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The work extends a methodology, for searching for optimal heat release profiles, by adding complex constraints on states. To find the optimum heat release profile a methodology, that uses available theory and methods, was developed that enables the use of state of the art optimal control software to find the optimum combustion trace for a model. The methodology is here extended to include constraints and the method is then applied to study how sensitive the solution is to different effects such as heat transfer, crevice flow, maximum rate of pressure rise, maximum pressure, knock and NO generation. The Gatowski single zone model is extended to a pseudo two zone model, to get an unburned zone that is used to describe the knocking and a burned zone for NO generation. A modification of the extended Zeldovich mechanism that makes it continuously differentiable, is used for NO generation.

Cylinder air-charge is one of the most important parts of the torque control in a gasoline engine, due to the necessity to keep a stoichiometric air-fuel ratio, for the three-way catalyst to work efficiently. Throttle and phasing of the camshafts are actuators that have a big effect on the cylinder air-charge, this results in a cross-coupling between the actuators. One approach to handle the cross-coupling that occurs with multiple actuators is to use model predictive control (MPC), that handles the cross-coupling through the use of models and optimization. Models that support computation of gradients and hessians are desirable for use in MPC. To support the model design experimental data of cylinder pressure, from an inline four-cylinder engine with dual independent cam phasing, supported by gas exchange simulation, the effects from variable valve timing on the cylinder air-charge are investigated during the valve overlap period.