Fast model-based calibration of multiple injections for a CI engine using nonlinear optimal control

Today's internal combustion engines are subject to strict regulations of pollutant emissions and to ambitious fuel consumption reduction targets. For direct-injection compression-ignition engines, multiple injections offer additional degrees of freedom that help to achieve these goals. Thus far, the calibration of multiple injections has been based on data -driven approaches using design of experiments. However, an ever increasing number of actuators causes the calibration of the engine to require much more time. In this paper, we propose a modelbased calibration method for multiple injections. The model, which is based on first principles, is identified by a low number of measurements and extrapolates well to various operating points. An optimal control problem which includes that model is then formulated to calculate the efficiency-optimal injector inputs while respecting constraints on cylinder pressure, pressure gradient, engine-out temperature, and engine-out NOx emissions. The optimal control problem is implemented on a rapid prototyping control system and is solved with the nonlinear optimal control framework acados. Due to the simple zero-dimensional formulation of the model and the fast convergence of the solver, the method allows for a fast calibration of two injections for an engine at steady-state operation. The method is used at various engine operating points to find various tradeoffs of relevant engine-out quantities. An experimental validation shows that the calibration time is reduced significantly compared to an approach based on a design of experiments. When compared to a full-factorial design of experiment, a reduction in measurements of up to 60% is possible.