This paper is concerned with the study of combined sizing and energy management algorithms for electric vehicles (EVs) endowed with batteries and supercapacitors (SCs). The main goal is to find the number of cells of each source that minimizes the installation and running costs of the EV, taking into account the performance requirements specified for the vehicle and the technical constraints of the energy sources. To tackle this problem, two methodologies will be investigated. The first considers a filter-based approach to perform the power split among the sources; it will be shown that, under some practical assumptions, the resultant sizing problem can be posed as a linear programming problem and solved using efficient numerical techniques. The second methodology employs an optimal noncausal energy management, which, when integrated with the sizing problem, yields a nonlinear optimization problem. These two methodologies will be then applied to size the storage unit of a small EV. The results indicate that the filter-based approach, although simple and numerically efficient, generally requires an oversized storage unit. Furthermore, it was also concluded that, if the range requirements of the EV are not very high (below 50 km, in our case study), the use of SCs enables energy savings of up to 7.8%.
Spurred by the problem of identifying, in real-time, the adhesion levels between the tyre and the road, a practical, linear parameterisation (LP) model is proposed to represent the tyre friction. Towards that aim, results from the theory of function approximation, together with optimisation techniques, are explored to approximate the non-linear Burckhardt model with a new LP representation. It is shown that, compared with other approximations described in the literature, the proposed LP model is more efficient, that is, it requires a smaller number of parameters, and provides better approximation capabilities. Next, a modified version of the recursive least squares, subject to a set of equality constraints on parameters, is employed to identify the LP in real time. The inclusion of these constraints, arising from the parametric relationships present when the tyre is in free-rolling mode, reduces the variance of the parametric estimation and improves the convergence of the identification algorithm, particularly in situations with low tyre slips. The simulation results obtained with the full-vehicle CarSim model under different road adhesion conditions demonstrate the effectiveness of the proposed LP and the robustness of the friction peak estimation method. Furthermore, the experimental tests, performed with an electric vehicle under low-grip roads, provide further validation of the accuracy and potential of the estimation technique.
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