Vehicle Dynamic and Control of Constrained Multi-Actuation Systems at the Limits of Handling

Abstract

With recent advances in electric vehicles, having electric motors directly driving the wheels is gaining attraction. When a vehicle is equipped with four independent electric hub motors or independently controlled brakes in each of the four wheels, it gives the control designers the option of controlling each wheel independently in real-time. Independent torque distribution enables developing optimal torque distribution systems for various objective functions. A good example of the benefits of an independent torque distribution strategy is the ability to maximize the vehicle's lateral grip. When a vehicle is operated at the friction handling limits, optimizing the lateral grip will maximize the vehicle maneuverability resulting in reduced vehicle’s oversteer or understeer behavior. Vehicle dynamics at the limits of handling is highly nonlinear, and hence, detailed dynamic analysis is necessary to understand the behavior of the vehicle. In this dissertation, the equations of motion of a vehicle driven on a road with the bank and grade angles are derived. The effect of these angles on the nonlinear vehicle dynamic model is studied and compared with a high-fidelity CarSim model for evaluation. A comprehensive dynamic analysis, based on the phase portrait method, is performed to investigate the effect of axle torque distribution on the stability of the vehicle dynamics. Inspired by the dynamic square method, an optimal torque distribution method is studied with the objective of maximizing the vehicle's lateral grip while the vehicle remains at its friction handling limit is developed. An optimal torque distribution algorithm is then developed in the form of a feedforward controller for two different configurations, one for the axial torque distribution and one for the corner torque distribution. The controllers are evaluated through simulation and experimental studies and results show improvement in both maneuverability and stability when the vehicle is operated at the handling limits. The new optimal actuation strategy is extended to controller design for performance vehicles equipped with active aerodynamic systems. Active aerodynamic systems are one of the few actuators capable of increasing normal loads acting on the wheels. Increasing the wheels' normal loads would result into higher tire-ground forces, hence providing higher brake/drive torque inputs. A control platform consists of a feedforward controller and a constrained feedback model predictive controller (MPC) is developed for such performance vehicles equipped with a front and rear active aerodynamic system. The objective function of the feedback MPC is for the yaw tracking, while the objective of the feedforward controller is to maximize the vehicle lateral grip. This new controller will optimize the active aerodynamic actuation system to maximize vehicle performance and maneuverability. The controller provides the optimal angle of attack for each aero surface so that the yaw tracking error be minimized. The controller has been evaluated in the CarSim simulation environment. Subsequently, the optimal torque distribution and the active aerodynamic controller are integrated into the form of a constrained multi-actuation model predictive control structure. The actuators of this control system are the four in-wheel independent electric motors and the two active aerodynamic surfaces at the front and rear of the vehicle. The control structure has constraints on the vehicle states, input amplitudes, and the input increments. The objective of the controller is to stabilize the vehicle while minimizing the yaw tracking error. A constraint adjustment module is designed to observe the actuators' constraints. This module prevents any excessive actuation command by adjusting the input constraints. This will minimize the cost and energy and reduce the computational time of the optimization solver by deactivating unnecessary actuators. The proposed multi-actuation controller is simulated and verified on CarSim and the obtained results are presented with detailed explanations.