Analytical solution of vehicle phase-plane equilibria through the Root-Rational tyre model

Passenger vehicle steady-state behaviour has been investigated for a long time. Among the existing methods, the phase portrait is rather popular and useful. However, the computation of vehicle equilibria may only be done numerically. Furthermore, the numerical procedure must be repeated in case of changes in the inputs (e.g. steering angle). This paper proposes a new methodology to obtain an analytical solution of vehicle equilibria. The key is the definition of a new tyre model, denoted as Root-Rational (RR) tyre model, which allows inverting the vehicle dynamics equations in closed form. Using the proposed tyre model reduces the equilibria location problem to finding the roots of a third-order polynomial. After describing the procedure in detail, comparisons are made between the analytical solution and a classical numerical approach, either using the same RR tyre model or a more classical one. Results show great accuracy when locating the equilibria coordinates and a significantly re...