Optimal combustion calibration for direct-injection compression-ignition engines using multiple injections

Multiple injections are widely used for direct-injection compression-ignition engines to mainly increase efficiency, lower pollutant emissions, and increase exhaust enthalpy. However, with each additional injection the degrees of freedom increase, which makes finding an optimal injection input by design of experiments a time-consuming task. In this paper, we present a model-based calibration method that determines the number of injections for a predefined set of requirements. First, we derive a zero-dimensional crank-angle-resolved cylinder process model based on first principles. The model includes a fuel injector and requires a low calibration effort. Second, we use this model in an optimal control problem that minimizes the fuel consumption subject to several constraints such as load, maximal pressure, maximal pressure gradient, engine-out temperature, and the limitations of the fuel injector. The optimal injector inputs are used as feedforward control signals on a real engine to validate the simulative results. In general, the experimental results are in good agreement with those obtained in simulations. Finally, we compare our approach to a state-of-the-art method known as pressure reference tracking which consists of two separate steps: the creation of an optimal pressure reference and the tracking by a discrete injector. We show that our method, which combines these two steps in a single optimization problem, results in an increase in indicated efficiency compared to the solution obtained by pressure reference tracking.