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Auxiliary power units (APUs) are widely used for electric power generation in modern hybrid electric vehicles. In the consideration of the APU, a common shaft connects an internal combustion engine and an electrical induction motor which is used as a starting motor and as a battery charger. Dynamic models of both engine and motor are used for the design of the APU controller. A field oriented control scheme and a decoupling controller with two independent current control loops is used for the motor. A torque controller, based on a sliding mode torque estimator, regulates the engine transients. The control of the whole APU is obtained by coupling the engine and motor controllers through a reference governor of the requested power. Numerical experiments on a realistic case study show good performance both in steady state and during transients.