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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.

New generation of torque converter automatic transmissions (AT) include a large number of gears for improved fuel economy. Control requirements for such transmissions become more demanding, which calls for the development of new shift optimization and analysis tools. This paper presents two contributions to the field of transmission dynamics analysis: (i) bond graph method-based shift transient analysis, and (ii) deriving a unique set of conditions for beneficial use of a third (normally-open) clutch for any upshift or downshift, with emphasis on inertia phase. The derived conditions are examined on an example of 10-speed AT based on the clutch torque input trajectory optimization results. The examination results point out that the extra clutch has a potential of significant performance improvement for any single-transition upshift in the inertia phase, in terms of reduced vehicle jerk RMS value due to the suppressed inertia bump effect.