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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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.
5.
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.
6.
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.
7.
Van Nieuwstadt
,
M.
, and
Yanakiev
,
O.
,
2004
, “
A Diesel Lean NOx Trap Model for Control Strategy Verification
,”
SAE
Paper No. 2004-01-0526.
8.
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
.
9.
Yang
,
H.
,
2010
, “
LNT NOx Storage Modeling and Estimation Via NARX
,”
SAE
Paper No. 2010-01-1937.
10.
Nakagawa
,
S.
,
Hori
,
T.
, and
Nagano
,
M.
,
2004
, “
A New Feedback Control of a Lean NOx Trap Catalyst
,”
SAE
Paper No. 2004-01-0527.
11.
Johnson
,
T. V.
,
2015
, “
Review of Vehicular Emissions Trends
,”
SAE Int. J. Engines
,
8
(
3
), pp.
1152
1167
.
12.
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
.
13.
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
.
14.
Novara
,
C.
,
2015
, “
Polynomial Model Inversion Control: Numerical Tests and Applications
,” eprint
arXiv:1509.01421
.https://arxiv.org/abs/1509.01421
15.
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
.
16.
Hsu
,
K.
,
Novara
,
C.
,
Vincent
,
T.
,
Milanese
,
M.
, and
Poolla
,
K.
,
2006
, “
Parametric and Nonparametric Curve Fitting
,”
Automatica
,
42/11
(
11
), pp.
1869
1873
.
17.
Novara
,
C.
,
Vincent
,
T.
,
Hsu
,
K.
,
Milanese
,
M.
, and
Poolla
,
K.
,
2011
, “
Parametric Identification of Structured Nonlinear Systems
,”
Automatica
,
47
(
4
), pp.
711
721
.
18.
Novara
,
C.
, and
Milanese
,
M.
,
2014
, “
Control of Nonlinear Systems: A Model Inversion Approach
,” eprint
arXiv:1407.1069
.https://arxiv.org/abs/1407.1069
19.
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
20.
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
.
21.
Novara
,
C.
,
2012
, “
Sparse Identification of Nonlinear Functions and Parametric Set Membership Optimality Analysis
,”
IEEE Trans. Autom. Control
,
57
(
12
), pp.
3236
3241
.
22.
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
23.
Siemens
, 2016, “LMS Imagine.Lab Amesim IFP Drive Library 15 Users Guide,” Siemens Industry Software NV, Leuven, Belgium.
24.
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
.
25.
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
You do not currently have access to this content.