In a system for controlling rotation of torque applied to a rotating shaft of an engine of a vehicle that uses the engine as a drive source thereof, a motor is provided. A main controller controls the engine and the motor. The main controller selectably activates the motor that applies first torque to the rotating shaft of the engine, and deactivates the motor. A rotary electric machine includes a rotor connected to the rotating shaft of the engine. A rotation parameter detector measures a rotation parameter associated with rotation of the rotor of the rotary electric machine. A sequence controller performs, in response to an occurrence of a trigger situation, a control sequence that controls, independently of the main controller, the rotary electric machine based on the rotation parameter measured by the rotation parameter detector, thus applying second torque to the rotating shaft of the engine.