This paper introduces a two-scale command shaping strategy for reducing vibrations in conventional and hybrid electric vehicle (HEV) powertrains during engine restart. The approach introduces no additional system components and thus few additional costs. The torque profile from an electric machine (EM) is tailored to start the internal combustion engine (ICE) while minimizing residual vibrations. It is shown that the tailored EM torque profile, composed of a linear combination of constant and time-varying components, results in significant mitigation of powertrain vibrations and smoother ICE startup. The time-varying EM torque component is calculated using an analytical ICE model and a perturbation technique for separating scales, which isolates the ICE nonlinear response. Command shaping is then applied to the linear problem at the remaining scale. Simulation results suggest a promising and straightforward technique for reducing vibrations and improving drivability during ICE restart. Furthermore, two-scale command shaping may also be useful in mitigating other HEV-related drivability issues associated with powertrain mode changes (e.g., blending of hybrid power sources, engaging and disengaging of clutches, etc.).

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