Reviewing control allocation using quadratic programming for motion control and power coordination of battery electric vehicles

This paper evaluates the performance of control allocation (CA) problem formulations for battery electric vehicles. Optimisation-based CA formulations such as mixed optimisation, power loss minimisation and their various configurations are solved as a constrained quadratic programming (QP) problem. Metrics such as the numerical error of the solution, the condition number of the hessian matrix and energy efficiency associated with the solution obtained for the QP formulation are used to analyse the problem formulations with three decision variables. For the mixed optimisation formulation, these metrics aid in tuning the weighting term and actuator priority matrix parameters. The sensitivity of the solution due to the weighting term in the the mixed optimisation formulation is avoided by explicitly setting an equality constraint for the motion control. Additionally, implementing motion control requests as equality constraints, avoids the need of tuning the parameters and leads to the formulation as a pure power loss minimisation problem. Finally, it is also shown that the actuator coordination is not sensitive to the normalisation of the virtual control request and actuator capabilities.