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Research Papers

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

[+] Author and Article Information
Ming-Feng Hsieh

Department of Mechanical Engineering, Center for Automotive Research, Ohio State University, Columbus, OH 43210hsieh.122@osu.edu

Junmin Wang1

Department of Mechanical Engineering, Center for Automotive Research, Ohio State University, Columbus, OH 43210wang.1381@osu.edu

Marcello Canova

Department of Mechanical Engineering, Center for Automotive Research, Ohio State University, Columbus, OH 43210canova.1@osu.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(4), 041001 (Jun 15, 2010) (13 pages) doi:10.1115/1.4001710 History: Received January 16, 2009; Revised April 20, 2010; Published June 15, 2010; Online June 15, 2010

## Abstract

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.

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## Figures

Figure 9

HLC NMPC scheme for regeneration trigger control

Figure 10

Comparison of the NOx storages with different AFR control strategies during the first LNT regeneration, the PID control and MPC with k=0.8 have the same NOx storage level at the end

Figure 2

Experimental setup for LNT model validation

Figure 3

Comparison of NOx emissions and catalyst temperatures during a validation test

Figure 4

Comparison of NOx emissions and catalyst temperatures during a single storage and regeneration cycle (2000 r/min, 120 Nm)

Figure 5

Two-level MPC control scheme for LNT control

Figure 6

Input-output diagram of the rich LNT model for state prediction in LLC NMPC

Figure 7

LLC MPC scheme for regeneration AFR control

Figure 8

Input/output diagram of the two-mode LNT model for state prediction in HLC NMPC

Figure 11

Comparison of the fuel consumptions, the PID control and MPC with k=0.8 have the same NOx storage level at the end

Figure 12

Comparison of the AFR commands during the first LNT regeneration

Figure 13

Comparison of the tailpipe NOx emissions during the FTP 75 cycle

Figure 14

Comparison of the fuel consumptions at the end of the FTP 75 cycle

Figure 1

Structure of the LNT model

Figure 15

Comparison of the NOx storages during the FTP 75 cycle

Figure 23

Comparison of the cold-start tailpipe NOx emissions during the FTP 75 cycle; the high values of NOx emission at the first few seconds were due to the low mileage at the start of the cycle that leads to small denominators of g/mile

Figure 24

Comparison of AFR controls during the first regeneration as in Fig. 1 with different NOx release rate and MAF sensor uncertainties

Figure 25

Comparison of total fuel cost at the end of the FTP cycle with different NOx release/storage/conversion rates and MAF sensor uncertainties

Figure 26

Comparison of regeneration triggers with different NOx release/storage/conversion rates and MAF sensor uncertainties

Figure 27

Comparison of tailpipe NOx emission with different NOx release/storage/conversion rates and MAF sensor uncertainties

Figure 16

Comparison of the regeneration timings between the conventional regeneration trigger control and the NMPC based regeneration trigger control with reference to the vehicle speed profile during the FTP 75 cycle

Figure 17

Comparison of the first regeneration timing between the conventional regeneration trigger control and the MPC based regeneration trigger control

Figure 18

Comparison of regeneration timing, engine output power, MAF, and AFR in the first regeneration region

Figure 19

Comparison of the LNT temperatures with initial temperatures equal to 25°C

Figure 20

Comparison of the regeneration triggers during the FTP 75 cycle. The conventional control strategy and the MPC control strategy without temperature consideration triggered regenerations at temperatures below 150°C.

Figure 21

Comparison of the cold-start LNT NOx storages during the FTP cycle

Figure 22

Comparison of the cold-start fuel consumptions at the end of the FTP 75 cycle

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