  Accurate control of combustion phasing is indispensable for diesel engines
due to the strong impact of combustion timing on efficiency. In this work, a
non-linear combustion phasing model is developed and integrated with a
cylinder-specific model of intake gas. The combustion phasing model uses a
knock integral model, a burn duration model and a Wiebe function to predict
CA50 (the crank angle at which 50% of the mass of fuel has burned). Meanwhile,
the intake gas property model predicts the EGR fraction and the in-cylinder
pressure and temperature at intake valve closing (IVC) for different cylinders.
As such, cylinder-to-cylinder variation of the pressure and temperature at
intake valves closing is also considered in this model. This combined model is
simplified for controller design and validated. Based on these models, two
combustion phasing control strategies are explored. The first is an adaptive
controller that is designed for closed-loop control and the second is a
feedforward model-based control strategy for open-loop control. These two
control approaches were tested in simulations for all six cylinders and the
results demonstrate that the CA50 can reach steady state conditions within 10
cycles. In addition, the steady state errors are less than +/-0.1 crank angle
degree (CAD) with the adaptive control approach, and less than +/-1.3 CAD with
feedforward model-based control. The impact of errors on the control algorithms
is also discussed in the paper.
