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A transmission system model is developed at various complexities in order to capture the transient behaviors in drivability and fuel economy simulations. A large number of model parameters bring more degree of freedom to correlate with vehicular test data. However, in practice, it requires extensive time and effort to tune the parameters to satisfy the model performance requirements. Among the transmission model, a hydraulic clutch actuator plays a critical role in transient shift simulations. It is particularly difficult to tune the actuator model when it is over-parameterized. Therefore, it is of great importance to develop a hydraulic actuator model that is easy to adjust while retaining sufficient complexity for replicating realistic transient behaviors. This paper describes a systematic approach for reducing the hydraulic actuator model into a piecewise 1st order representation based on piston movement.

Plug-in hybrid electric vehicles (PHEVs) with post-transmission parallel configuration attracted considerable attention due to their capacity to operate in either electric vehicle (EV) mode or hybrid electric vehicle (HEV) mode. Meanwhile, the added flexibility and multiple operation modes add additional challenges to vehicle control with acceptable drivability, particularly during the mode transition from the EV and HEV, since proper control is needed for the internal combustion engine (ICE), motor and coupling device to achieve smooth and fast transition, under various vehicle operation constraints such as mode-transition duration, vehicle acceleration fluctuation and friction loss of the dry clutch. In addition, the engagement of dry clutch features torque discontinuity due to slip-stick phenomenon and the dynamic behavior of the ICE further increases the nonlinearity of the powertrain system.