Research Papers

A Data-Driven Model Predictive Control Approach to Lean NOx Trap Regeneration

[+] Author and Article Information
Milad Karimshoushtari

Politecnico di Torino,
Turin 10138, Italy
e-mail: milad.karimshoushtari@polito.it

Carlo Novara

Politecnico di Torino,
Turin 10138, Italy
e-mail: carlo.novara@polito.it

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 28, 2017; final manuscript received August 28, 2018; published online October 4, 2018. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 141(1), 011016 (Oct 04, 2018) (9 pages) Paper No: DS-17-1327; doi: 10.1115/1.4041354 History: Received June 28, 2017; Revised August 28, 2018

Lean NOx trap (LNT) is one of the most effective after-treatment technologies used to reduce NOx emissions of diesel engines. One relevant problem in this context is LNT regeneration timing control. This problem is indeed difficult due to the fact that LNTs are highly nonlinear systems, involving complex physical/chemical processes, that are hard to model. In this paper, a novel approach for regeneration timing of LNTs is proposed, allowing us to overcome these issues. This approach, named data-driven model predictive control (D2-MPC), does not require a physical model of the engine/trap system but is based on low-complexity polynomial prediction models, directly identified from data. The regeneration timing is computed through an optimization algorithm, which uses the identified models to predict the LNT behavior. Two D2-MPC strategies are proposed, and tested in a co-simulation study, where the plant is represented by a detailed LNT model, built using the well-known commercial tool AMEsim, and the controller is implemented in matlab/simulink.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Gao, Z. , Chakravarthy, K. , Daw, C. , and Conklin, J. , 2010, “ Lean NOx Trap Modeling for Vehicle Systems Simulations,” SAE Int. J. Fuels Lubr., 3(1), pp. 468–485. [CrossRef]
Lindholm, A. , Currier, N. W. , Li, J. , Yezerets, A. , and Olsson, L. , 2008, “ Detailed Kinetic Modeling of NOx Storage and Reduction With Hydrogen as the Reducing Agent and in the Presence of CO2 and H2O over a pt/ba/al Catalyst,” J. Catal., 258(1), pp. 273–288. [CrossRef]
Wang, Y. , Raman, S. , and Grizzle, J. W. , 1999, “ Dynamic Modeling of a Lean NOx Trap for Lean Burn Engine Control,” American Control Conference, San Diego, CA, June 2–4, pp. 1208–1212.
Ketfi-Cherif, A. , von Wissel, D. , Beurthey, S. , and Sorine, M. , 2000, “ Modeling and Control of a NOx Trap Catalyst,” SAE Paper No. 2000-01-1199.
Kim, Y.-W. , Sun, J. , Kolmanovsky, I. , and Koncsol, J. , 2003, “ A Phenomenological Control Oriented Lean NOx Trap Model,” SAE Paper No. 2003-01-1164.
Canova, M. , Midlam-Mohler, S. , Soliman, A. , Guezennec, Y. , and Rizzoni, G. , 2007, “ Control-Oriented Modeling of NOx Aftertreatment Systems,” SAE Paper No. 2007-24-0106.
Van Nieuwstadt, M. , and Yanakiev, O. , 2004, “ A Diesel Lean NOx Trap Model for Control Strategy Verification,” SAE Paper No. 2004-01-0526.
Hsieh, M.-F. , Wang, J. , and Canova, M. , 2010, “ Two-Level Nonlinear Model Predictive Control for Lean NOx Trap Regenerations,” ASME J. Dyn. Syst. Meas. Control, 132(4), p. 041001. [CrossRef]
Yang, H. , 2010, “ LNT NOx Storage Modeling and Estimation Via NARX,” SAE Paper No. 2010-01-1937.
Nakagawa, S. , Hori, T. , and Nagano, M. , 2004, “ A New Feedback Control of a Lean NOx Trap Catalyst,” SAE Paper No. 2004-01-0527.
Johnson, T. V. , 2015, “ Review of Vehicular Emissions Trends,” SAE Int. J. Engines, 8(3), pp. 1152–1167. [CrossRef]
Novara, C. , Formentin, S. , Savaresi, S. , and Milanese, M. , 2016, “ Data-Driven Design of Two Degree-of-Freedom Nonlinear Controllers: The D2-IBC Approach,” Automatica, 72, pp. 19–27. [CrossRef]
Formentin, S. , Novara, C. , Savaresi, S. , and Milanese, M. , 2015, “ Active Braking Control System Design: The D2-IBC Approach,” IEEE/ASME Trans. Mechatronics, 20(4), pp. 1573–1584. [CrossRef]
Novara, C. , 2015, “ Polynomial Model Inversion Control: Numerical Tests and Applications,” eprint arXiv:1509.01421. https://arxiv.org/abs/1509.01421
Sjöberg, J. , Zhang, Q. , Ljung, L. , Benveniste, A. , Delyon, B. , Glorennec, P. , Hjalmarsson, H. , and Juditsky, A. , 1995, “ Nonlinear Black-Box Modeling in System Identification: A Unified Overview,” Automatica, 31(12), pp. 1691–1723. [CrossRef]
Hsu, K. , Novara, C. , Vincent, T. , Milanese, M. , and Poolla, K. , 2006, “ Parametric and Nonparametric Curve Fitting,” Automatica, 42/11 (11), pp. 1869–1873. [CrossRef]
Novara, C. , Vincent, T. , Hsu, K. , Milanese, M. , and Poolla, K. , 2011, “ Parametric Identification of Structured Nonlinear Systems,” Automatica, 47(4), pp. 711–721. [CrossRef]
Novara, C. , and Milanese, M. , 2014, “ Control of Nonlinear Systems: A Model Inversion Approach,” eprint arXiv:1407.1069. https://arxiv.org/abs/1407.1069
Tibshirani, R. , 1996, “ Regression Shrinkage and Selection Via the Lasso,” R. Statist Soc B., 58(1), pp. 267–288. https://www.jstor.org/stable/2346178?seq=1#page_scan_tab_contents
Donoho, D. , Elad, M. , and Temlyakov, V. , 2006, “ Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise,” IEEE Trans. Inf. Theory, 52(1), pp. 6–18. [CrossRef]
Novara, C. , 2012, “ Sparse Identification of Nonlinear Functions and Parametric Set Membership Optimality Analysis,” IEEE Trans. Autom. Control, 57(12), pp. 3236–3241. [CrossRef]
Novara, C. , and Formentin, S. , 2014, “ Data-Driven Controller Design for Nonlinear Systems: A Two Degrees of Freedom Architecture,” eprint arXiv:1407.2068. https://arxiv.org/abs/1407.2068
Siemens, 2016, “LMS Imagine.Lab Amesim IFP Drive Library 15 Users Guide,” Siemens Industry Software NV, Leuven, Belgium.
Zavala, J. C. , Sanketi, P. R. , Wilcutts, M. , Kaga, T. , and Hedrick, J. , 2007, “ Simplified Models of Engine HC Emissions, Exhaust Temperature and Catalyst Temperature for Automotive Coldstart,” IFAC Proc. Volumes, 40(10), pp. 199–205. [CrossRef]
Ajtay, D. E. , 2005, “ Modal Pollutant Emissions Model of Diesel and Gasoline Engines,” Ph.D. thesis, ETH Zurich, Zurich, Switzerland. https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/149176/eth-28554-01.pdf?sequence=1


Grahic Jump Location
Fig. 1

LNT storage and purge reactions

Grahic Jump Location
Fig. 2

amesim/matlab co-simulation

Grahic Jump Location
Fig. 3

Validation of the NOx stored quantity prediction model during the NEDC driving cycle

Grahic Jump Location
Fig. 4

D2-MPC1 scheme for regeneration trigger control

Grahic Jump Location
Fig. 5

D2-MPC2 scheme for regeneration trigger control

Grahic Jump Location
Fig. 6

(a) regeneration trigger, (b) NOx stored quantity (g), (c) LNT input NOx (mg/s), and (d) Tailpipe NOx(mg/s)

Grahic Jump Location
Fig. 7

Cumulative tailpipe NOx emissions

Grahic Jump Location
Fig. 8

Comparison between D2-MPC1 and controller 4



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In