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Introduction
Usually, electric vehicle (EV) is equipped with only a single-speed transmission for the wide torque characteristics of the traction motor and the strict restrictions on the size, mass, and cost of the transmission system.[1] Recent studies[2],[3] consider that the adoption of multi-speed transmission in the driveline system of EVs has significantly great improvements on the dynamic and economic performances. However, it must be pointed out that the introduced multi-speed transmission should be able to accomplish seamless shifts to be competitive with the single-speed transmission for EVs.[4]
As well known, conventional automated mechanical transmission (AMT) exhibits the problem of torque interruption during shifts, which has seriously bad impacts on the shift smoothness.[5] In order to achieve seamless shifts, several kinds of transmissions, such as dual-clutch transmission (DCT) and hydraulic automatic transmission (AT) which shift based on the overlapping between the friction components (such as the friction clutch and brake), have been introduced in the driveline system of EVs.[6],[7] So far, DCT and AT have not been successfully popularized in the driveline system of EVs owing to the high cost and significant control complexity. In order to provide seamless shifts for EVs and simultaneously keep the structures of the transmission and the corresponding actuators compact, some overlapping friction components are suggested to be replaced with simpler and mechanically more robust switch components (such as one-way clutch, synchronizer, and dog clutch).[8]-[10]
The overlapping shift process between the friction components (or between the friction component and the switch component) is usually divided into two phases: torque phase and inertia phase.[11] Nowadays, the linear feed-forward control strategy is always applied in the torque phase, while major focus is directed toward the trajectory optimization (i.e. control strategy) in the inertia phase.[12] Recently, extensive studies on the trajectory optimization in the inertia phase have been carried out and could be summarized up as the following two main routes. On one hand, several kinds of empirical trajectories of the mismatch speeds of the on-coming clutch have been proposed, and some feedback controllers, such as proportional integral derivative controller,[13],[14] back-stepping controller,[15] sliding mode controller,[16] and model predictive controller,[17] are used to track these referenced mismatch speeds. On the other hand,...