Automatic transmission (AT) upshift control performance in terms of shift duration and comfort can be improved during the inertia phase by coordinating the off-going clutch together with oncoming clutch and engine torque. The performance improvement is highest in low gear shifts (i.e., for high ratio steps), which are typically performed with open torque converter. In this paper, a discrete-time, linear quadratic regulation (LQR) is applied during the upshift inertia phase, as it provides an optimal multi-input/multi-output control action with respect to the prescribed cost function. The LQR law is based on a reduced-order drivetrain model, which is applicable to actual transmissions characterized by a limited number of available state measurements. The reduced-order model includes the linearized torque converter model. The shift duration is ensured by precise tracking of a linear-like oncoming clutch slip speed reference profile. To facilitate the tracking accuracy, the LQR law is extended by an integral action. A clipped optimal approach is applied to account for the clutch energy passivity. By using a set of differently weighted conflicting criteria in the discrete cost function, including shift duration, comfort, and efficiency, Pareto frontiers are obtained based on post-processing the multi-run simulation results. The Pareto frontiers are compared with benchmark frontiers determined off-line by applying a multi-objective genetic algorithm-based control parameter optimization relying on full-order, nonlinear drivetrain model. It is shown that the LQR approach results in comparable Pareto frontiers to those obtained by multi-objective optimization.
