Fuzzy observer for detection of impending vehicle rollover with road bank angle considerations

The lateral vehicle rollover represents a significant part of vehicle accidents. Driver assistance systems, previously only intended for yaw stabilization, are now being extended to incorporate rollover mitigation via braking. Preventing this kind of accident requires the knowledge of the rollover index which depends on the vehicle dynamic states and other parameters. In this paper we estimate vehicle dynamic states in presence of the road bank angle as disturbance in the vehicle model. Roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. The used nonlinear model deduced from the vehicle lateral and roll dynamics is represented by a Takagi-Sugeno (T-S) fuzzy model. The proposed observer is designed with unmeasurable premise variables. Stability conditions of such observers are given in terms of Linear Matrix Inequalities (LMI). The estimated states and computed rollover index are illustrated through simulation results.