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A Phase Portrait Approach to Vehicle Stabilization and Envelope Control


Loss of control accidents, which lead to thousands of deaths every year in America alone, are often caused by a miscalculated action of the driver or a sudden change in the road surface. Recent years have seen several technologies arise in an attempt to decrease accident rates, one of which is Electronic Stability Control. While ESC is effective at stabilizing the vehicle, it functions without full knowledge of the vehicle states or tire-road coefficient of friction. As more sensors become available and control objectives become more complicated, car designers will need to implement a more holistic control scheme like aircraft envelope control, which integrates multiple sensors and actuators to keep the vehicle within a safe operating regime.

This dissertation outlines two initial building blocks for a full vehicle control system. The first, called Vehicle Envelope Control, stabilizes the car by keeping it within a safe region of the yaw rate-sideslip state space. An analysis of the yaw acceleration isoclines in the yaw rate-sideslip phase plane allows for determination of an envelope boundary that is consistent with the natural system dynamics. The chosen boundary is defined by the yaw acceleration nullcline at the maximum steering angle that results in open loop stable dynamics, and the lines of maximum rear slip angle, which prevent rear tire saturation. The envelope boundaries are enforced by an attractive controller defined by the distance of the vehicle states from the safe boundary. An inner boundary proportional controller provides a soft landing at the yaw rate boundaries by limiting the driver's steering angle to the maximum stable steering angle as the vehicle approaches the boundary. To prove the effectiveness of the controller, Stanford's steer-by-wire vehicle, P1, performs several maneuvers during which the controller must activate to stabilize the car.

The second building block for the full-vehicle control system involves determining and implementing the mechanical changes necessary to enhance estimation of tireroad coefficient of friction and peak lateral tire force. The ability to estimate friction reliably allows for real-time updates to the envelope boundaries, relaxing them as the friction increases, and constraining them as the friction decreases. Isolating the aligning moment, the portion of steer-axis reaction torque from lateral tire forces, gives information on friction; however, there are typically several other torques felt about the steering axis that must be estimated and subtracted out before the aligning moment can be determined. The suggested suspension design eliminates contributions from these other torques, so that the aligning moment is measured directly.

Carrie Bobier
Publication Date
August, 2012