Triple-step method to design non-linear controller for rail pressure of gasoline direct injection engines

The precise control of rail pressure in gasoline direct injection (GDI) engines is considered as an important issue. This study presents a novel approach for rail pressure control of GDI engines. The control objective is to make the rail pressure track a given reference. Different from the existing non-linear controller design methods, the proposed method can be formalised as a triple-step procedure: (i) a steady-state control is deduced, playing the similar role of the map-based control strategy widely used in automotive control; (ii) a feed-forward control is derived concerning the variation of the tracking reference; and (iii) the previous two steps result in an explicit and affine expression of the tracking error dynamics, based on that a non-linear error feedback can be easily designed for enhancing the closed-loop performance and rearranged into a state-dependent PID. The structure of the designed non-linear controller is concise and is comparable to those widely used in modern automotive control. In addition, this procedure provides a concise design process so that the derivation of the control law is simplified and straightforward. A guideline of the control parameters tuning is given based on robustness analysis. Finally, the simulation results in the environment of AMESim with a realistic common rail injection system model show the efficiency of the proposed approach.