Functional switched H∞ Proportional Integral observer applied for road bank and vehicle roll angles estimation

The estimation problem of the road bank angle and the roll vehicle angle is presented in this work. These angles play an important role for the vehicle stability and the Vehicle Dynamic Control (VDC). However, the estimation of these angles requires a global vehicle model; unfortunately, the requirements related to the knowledge of the vehicle model are difficult to satisfy, this is due to the uncertainties which affect the parameters of the vehicle model, for example, the longitudinal speed that changes the values of the vehicle model parameters, the front and rear cornering stiffnesses. In order to overcome all these constraints on the knowledge of the vehicle model, a switched proportional integral H
_∞
observer is proposed. This observer is designed using non-increasing condition applied on the Lyapunov functions. Sufficient conditions of global convergence of this observer are presented and proved. All these conditions are expressed in term of the linear matrix inequality (LMI). An experimental validation shows the ability of the SPIH
_∞
observer to estimate simultaneously the banking angle and vehicle dynamics parameters.