Optimization of Shift Control Trajectories for Step Gear Automatic Transmissions

New generation of torque converter automatic transmissions (AT) include a large number of gears for improved fuel economy and performance. Control requirements for such a transmission become more demanding, which calls for the development of new shift control optimization tools. A pseudospectral collocation method is used in the paper to optimize AT clutch and engine control trajectories for comfortable and efficient shifts. Since the optimization method requires a smooth formulation of plant model, the emphasized clutch model nonlinearity around the zero slip speed has been found to be a major difficulty to be resolved through proper modeling of the optimization problem. Therefore, different approaches of describing the friction behavior are considered and assessed, starting from simple static models, through dynamics models, towards torque-source approaches subject to the clutch passivity constraint. Apart from the conventional optimization approach based on minimizing the cost function (including the vehicle jerk and clutch energy loss terms), the so-called feasibility approach based on restricting the cost through an inequality constraint is considered, as well. The proposed optimization method has been verified on a characteristic example of 10-speed AT for both single- and double-transition shifts. It has been found out that the clutch passivity constraint-based approach results in numerically most efficient optimizations for a wide range of shift tasks and scenarios.