Clutch to clutch shift control technology, which is the key enabler for a compact and low cost transmission design, is important for both automatic and hybrid transmissions. To ensure a smooth clutch to clutch shift, precise synchronization between the on-coming and off-going clutches is critical. This further requires the on-coming clutch to be filled and ready for engagement at the predetermined time. Due to the compact design, currently there is no pressure sensor inside the clutch chamber, and therefore the clutch fill can only be controlled in an open loop fashion. The traditional clutch fill approach, by which the clutch fill input pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak flow demand during clutch fill. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model, which captures the key dynamics in the clutch fill process, is constructed and analyzed. Second, the applicability of the conventional numerical dynamic programming (DP) method to the clutch fill control problem, which has a stiff dynamic model, is explored and shown to be ineffective. Thus, we proposed a customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. The customized DP method not only reduces the computational burden significantly, but also improves the accuracy of the result by eliminating the interpolation errors. To validate the proposed method, a transmission clutch fixture has been designed and built in the laboratory. Both simulation and experimental results demonstrate that the proposed customized DP approach is effective, efficient and robust for solving the clutch fill optimal control problem.
A polyhedral approximation approach to concave numerical dynamic programming
