Wheel forces estimation via adaptive sub-optimal second order sliding mode observers

In this work a system for the estimation of the forces (both longitudinal and lateral) exerted between the tires and the road is presented. Starting from two of the most commonly used descriptions of the vehicle dynamics, the single-corner and the single-track models, a system composed of Sub-Optimal Second Order Sliding Mode observers in a cascade structure plus an adaptive element is developed and verified to be effective in conditions in which the effect of the weight transfer can be neglected. One notable property of this approach is that only standard sensors, which are present in most of the stock cars, are exploited. The practical implementation is done using a switched/time-based adaptation law for the gains of the observers, in order to be able to track the quantities in a wide range of conditions while keeping the chattering low. Simulation results are presented in IPG Car-Maker.