Nonlinear Modeling and Control of Automobiles with Dynamic Wheel-Road Friction and Wheel Torque Inputs
Villella, Matthew G.
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This thesis presents a new nonlinear automobile dynamical model and investigates the possibility of automobile dynamic control with wheel torque utilizing this model. The model has been developed from first principles by applying classical mechanics. Inputs to the model are the four independent wheel torques, while the steer angles at each wheel are specified as independent time-varying signals. In this way, consideration of a variety of steering system architectures, including rear-wheel steer, is possible, and steering introduces time-varying structure into the vehicle model. The frictional contact at the wheel-road interface is modeled by use of the LuGre dynamic friction model. Extensions to the existing two-dimensional LuGre friction model are derived and the steady-state of the friction model is compared to existing static friction models. Simulation results are presented to validate the model mathematics and to explore automobile behavior in a variety of scenarios. Vehicle control with wheel torque is explored using the theory of input-output linearization for multi-input multi-output systems. System relative degree is analyzed and use of steady-state LuGre friction in a control design model is shown to give rise to relative degree singularities when no wheel slip occurs. Dynamic LuGre friction does not cause such singularities, but instead has an ill-defined nature under the same no-slip condition. A method for treating this ill-defined condition is developed, leading to the potential for the system to have relative degree. Longitudinal velocity control and combined longitudinal and angular vehicle velocity control are demonstrated in simulation using input-output linearization, and are shown to produce improved vehicle response as compared to the open-loop behavior of the automobile. Robustness of the longitudinal velocity control to friction model parameter variation is explored and little impact to the controller's ability to track the desired trajectory is observed.