Input-output linearization of an automobile model with 2-D LuGre friction

An automobile model is developed through application of LuGre friction. The two-dimensional LuGre friction model is extended to account for an effect of rotational motion. An algebraic solution for normal force distribution is described, eliminating the need for a dynamic suspension model. The relative velocity norm is approximated to produce a sufficiently smooth design model for input-output linearization. Relative degree is evaluated and singularities lead to reduction from three to two outputs. Well defined relative degree for the two output case is shown to require small friction forces. A control design is presented as well as the zero dynamics of the system. Finally, the controller is simulated and results are presented.