An approach to optimal integer and fractional-order modeling of electro-injectors in compression-ignition engines

The automotive industry continuously spends resources to reduce fuel consumption, operating costs, and harmful emissions. Namely, regulations are becoming more restrictive and customers' expectations are growing. To achieve these goals in compression-ignition engines, an approach employs innovative Common Rail Injection Systems, based on advanced control units and electro-injectors. The latter require an accurate model for optimizing layout and operation and for controlling injection rate shaping strategies that are fundamental for reducing consumption and emission. This work proposes a complete innovative electro-injector model, which integrates an integer-order representation of inner volumes and mechanical and electromagnetic elements, and a fractional-order model for the high-pressure fuel propagation inside a specific pipe in the injector. Fractional order modeling of this complex process is motivated by the superior description ability of a fractional-order system with respect to an integer-order system. Then a new numerical method is proposed and tuned to simulate the system. A differential evolution technique optimizes the model parameters. Simulation results show that benefits are gained in model prediction capability.