LPV modeling and robust control of yaw and roll modes of road vehicles

Abstract

In this thesis, the usefulness of linear parameter varying (LPV) modeling of vehicle dynamics is investigated for controller synthesis to take nonlinear tire behavior into account. The H infinity control framework is used to design combined active steering and differential controllers to improve vehicle handling during maneuvers involving large driver commanded steering angles. Two approaches are undertaken to reduce the size of the parameter set to minimize solver time during the controller synthesis step. The first approach is built on modeling tire stiffnesses as parametric uncertainties. This leads to a linear fractional transformation (LFT) model of the combined vehicle body and tire subsystems and to the design of a static state feedback controller intended to be robust against large variations in parameters. In the second approach, a rational fit is proposed for the nonlinear tire model used, and original parametric vehicle models are derived by integrating the fitting model into the equations of motion. This leads to the design of gainscheduled LPV controllers where scheduling is based on lateral and longitudinal tire slips. At small driver commanded steering angles, both controllers achieve decoupling of sideslip and yaw rate modes. However, at large driver commanded steering angles, the steering response of the first controller is observed to be unstable at the physical limit of the vehicle due to the shortcomings of the parametric uncertainty model in predicting tire behavior at large lateral slip. Meanwhile, the second controller achieves decoupling of all vehicle modes for the whole range of driver commanded steering angles up to and at the physical limit of the vehicle, revealing the importance of incorporating the tire friction circle concept into the controller synthesis.