.
2. A map-based model predictive control approach for train operation(arXiv)
Author : Michael Hauck, Patrick Schmidt, Alexander Kobelski, Stefan Streif
Abstract : Trains are a corner stone of public transport and play an important role in daily life. A challenging task in train operation is to avoid skidding and sliding during fast changes of traction conditions, which can, for example, occur due to changing weather conditions, crossings, tunnels or forest entries. The latter depends on local track conditions and can be recorded in a map together with other location-dependent information like speed limits and inclination. In this paper, a model predictive control (MPC) approach is developed. Thanks to the knowledge of future changes of traction conditions, the approach is able to avoid short-term skidding and sliding even under fast changes of traction conditions. In a first step, an optimal reference trajectory is determined by a multiple-shooting approach. In a second step, the reference trajectory is tracked by an MPC setup. The developed method is simulated along a track with fast-changing traction conditions for different scenarios, like changing weather conditions and unexpected delays. In all cases, skidding and sliding is avoided
