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High fuel efficiency and low emission technologies, such as Direct Injection (DI) gasoline and diesel engines and hybrid powertrains, have been developed to resolve environmental and energy resource issues. The hybrid powertrain system has achieved superior power performance as well as higher system efficiency and is expected to be a core powertrain technology because it is compatible with various power sources including fuel cells. It becomes important to control complicated hybrid systems that consist of not only a powertrain but also vehicle systems such as regenerative braking. Model-based control and calibration enables both control strategy optimization and control system development efficiency improvement.

Recent engine systems have become complex due to the requirements of fuel efficiency, exhaust gas emission control and good drivability. To decrease engine development period, model-based development has been adopted [1]. For torque-based vehicle control, engine torque estimation models are necessary. Simple mean-value torque models are available but these models require large amount of test data for development and validation. In addition, they cannot estimate transient torque precisely. On the other hand, complex physical models require considerable time for modeling and simulation. In order to decrease modeling time and retain model accuracy, the Wiebe function is utilized to calculate the heat release rate.