Vehicle yaw rate control based on piecewise affine regions

This paper shows that an active front steering control, that considers the nonlinear behaviour of the tire-road forces, can be designed by parameterizing the vehicle dynamics with respect to the measurable yaw rate and taking into account the steady state behaviour of the vehicle. In order to ensure the tracking of the yaw rate reference signal on the basis of the yaw rate tracking error, despite constant disturbances and parameters uncertainties, the proposed control strategy uses a proportional integral (PI) control, in which the gains depend on the defined parametrized vehicle dynamics. The proposed control system switches depending on the yaw rate as it is a variable measured at low cost. The stability is proved by a piecewise quadratic Lyapunov function using linear matrix inequalities technique. Several simulations, including disturbances rejections and step references, are carried out on a standard nonlinear CarSim D-Class vehicle model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tire forces, pitch, roll and driver dynamics. The simulations confirm that the proposed piecewise linear (PWL) control can greatly improve the vehicle stability and is advantageous in very demanding manoeuvres.