Sliding Mode Observer Design With Emphasis on Vehicle Dynamics Applications

The use of sliding mode observers has been proposed by many authors for state estimation in nonlinear dynamic systems. However most of the hitherto proposed schemes are somewhat limited in their applicability, in that, these schemes do not assure convergence of the observer state to the system states for nonlinear systems whose inputs do not satisfy a rather restrictive set of assumptions. This paper proposes a sliding mode observer design scheme that extends an earlier design to nonlinear systems with inputs, under the assumption that the derivatives of the inputs are known. The paper proves that the observer error can be made to converge to zero in a finite time interval (arbitrarily determinable by proper choice of the observer gains). An application of the observer to state estimation for an automobile steering control system is presented. A bicycle model of the vehicle is used. The model reproduces the in-plane motions (longitudinal velocity, lateral velocity and yaw rate) of the vehicle. The proposed observer design is implemented to estimate the states of this model and also estimate the tire cornering stiffness parameter. This parameter estimation greatly enhances the robustness of the observer since the cornering stiffness exhibits considerable variability depending on tire and road conditions, and this variation if left unaccounted for will introduce large errors in the state estimates. The observer design is validated using simulation and work is currently in progress on experimental implementation on-board an automobile at the Transportation Research Center of Ohio.