Homogeneous Charge Compression Ignition (HCCI) presents several advantages over conventional IC engines, including improved efficiency and emissions. It is, however, difficult to implement and control due to the lack of an external combustion trigger. One way to achieve HCCI is to trap and recompress a portion of the exhaust in the cylinder to increase the sensible energy of the air-fuel mixture. Such a strategy, however, introduces a cyclic coupling through the exhaust gas retained from cycle to cycle, making dynamic control non-trivial. In order to develop model-based controllers for HCCI, the authors present a physically motivated two-state model of the HCCI process. This model specifically captures the behavior of a direct inject gasoline engine with an exhaust-recompression strategy used to achieve HCCI. As the trapped exhaust is pivotal in setting up the cyclic coupling, its temperature and the amount of oxygen present in it are selected as the states of the system. The system's dynamics are developed through these states to give a discrete-time nonlinear model that can be validated against a more complex continuous-time model. In this form, the model represents a control-oriented description of the HCCI engine as a thermodynamic system, and can therefore be used as a platform to synthesize various control strategies. As a demonstrative example, a linear representation of the system is derived and used to synthesize an LQR controller to track a desired state trajectory in simulation.

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