Nonlinear optimization of a new polynomial tyre model

Tyre behaviour is strongly nonlinear. This article presents the validation of a new polynomial tyre model with real test data, analysing the convergence properties during the optimization process to calculate the values of the parameters. A multivariate model with 13 parameters is shown, including normal load and camber angle. The article reviews the methods of getting polynomial approximations of the magic formula tyre model used to develop the new polynomial model, the numerical optimization methods which calculate the parameters of the model from real test data, and it explains how the terms of the Jacobian matrix are modified when we impose constraints to the curve; this can be useful to improve the adjustment in some areas of the curve. The convergence properties are shown both for the magic formula tyre model and for this polynomial tyre model. The proposed model presents a fast convergence both in one and in three variables. This is an additional advantage to its excellent analytical properties, and the model is very easy to compute and can be easily derived and integrated. It is very well adapted for real-time computing.