An input linearized powertrain model for the optimal control of hybrid electric vehicles

Models of hybrid powertrains are used to establish the best combination of conventional engine power and electric motor power for the current driving situation. The model is characteristic for having two control inputs and one output constraint: the total torque should be equal to the torque requested by the driver. To eliminate the constraint, several alternative formulations are used, considering engine power or motor power or even the ratio between them as a single control input. From this input and the constraint, both power levels can be deduced. There are different popular choices for this one control input.

This paper presents a novel model based on an input linearizing transformation. It is demonstrably superior to alternative model forms, in that the core dynamics of the model (battery state of energy) are linear, and the non-linearities of the model are pushed into the inputs and outputs in a Wiener/Hammerstein form. The output non-linearities can be approximated using a quadratic model, which creates a problem in the linear-quadratic framework. This facilitates the direct application of linear control approaches such as LQR control, predictive control, or Model Predictive Control (MPC).

The paper demonstrates the approach using the ELectrified Vehicle library for sImulation and Optimization (ELVIO). It is an open-source MATLAB/Simulink library designed for the quick and easy simulation and optimization of different powertrain and drivetrain architectures. It follows a modelling methodology that combines backward-facing and forward-facing signal path, which means that no driver model is required. The results show that the approximated solution provides a performance that is very close to the solution of the original problem except for extreme parts of the operating range (in which case the solution tends to be driven by constraints anyway).