Multistage Time-Optimal Control for Synchronization Process in Electric-Driven Mechanical Transmission With Angle Alignment Considering Torque Response Process

The synchronization process takes up almost one half of the time of the gear-shifting process, and also influences the impacts between the sleeve and the gear ring. To avoid impacts and reduce time duration, a time-optimal control strategy with angle alignment is necessary for the synchronization process. Moreover, to be better accord with practice, the motor torque response process should be taken into account. The parameters in the torque response process depend on control commands, which makes the control problem a multistage one. To solve these issues, a rule-based control strategy is extracted from the dynamic programming (DP) solution of the multistage time-optimal control problem. To obtain this strategy, the dynamic model for the synchronization process with a modified Sigmoid model to precisely depict the torque response process is first solved. Then, the control problem is formulated as a multistage time-optimal control problem with three states and solved by DP. Based on the DP results, a three-stage and a four-stage rule-based control strategies are extracted for normal operation situation and startup situation, respectively. Finally, through comparative studies, the proposed rule-based control strategy can eliminate the speed difference and angle difference simultaneously with almost the same time of the bang–bang control, while the bang–bang control cannot obtain the zero terminals. Moreover, the proposed control strategy only takes 20 ms more than the pure speed synchronization control in the worst case. It would decrease when the initial speed difference increases.