Analyzing the Robustness of Two-Scale Command Shaping for Reducing Powertrain Vibration During Engine Restart
This paper analyzes the robustness of a two-scale command shaping strategy for reducing vibrations in hybrid electric vehicle (HEV) powertrains during engine restart. Propagation of HEVs through the automobile market depends on their perceived quality and performance. In this work, a two-scale command shaping strategy addresses the drivability of the vehicle by focusing on the reduction of noise, vibration, and harshness (NVH) issues associated with restarting the internal combustion engine (ICE) during a mode transition. The strategy tailors the electric machine (EM) torque profile, which consists of a linear and time-varying component, to significantly mitigate the powertrain and chassis vibrations for a smoother ICE startup. The time-varying EM torque component is calculated by applying a perturbation technique for separating the scales of an analytical ICE model, which isolates the ICE nonlinear response. Command shaping is then applied to the linear problem governed by the remaining scale. Simulations confirm that the two-scale command shaping strategy is a straightforward technique for reducing powertrain and chassis vibrations during ICE restart. In real-time implementation, inaccuracies or variations in system parameters and initial conditions arising from the operating condition or from general wear during a vehicle’s life cycle will occur. Therefore, successful implementation of the two-scale command shaping strategy relies upon the robustness of the perturbation technique and command shaping to these variations. This paper validates the perturbation technique’s robustness to variations in the ICE parameters and initial conditions. Robust command shaping methods are also explored to decrease the impact of system parameter variations on the efficacy of command shaping. Improving the overall robustness of the two-scale command shaping strategy will increase the applicability to consumer HEVs by ensuring its performance under variations in system parameters.