Constrained Optimization of Energy Management for a Mild-Hybrid Vehicle

Abstract

-Optimisation sous contraintes de la répartition d'énergie d'un véhicule de type microhybride-Les véhicules hybrides constituent l'une des technologies les plus prometteuses pour réduire la consommation de carburant et les émissions de polluant. Le travail présenté est basé sur une architecture de type micro-hybride. Le véhicule complet est modélisé sous AMESim, la consommation de carburant pour un cycle défini étant ensuite calculée. Le contrôle de la répartition d'énergie entre les deux sources de puissance est optimisé par rapport à la consommation de carburant, à l'aide d'un algorithme de programmation dynamique (DP). Nous proposons par la suite une autre méthode basée sur le Principe du Minimum de Pontryagin, qui fournit des résultats très proches de ceux de (DP) en un temps de calcul plus faible. Les résultats d'optimisation fournissent la loi de contrôle optimale à partir de laquelle peuvent être dérivées des lois de contrôle implémentables sur véhicule. Différentes tailles de batterie / moteur électriques sont testés, ainsi que différents types de moteur thermique, afin d'évaluer le gain en consommation.

Comparative Study of Dynamic Programming and Pontryagin’s Minimum Principle on Energy Management for a Parallel Hybrid Electric Vehicle

“…To remedy this problem, the stochastic dynamic programming (SDP) method [9][10][11] and the driving pattern detection within multiple driving cycles [12] had been suggested as the possible solutions. As a general case of the Euler-Lagrange equation, Pontryagin's minimum principle (PMP) was also introduced to obtain optimal control solution for hybrid vehicles [13][14][15][16], where the Hamiltonian is considered as an analytical function. Based on the theoretical backgrounds of PMP, the equivalent consumption minimization strategy (ECMS) [17][18][19] was proposed to associate the electrical energy usage with future fuel consumption, and the equivalent fuel consumption is minimized at each time instant.…”

Optimal Control of Hybrid Electric Vehicles Based on Pontryagin's Minimum Principle

“…Therefore, the control based on PMP can be considered as inferior to the (globally optimal) control based on DP. On the other hand, DP requires more computing time than PMP because DP solves all possible optimal controls to fill the optimal field [11]. Since DP is a numerical representation of the HJB equation, DP needs a similar computation load as the HJB equation, which solves a partial differential equation (PDE), whereas PMP solves just nonlinear second-order differential equations.…”

“…Real-time applications of ECMS were suggested in [9], [10]. As a general case of the Euler-Lagrange equation, Pontryagin's minimum principle (PMP) was also introduced as an optimal control solution [11], [12], [13], wherein the Hamiltonian is considered as a mathematical function. In this paper, we show that the Hamiltonian can be calculated from numerical models and further, prove that the control concept based on PMP can be a global optimal solution under reasonable assumptions.…”

Towards a Friendly Energy Management Strategy for Hybrid Electric Vehicles with Respect to Pollution, Battery and Drivability

“…In a hybrid electric vehicle, the torque split (the ratio between electrical and thermal torque) makes it possible to minimize fuel consumption and, hence, CO 2 emissions over the whole driving cycle. Most of the time, energy optimization in hybrid vehicles consists in minimizing the fuel consumption [1,2]:…”

“…where Φ x(t f ) is a penalty function, which can be chosen to maintain the state of charge x(t f ) = x(t 0 ) [2,3]. Moreover, since the battery state of charge x is directly impacted by the chosen control, it is necessary to respect its dynamics:ẋ = f (x, u) It is possible to add constraints to the energy management strategy, such as pollutant emission [4,5], engine events [6] or gear events [6,7], and this is what we will show in this paper.…”