Two-Level Nonlinear Model Predictive Control for Lean $NOx$ Trap Regenerations

This paper describes a two-level nonlinear model predictive control (NMPC) scheme for diesel engine lean $NOx$ trap (LNT) regeneration control. Based on the physical insights into the LNT operational characteristics, a two-level NMPC architecture with the higher-level for the regeneration timing control and the lower-level for the regeneration air to fuel ratio profile control is proposed. A physically based and experimentally validated nonlinear LNT dynamic model is employed to construct the NMPC control algorithms. The control objective is to minimize the fuel penalty induced by LNT regenerations while keeping the tailpipe $NOx$ emissions below the regulations. Based on the physical insights into the LNT system dynamics, different choices of cost function were examined in terms of the impacts on fuel penalty and tailpipe $NOx$ slip amount. The designed control system was evaluated on an experimentally validated vehicle simulator, cX-Emissions, with a 1.9 l diesel engine model through the FTP75 driving cycle. Compared with a conventional LNT control strategy, 31.9% of regeneration fuel penalty reduction was observed during a single regeneration. For the entire cold-start FTP75 test cycle, a 28.1% of tailpipe $NOx$ reduction and 40.9% of fuel penalty reduction were achieved.