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In recent years, electrification of powertrains has been promoted to improve fuel efficiency and CO2 emissions. Along with electrification, it is possible to reduce engine usage frequency and improve the fuel efficiency in traveling. Especially in a hybrid electric vehicle (HEV), the state changes from motor assist mode to engine firing mode. As a result, stay time in eigenvalue of a powertrain is shortened, and vibration of the vehicle body at the engine start situation is able to be reduced as compared with conventional engine-driven vehicle. However, since the HEV is equipped with a high compression ratio engine for improving fuel economy, there is cause for concern that excitation force generated by the powertrain at the time of engine start increases. Also, the vehicle body vibration at engine start situations requires further consideration, because the operation frequency of engine decreases.

Idling stop systems are being increasingly adopted in conventional engine vehicles as well as hybrid electric vehicles to increase fuel efficiency. When the engine starts, body vibration occurs that is caused by the rigid body eigenvalues of the power plant during initial combustion. Engine restart vibration after an idling stop is caused by the input force from the transmission, and the reaction force from the drive shaft as well as the input force from the engine. This phenomenon occurs frequently when the engine is restarted from the idling stop, the vibration is increasingly annoying to passengers. Usually, the vehicle development process is carried out in accordance with the V process. The V process divides the vehicle development process into two stages. The first stage is called the vehicle design stage to determine the characteristic. The second stage is called the vehicle verification stage to verify the performance.