Optimization of control variables for automated transmission engagement

A back propagation through time-like conjugate gradient-based optimal control algorithm is used to optimize control variable trajectories of an automated automotive transmission for the engagement task. The optimization criterion is to maximize the end vehicle speed and minimize the dissipated clutch energy and the shuffle mode vibration content. The optimization results are obtained for different engagement times using a simple second-order power train model. They give optimal profiles of engine speed and clutch slip speed state variables, which can be used as reference variables of optimal feedback controller. The optimization results are verified by computer simulation using a sixth-order power train model including the halfshaft and clutch compliance effects.