Tooth Aligned Control of Shifting Process in a Dedicated Hybrid Transmission

The shifting process of a dedicated hybrid transmission (DHT) can be implemented via motor control to achieve tooth-aligned control (TAC), aiming to attain both ‘zero speed difference’ and ‘zero angle difference’ between the clutch gear and sleeve. TAC not only enables smooth collision-free gear engagement but also enhances drivability. To accomplish TAC with short duration and high precision, a novel model predictive control (MPC) approach based on Pontryagin's minimum principle (PMP-MPC) is proposed. PMP is employed to derive the optimal switching trajectory and reference state for TAC. Upon completing the first trajectory switching, the system enters the vicinity of the reference state. Subsequently, MPC is activated to precisely regulate the system state toward the reference target. MATLAB/Simulink simulations validate the proposed strategy, demonstrating that the PMP-MPC-controlled shifting process achieves TAC within 0.281s, which is 0.219s faster than standalone MPC. Furthermore, under harmonic disturbances on the DHT input shaft, the angular error remains bounded within ±0.057°, confirming the controller's robustness. These results indicate that the PMP+MPC hybrid strategy effectively realizes rapid TAC execution, thereby significantly improving shift quality.