Failure diagnosis and tolerant control method for hydrothermally aged SCR system by utilizing EKF observer and MRAC controller

Accepted Manuscript Failure Diagnosis and Tolerant Control Method for Hydrothermally Aged SCR System by Utilizing EKF Observer and MRAC Controller

Jie Hu, Jiawei Zeng, Li Wei PII:

S0360-5442(18)30911-3

DOI:

10.1016/j.energy.2018.05.094

Reference:

EGY 12929

To appear in:

Energy

Received Date:

06 November 2017

Accepted Date:

13 May 2018

Please cite this article as: Jie Hu, Jiawei Zeng, Li Wei, Failure Diagnosis and Tolerant Control Method for Hydrothermally Aged SCR System by Utilizing EKF Observer and MRAC Controller, Energy (2018), doi: 10.1016/j.energy.2018.05.094

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ACCEPTED MANUSCRIPT 1

Failure Diagnosis and Tolerant Control Method for Hydrothermally Aged SCR System by

2

Utilizing EKF Observer and MRAC Controller

3

Jie Hu*, Jiawei Zeng**, Li Wei

4

aHubei

5

Technology), Wuhan 430070, China

6

bHubei

7

China

8

*Corresponding

9

Components (Wuhan University of Technology), Wuhan 430070, China.

Key Laboratory of Advanced Technology for Automotive Components (Wuhan University of

Collaborative Innovation Center for Automotive Components Technology, Wuhan 430070,

author. Hubei Key Laboratory of Advanced Technology for Automotive

10

**Corresponding

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Components (Wuhan University of Technology), Wuhan 430070, China.

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E-mail addresses: [email protected] (Jie Hu), [email protected] (Jiawei Zeng).

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Abstract: For ensuring emission performances of a selective catalytic reduction (SCR) system, it

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shall be critically robust and adaptive against any hydrothermal aging failure throughout its whole

15

service life. Simulation was carried out here to investigate its hydrothermal aging effect by using such

16

hydrothermal aging model and the corresponding results showed that its performances were

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significantly influenced while the catalyst (V2O5/WO3-TiO2) was hydrothermally aged. On this basis,

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an extended-Kalman-filter-based (EKF-based) observer was designed to identify its hydrothermal

19

aging states and the corresponding results indicated that the actual hydrothermal aging degree could

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be estimated quickly and accurately. Moreover, a Lyapunov-based model reference adaptive

21

controller (MRAC) was designed to improve its control performances based on the diagnosis

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information from the EKF-based observer while V2O5/WO3-TiO2 was hydrothermally aged. Thus, its

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hydrothermally aged failure-tolerant control performances could be remarkable improved by means

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of Lyapunov-based MRAC.

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Keywords: Diesel engine; Urea-SCR; Failure-diagnosis; Failure-tolerant control; EKF-based

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observer; MRAC

author. Hubei Key Laboratory of Advanced Technology for Automotive

1

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1. Introduction

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Diesel engines take a few advantages (such as power and thermal efficiency, reliability,

29

durability, and relatively low operating cost) as power sources for highway trucks, urban buses, off-

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road vehicles, marine carriers and industrial devices [1]. Moreover, they emit unburned hydrocarbon

31

(HC) and carbon monoxide (CO) at lower levels in comparison with those of comparable gasoline

32

engines, however their nitrogen oxides (NOx) and particulate matters (PM) emission levels are higher

33

due to there being excess oxygen in fuel/air mixtures and heterogeneous combustion of the fuel/air

34

mixture in their combustion chambers [2-5]. To meet future legislation for both PM and NOx

35

emissions, typical after-treatment such as diesel oxidation catalyst (DOC), diesel particulate filter

36

(DPF) and selective catalytic reduction (SCR) catalyst are necessary, especially for heavy duty diesel

37

engines [6,7].

38

It is well known that the urea-based SCR (Urea-SCR) technology is regarded as the most

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promising and efficient technique for NOx removal [8-11] due to injection of aqueous urea into the

40

upstream of SCR catalyst where urea is decomposed into gaseous NH3 and stored inside catalyst so

41

that NOx can be converted into nitrogen and water for removal out of the vehicle tailpipe. Clearly,

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the urea dosing control dominates the overall SCR system performances: its insufficient injection will

43

result in the inadequate input of NH3 and non-optimized NOx reduction effect, but its excess injection

44

will give rise to high urea consumption and undesirable NH3 slip to the tailpipe [12]. Nevertheless,

45

the trade-off between NOx conversion efficiency and NH3 leakage should be taken into account due

46

to NH3 being also a kind of pollutant so that some effective control strategies (including open-loop

47

and closed-loop control strategies) were put forward to solve such trade-off issue. Open-loop control

48

strategies were presented to meet requirements of the Euro-IV emission standards [13, 14]. Whereas,

49

more efficient control strategies should be necessary for compliance to requirements of the Euro-V

50

and stricter emission regulations [15]. In contrast, closed-loop control strategies were given to further

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balance NOx and NH3 emissions at any tailpipe. The ammonia coverage ratio was recently regarded

52

as a control target in view of its directly influencing the tailpipe NOx concentration and NH3 slip. Wei 2

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et al. [16] presented a non-linear model predictive control (NMPC) method to optimize the SCR

54

system by limiting the desired ammonia coverage ratio and comparison the experimental and

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simulation results showed that this control strategy was effective and acceptable. Bonfils et al. [17]

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developed an ammonia coverage ratio observer based on NOx sensor measurements to mitigate the

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trade-off between NOx conversion efficiency and NH3 leakage and the transient test results

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demonstrated that this control strategy might be feasible in most cases. Feng [18] put forward a

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model-based ammonia storage control strategy based on the NOx sensor feedback technique to better

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compromise the high NOx reduction efficiency but low NH3-slip. Opitz et al. [19] proposed a catalyst-

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temperature-based control strategy to control the average ammonia storage level and the

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corresponding results indicated that such strategy worked well under the test cycle. Evidently, the

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above SCR control strategies were utilized to remarkably reduce NOx emissions and simultaneously

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avoid the NH3 leakage out of the corresponding limits.

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However, the SCR catalyst as one of the most important functional components in SCR system

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will be hydrothermally aged after long-time service in high-temperature and humid environment. If

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the hydrothermal aging effect is not under consideration as for any SCR control strategy, the NOx

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emission and NH3 leakage at tailpipe will not be well balanced. Furthermore, with the enactment of

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the European-VI emission regulations, a DOC+DPF+SCR system was proposed to further reduce

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NOx and PM from the diesel engine. DPF technology is regarded as one most effective method for

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removal of PM [20]. However, the DPF can be gradually blocked with carbon deposits so that the

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exhaust backpressure may rise but the engine power may decrease [21]. Owing to this fact, DPF is

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dependent on regeneration for removal of carbon deposit [22]. DPF regeneration can be typically

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performed by active and passive methods, and the exhaust temperature rises above 500°C for

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performance of PM incineration as for the former method [23]. Hence, SCR catalyst in a

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DOC+DPF+SCR system will be aging faster than that in only a SCR system .

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V2O5/WO3-TiO2 as popular SCR catalyst are efficient to reduce NOx emissions out of diesel

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engines, for which a major problem (hydrothermal aging failure) may occur after considerable service 3

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time while the engine exhaust gas temperature is more than 450°C. And high temperature exposure

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of V2O5/WO3-TiO2 will lead to those issues such as TiO2 sintering and volatilization of vanadia and

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tungsta species [24]. Thus, the activity of V2O5/WO3-TiO2 will significantly degrade due to any

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hydrothermal aging failure. A lot of works were performed with regard to V2O5/WO3-TiO2 catalyst

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hydrothermal aging. Pang et al. [25] prepared the V2O5/WO3-TiO2 catalyst based on the conventional

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impregnation (VWTi-con) and ultrasound-assisted impregnation methods (VWTi-HUST),

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respectively. The NO reduction activity was significantly lost after a hydrothermal treatment as for

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the former method but a good hydrothermal stability still existed for the latter method. Li et al. [26]

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investigated the hydrothermal stability of V2O5/WO3-TiO2 prepared by means of the VWTi-con

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method and its corresponding NH3-SCR activity was poor after a hydrothermal treatment (@ 670°C

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in 5% H2O/air for 64h) and turned weaker in a higher temperature. Seo et al. [27] studied the

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physicochemical characteristics of hydrothermally aged V2O5/WO3-TiO2 catalyst. The results

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showed that particles in V2O5/WO3-TiO2 were agglomerated and the corresponding NOx conversion

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capability fell significantly after the hydrothermal aging (@800°C for 24h). Liu et al. [28] prepared

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V2O5/WO3-TiO2 by means of the wetness impregnation method and the hydrothermally aging was

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achieved at 750°C in H2O/air (volume percentage: 10%) for 24h. The corresponding results indicated

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that its NOx removal ability deteriorated greatly over the entire measured temperature range due to

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the hydrothermal aging effect. In the existing studies, the aging effect of V2O5/WO3-TiO2 was focused

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by means of the experimental investigation method. However, the experimental investigation method

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may be high-cost and time consuming. Hence, it is worthwhile to study the catalyst aging effect on

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emission control performance of SCR system by means of simulation methods. To achieve this goal,

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a simulation-based fault injection technique was utilized for modeling and quantitative analysis of

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hydrothermally aged SCR catalyst.

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Owing to the fact that the emission control performance of SCR system can significantly degrade

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due to SCR catalyst hydrothermal aging, a real-time fault-tolerant control system is necessary against

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the negative effect of SCR catalyst hydrothermal aging. The foremost step of fault-tolerant control is 4

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fault diagnosis. The diagnosis approaches can be divided into two categories: model-free and model-

106

based methods [29]. The former was based on only measurements and a large database was necessary

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during a long operation period so that they should not be actually feasible [30] and the latter was

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developed to solve the existing issues. Ma et al. [31] proposed two model-based observers to estimate

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the SCR aging situations. However, the simulation results showed that the aging degree of SCR

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catalyst can’t be rapidly and accurately estimated by the Lyapunov-based observer when the

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measurements were disturbed. In recent years, the EKF algorithm was popular for fault diagnosis in

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various fields [32-34] due to their remarkable robustness against measurement noises [35, 36].

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Despite of their benefits, the EKF algorithm was not utilized for diagnosis of the SCR hydrothermal

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aging failure so far. Hence, an EKF-based observer was first designed here for getting diagnosis

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information about SCR hydrothermal aging situations.

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The fault-tolerant controller as the core components of fault-tolerant control system should be

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designed with a proper method. Chen et al. [37] developed a robust and adaptive SCR failure-tolerant

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control method against the SCR catalyst aging effect by utilizing two observers (ammonia coverage

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ratio observer and storage capacity observer) and a NMPC controller. Stadlbauer et al. [38] proposed

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a NMPC controller as well to adaptively adjust the ammonia storage of SCR catalyst based on current

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SCR catalyst aging degree for fault-tolerant control. However, the computational load of NMPC

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algorithm is intensive for real-time control. Recently, the adaptive-based failure-tolerant methods

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were widely applied for solving some engineering issues due to their good real-time performance and

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resistance to system uncertainties [39, 40]. The adaptive control methods were primarily categorized

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into the two types (namely MRAC and self-adaptive methods). The former was an effective adaptive

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control method that provides feedback controller structure and adaptive law to ensure closed-loop

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signals could be convergent and the independent reference signals can be tracked asymptotically [41].

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It has been very popular due to its remarkable robustness in failure-tolerant control applications in

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recent years [42, 43]. Thus, an MARC was presented here to dominate how catalyst aging conditions

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should be managed in a SCR control system in accordance to diagnosis information from the EKF 5

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observer.

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The goal of this study is hence threefold, namely:

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1. The aging condition of SCR catalyst can be quantitatively described and the aging effect on

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the SCR control system can be investigated by means of simulation methods. Thus, it contributes to

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reducing the cost and time in studying the hydrothermal deactivation of SCR catalyst.

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2. The EKF-based diagnosis system can be achieved to obtain the real-time information of SCR catalyst aging degree. It is conductive to monitoring health condition of SCR catalyst.

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3. The Lyapunov-based MRAC failure-tolerant control system can be developed to ensure the

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sustainability of emission control performance of SCR system. Owing to its low computational load,

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the MRAC failure-tolerant control system can regulate the urea dosage in real-time to keep the

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exhausts clean according to the diagnosis information of SCR catalyst aging condition.

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Our primary contents are organized as follows:

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Section 2: SCR modeling and control strategy

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2.1 SCR operation principle

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2.2 SCR aging model

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2.3. Baseline SCR control strategy

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Section 3: SCR aging failure diagnosis and tolerance method

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3.1 SCR aging factor observer design

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3.2 Design of the SCR aging failure-tolerant controller

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Section 4: Results and discussion

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4.1 Validation of the SCR model

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4.2 SCR performances vs. hydrothermal aging

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4.3 Failure-diagnosis and tolerant control performances of a hydrothermally aged SCR

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system

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Section 5: Conclusions

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2. SCR modeling and control strategy

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2.1 SCR operation principle

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The schematic operating processes of a urea-SCR system are described as follows [44]:

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1. Urea is injected into the exhaust tailpipe.

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2. What left after complete evaporation of urea solution are solid substances under the

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corresponding thermal decomposition temperature.

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3. The above solid substances are decomposed into gaseous NH3.

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4. Gaseous NH3 is adsorbed in catalyst while desorption of NH3 occurs simultaneously.

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5. N2 and H2O are produced based on the reaction between NH3 and NOx.

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Their corresponding chemical reaction equations are as follows [45]:

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Urea evaporation reaction: NH 2  CO  NH 2  liquid   NH 2  CO  NH*2 (solid)  nH 2 O

(1)

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Urea decomposition reaction: NH 2  CO  NH*2 (solid)  H 2 O  2NH 3  CO 2

(2)

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NH3 adsorption and desorption reaction:

170

Where: Sfree represents free catalyst sites.

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Major decomposition of NOx in the catalyst convertor [46]:

NH 3  Sfree  NH3

(3)

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4NH3  4NO  O 2  4N 2  6H 2 O

(4)

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2NH3  NO  NO 2  2N 2  3H 2 O

(5)

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4NH3  3NO 2  3.5N 2  6H 2 O

(6)

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Reaction (4) is regarded as the standard SCR reaction since its reaction rate is relatively fast in

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conventional V2O5-WO3/TiO2 and NO accounts for 90% in NOx emissions in a typical diesel exhaust.

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Moreover, Reaction (5) is known as the fast SCR reaction whose rate is approximately 10 times faster

178

than that of the standard SCR reaction. In addition, Reaction (6) is the slow SCR reaction whose rate

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in V2O5-WO3/TiO2 is very low [47].

180 181

Besides, NH3 and O2 react in the catalyst converter so that more urea consumption shall be necessary. The NH3 oxidation reaction is described as [48]: 7

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4NH3  3O 2  2N 2  6H 2 O

(7)

2.2 SCR aging model It’s well known that a SCR catalyst convertor is very complicated for reaction. For simplifying the SCR model, the following assumptions are made [49, 50]:

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1. the exhaust gas components are assumed to be homogeneous and incompressible.

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2. Moisture and oxygen remain constant in the exhaust gas.

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3. All variables are homogeneous and only axially vary in the catalyst convertor.

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4. only adsorbed NH3 shall be involved in NOx removal reaction.

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According to the Arrhenius law, the main reaction rates are modeled as [49]: RT CNH3 (1   ) 2πM NH3

Rads  CsSc α prob 191

192

193

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Adsorption reaction:

Desorption reaction:

SCR reaction:

NH3 oxidation reaction:

Rdes  Cs k des e



Edes RT

Rscr  Cs RTk scr e

Rox  Cs k ox e



Eox RT



 Escr RT

(8)

(9)  CNO

x



(10)

(11)

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Where: Cs represents the concentration of active atoms with respect to converter volume. Sc represents

196

the area of 1mol active surface atoms. αprob represents the sticking probability. MNH3 represents the

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NH3 molar mass. R represents the universal gas constant. T represents the gas temperature of the

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catalyst convertor. θ represents the ammonia surface coverage. Rads, Rdes, Rscr and Rox represent

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reaction rates of adsorption, desorption, SCR and oxidation, respectively. Eads, Edes, Escr and Eox

200

represent activation energies of adsorption, desorption, SCR and oxidation, respectively.

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For convenience, the following coefficients are defined:

8

ACCEPTED MANUSCRIPT

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R EG 1  a1  p , a 2  V , amb c  E   des RT , a4  Cs k des e RT , a3  Cs Sc α prob 2πM NH3   Escr E ox  a  C R T k e  RT , a  C k e  RT . s scr 6 s ox  5

(12)

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Where: REG represents the exhaust gas specific constant. pamb represents the ambient pressure. ε

204

represents the ratio of the gas volume and the total convertor volume. Vc represents the converter

205

volume.

206 207

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By applying the mass conservation law to NOx, NH3 and stored NH3, the SCR model can be established as [49]: C NO x  a 2 nNO x ,in  CNOx (a1a 2 mEGT  a5 )  C NH3  a 2 nNH3 ,in  a 4  CNH3 [a1a 2 mEGT  a3 (1   )]    [a3 (1   )CNH3  a4  a5CNOx   a6 ]/Cs

(13)

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Where: CNOx represents the downstream NOx concentration. CNH3 represents the NH3 leakage at the

210

inlet state. nNOx,in represents the NOx molar flowrate at the inlet of catalyst convertor. nNH3,in represents

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the NH3 molar flow rate at the inlet of catalyst convertor. mEG represents the mass flowrate of the

212

exhaust gas.

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For modeling of aged SCR catalyst, the fault should be firstly injected into the SCR model. As

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many existing investigations show, one major consequence of SCR catalyst aging may lead to the

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reduction of the ammonia storage capacity of the SCR catalyst [31, 38, 50], which corresponds to the

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concentration of active atoms with respect to the volume of SCR catalyst (Cs) here. Thus, Cs can be

217

regarded as a major parameter affected by SCR catalyst aging. The aging factor (α) is defined by: 

218

Cs,aged Cs,fresh

(14)

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Consequently, the SCR aging model is transformed by integration of Eqs. (12) ~ (14):

220

C NO x  a 2 nNO x ,in  CNOx (a1a 2 mEGT   a5 )  C NH3  a 2 nNH3 ,in   a 4  CNH3 [a1a 2 mEGT   a3 (1   )]    [a3 (1   )CNH3  a4  a5CNOx   a6 ]/Cs 9

(15)

ACCEPTED MANUSCRIPT 221

Where: Cs,aged and Cs,fresh represent the concentrations of active atoms with respect to the volumes of

222

aged and fresh SCR catalyst, respectively. For fresh SCR catalyst,  is defined as 100% and decreases

223

along with the growth of the aging degree of the SCR catalyst.

Feedforward Controller

Engine Speed, Torque and Exhaust Temperature

Diesel Engine Upstream NOx Emission

Basic Urea Dosage

+ Urea Dosage Correction

Feedback Controller

224 225 226

Catalyst Convertor

Actual Urea Dosage

Ammonia Coverage Ratio Estimated by EKF Desired Ammonia Coverage Ratio

Downstream NOx and NH 3 Emission Catalyst Temperature

Ammonia Coverage Ratio Reference

Figure 1 Schematic diagram of the ammonia-coverage-ratio-based closed-loop control strategy 2.3 Baseline SCR control strategy

227

Our SCR control system was based on the ammonia-coverage-ratio-based closed-loop control

228

strategy (Figure 1) which is regarded as an effective SCR control strategy due to its better and faster

229

disturbance rejection performance [51]. Moreover, its primary components are feedforward and

230

feedback controllers.

231

The urea dosage is calculated by means of the feedforward controller to guarantee the relative

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optimal NOx removal with respect to a limited NH3 slip, which depends on the exhaust mass flowrate,

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the engine outlet NOx concentration, the maximum NOx conversion efficiency (@ NH3 leakage =

234

10ppm) and the ratio (NH3:NOx) and whose computing formula is as follows:

235

madblue 

mexh  v  VNO x ,in  M urea  max  NSR

(16)

M exh  Cadblue

236

Where: madblue represents the urea dosage. mexh represents the exhaust mass flow rate. ηmax represents

237

the maximum NOx conversion efficiency. NSR is the ratio (NH3:NOx). Cadblue represents the urea

238

mass fraction in AdBlue (Cadblue=32.5%). VNOx,in represents the engine inlet NOx concentration. Murea

239

and Mexh represent the molar masses of urea and exhaust gas, respectively. v is the stoichiometric 10

ACCEPTED MANUSCRIPT 240 241

coefficients of urea decomposition (v = 0.5). t

deNH3

0

dt

uurea  K P eNH3  K I  eNH3 dt K D

(17)

242

Where: uurea represents the corrected urea dosage. KP, KI and KD represent the proportional, integral

243

and derivative factors, respectively. 𝑒NH represents the difference between the estimated and desired

244

ammonia coverage ratios.

3

245

The PID feedback controller conforming to Eq. (17) was designed to regulate the urea dosage

246

according to the feedback signal of the difference between the estimated ammonia coverage ratio

247

(estimated by EKF observer described in detail in Section 3.1) and the reference ammonia coverage

248

ratio (as a function of SCR temperature) which is necessary to prevent any ammonia leakage while

249

the temperature drastically changes [18]. The ammonia coverage ratio reference shown in Figure 2

250

is calibrated in following process [17, 52]:

251

1. Control the NH3 leakage within the emission limits (25 ppm at peak, 10 ppm on average) to

252

maximize the NOx conversion efficiency for a given emission test cycle by means of regulating the

253

urea dosage.

254 255 256 257 258 259

2. Calculate ammonia coverage ratio by Eqs. (18) and (19), and collect catalyst temperature data in the given test cycle. 3. Find the functional relationship between ammonia coverage ratio and catalyst temperature by means of fitting and interpolation method. 4. Limit ammonia coverage ratio for low catalyst temperature (e.g. below 523K) to prevent possible high NH3 leakage during temperature transient.

260

It is noted that the ammonia coverage ratio limit at low catalyst temperature in the European

261

steady-state cycle (ESC) is lower than that in the European transient cycle (ETC) against higher

262

temperature transient.

263

m  C m nNH3 ,storage    adblue adblue  exh  VDeNO x  VNH3  dt M exh  M urea  v 





11

(18)

ACCEPTED MANUSCRIPT

nNH3 ,storage

264

=

265

Where nNH ,storage is moles of ammonia storage. VDeNO is the amount of NOx reduction. VNH is the outlet

266

NH3 concentration.  is moles of maximum ammonia storage.  is ammonia coverage ratio.

(19)

 3

x

3

267 268

Figure 2 Ammonia coverage ratio reference vs. catalyst temperature

269 270

3. SCR aging failure diagnosis and tolerance method

271

3.1 SCR aging factor observer design

272

As presented in the Section 1, there is no doubt that the SCR performance will be significantly

273

affected by its aging failure so that its aging degree shall be necessarily identified accurately and

274

rapidly for its failure-tolerant control. The aging factor quantitatively reflects the aging degree of SCR

275

catalyst. However, the aging factor can’t be measured by means of any sensors but only estimated by

276

means of the observer. An EKF-based observer was designed here to estimate α as a state except for

277

other three states (namely the ammonia surface coverage, the downstream NOx concentration and the

278

downstream NH3 leakage) of the EKF. In addition, the measurements of the EKF is the actual NH3

279

and NOx concentration, which are collected by corresponding measuring instruments.

280

Generally, the state space model of EKF for a nonlinear system is expressed by:

281

 x(k )  f [ x(k  1), u (k )]  w(k )   z (k )  h[ x(k )]  v(k )

(20) 12

ACCEPTED MANUSCRIPT 282

Where: x(k) represents the state vector. u(k) represents the input vector. w(k) represents the process

283

noise with zero-mean Gaussian noise. f (x, u) represents the nonlinear state function. z(k) represents

284

the measurement vector. v(k) represents the measurement noise with zero-mean Gaussian noise. h(x)

285

represents the nonlinear measurement function.

286 287 288

The state vector can be estimated by means of an EKF in two steps (namely predicting and updating). The overall EKF estimation process is described as follows: Predicting Step: x(k |k  1)  f [ x(k  1|k  1), u (k )]

(21)

P(k |k  1)  F (k ) P(k  1|k  1) F (k )T  Q(k )

289

(22)

290

Where: P represents the error covariance matrix. F represents the Jacobian matrix of the nonlinear

291

state function f. Q represents the covariance of w(k).

292

Updating Step: the state vector x(k) and the error covariance matrix P are updated in accordance

293

with the difference between predicted and measured z(k). The updating step of the EKF can be

294

expressed as: 1

295

K (k )  P(k |k  1) H (k )T  H (k ) P(k |k  1) H (k )T  R(k ) 

296

x(k | k )  x(k | k  1)  K (k )  z (k )  h  x(k | k  1), u (k )

(24)

297

P(k |k )   I  K (k ) H (k )  P(k |k  1)

(25)

(23)

298

Where: K represents the Kalman gain. H represents the Jacobian matrix of the nonlinear measurement

299

function h. R represents the covariance of v(k). I represents the identity matrix.

300

The four-state EKF prediction model is gained here based on Eq. (15) and expressed as:

301

 (k  1|k  1)   (k |k  1)   (k  1|k  1)     (k |k  1)   (k  1|k  1)   (k  1|k  1)        t   x(k |k  1)  CNOx (k |k  1)  CNOx (k  1|k  1)  CNOx (k  1|k  1)        C NH (k  1|k  1)  CNH3 (k |k  1)  CNH (k  1|k  1)   

302

3

(26)

Where: Δt represents the step size for updating the EKF.  (k  1|k  1) 

303

3

a 2 n NO x ,in  a1a 2 mEGTCNOx (k  1|k  1)  C NOx (k  1|k  1) a5 CNOx (k  1|k  1)

(27) 13

ACCEPTED MANUSCRIPT 304 305 306

 (k  1|k  1)=

d  (k  1|k  1) dt

(28)

Then, the measurements of the downstream NOx concentration and NH3 leakage are selected as the observer vector here. The EKF measurement model is expressed as:

307

CNOx (k )  z (k )  h[ x(k )]    CNH3 (k ) 

308

The aging factor is observed based on the above EKF prediction and measurement models. The

309

predicted aging factor is unstable at the initial stage of the EKF estimation process so that it shall be

310

the invalid failure information and can not be used for any failure-tolerant control. Thus, the aging

311

factor changes slowly with time in the first period of EKF estimation so that it shall be necessarily

312

initialized to the latest stable estimated value recorded in the memory module or one if the catalyst

313

aging degree is predicted for the first time. It still remains unchanged until the EKF estimation of the

314

aging factor has been stable. In addition, the stability judgment principles were put forward here for

315

the EKF estimation process, which are as follows:

(29)

316

1. The latest 5 data points of the estimated aging factor are collected.

317

2. Their variance is calculated.

318

3. If the variance is less than its corresponding threshold value, the observed aging factor is

319

transferred into the failure-tolerant controller. Otherwise, the latest stable estimated value shall be

320

applied to the failure-tolerant control.

321

The diagnosis process is schematically shown in Figure 3.

14

ACCEPTED MANUSCRIPT Input signal

EKF observer

Collect 5 data points of estimated aging factor

Calculate their variance

No if the variance is less than its corresponding threshold value Call the latest stable estimated value from memory module

Yes

Output the diagnosis information

322 323 324

Figure 3 The schematic diagram of diagnosis process 3.2 Design of the SCR aging failure-tolerant controller

325

A failure-tolerant controller is necessarily designed based on the diagnosis information from the

326

EKF-based observer to withstand the hydrothermal aging effect. Thus, an MRAC is presented here

327

based on its advantages such as simple structure and fast and stable reconfiguring to achieve the SCR

328

aging failure-tolerant control [43]. It is generally mainly contains four structure parts (namely, a real

329

system, a controller, a reference model and an adjustment mechanism) [53] and the control processes

330

are briefly listed as follows [54]:

331

1. Diagnosis information is utilized to correct the reference model and the adjustment mechanism.

332

2. Input information is sent to the real system and the reference model simultaneously.

333

3. The difference between outputs of the real system and the reference model is applied to correct

334 335

the controller in accordance with the adjustment mechanism. Its structure and control process representation are shown in Figure 4.

15

ACCEPTED MANUSCRIPT Diagnosis information

Reference Model

Adjustment Mechanism

Input

Controller

Actual System

+ ﹣

Output

336 337

Figure 4 Structure and control process representation of MRAC

338

Our SCR system is under control to maximize the NOx conversion efficiency and minimize the

339

NH3 leakage by tracking the ammonia coverage ratio reference mentioned in Section 2.3 as a uniform

340

function of the SCR catalyst temperature. Thus, its initial value (  ref ) is described as:

341

  ref  f T 

342

On the other hand, Cs falls while the SCR catalyst is hydrothermally aged and  also decreases

343

to a certain value (0~1) rather than 1 as for any fresh catalyst. It is obvious that the ammonia adsorbed

344

in the SCR catalyst reduces so that the NOx removal capability of the SCR system will decrease

345

correspondingly. Thus, the ammonia coverage ratio reference should rise synchronously to prevent

346

the SCR aging effect. Moreover, the amount of adsorbed ammonia shall remain the same as that in a

347

healthy SCR system.

348

Proposition 1: The following equations as the MRAC reference model are utilized to provide a

349

proper ammonia coverage ratio reference signal (  ref ) for the controller against its SCR aging effect.

350

351

 ref' =

1



(30)

   ref

(31)

' 1,  ref 1  '  ref =  ref , 0   ref'  1  ' 0,  ref  0

(32)

16

ACCEPTED MANUSCRIPT 352

Where:  ref represents the ammonia coverage ratio reference as for the fresh SCR catalyst.  ref

353

represents the adaptive ammonia coverage ratio reference signal for the MRAC controller.

354

The feedback control law shall be applicable to the aging effect of the SCR system to ensure the

355

ammonia coverage ratio shall approach the corresponding reference value. As shown in Eq. (15),

356

nNOx,in, nNH3,in, mEG and T are four necessary input parameters for an SCR aging model, and nNH3,in is

357

only under control but other variables depend on the engine operating conditions. Meanwhile, our

358

SCR system was put into operation to trade-off the NOx conversion efficiency and ammonia leakage

359

based on controlling the ammonia coverage ratio for tracking its corresponding desired value. The

360

urea dosage control model is described as:

361

  [a3 (1   )CNH3  a4  a5CNOx   a6 ]/Cs  CNH3  a 2 nNH3 ,in   a 4  CNH3 [a1a 2 mEGT   a3 (1   )]

362

For convenience, the following parameters are defined:

363

e1     ref     CNH3  u  nNH3 ,in

364

So Eq. (33) can be rewritten as:

365

e1  f1 (e1 )  g1 (e1 )       f 2 (e1 ,  )  g 2  u

366

(34)

(35)

Where:



367

(33)



 f1 (e1 )=  a4 +a5CNO +a6   e1   ref  /Cs  ref x   f 2 (e1 ,  )   a 4  e1   ref     [a1a 2 mEGT   a3 (1  e1   ref )]   g1 (e1 )  a3 (1  e1   ref ) / Cs  g 2  a 2

(36)

368

Proposition 2: the control error (e1) shall converge to zero asymptotically by means of the following

369

MRAC law guarantees,

370

u =    g1 (e1 )  e1  f 2 (e1 ,  )  2 e2  / g 2

(37) 17

ACCEPTED MANUSCRIPT 371 372

Where:  =   f1 (e1 )  1e1  / g1  e2    

(38)

373

Where: 1 and 2 are positive constants.

374

Proof: A positive definite Lyapunov function candidate is selected as Eq. (39) to study the stability

375

of the control error system.

376

1 V1  e12 2

377

The derivative of V1 is described as:

(39)

V1  e1  e1

 e1   f1 (e1 )  g1 (e1 )   

378

(40)

  e  g1 (e1 )  e1e2 2 1 1

379 380

Furthermore, the error dynamic equations are gained in accordance with Eqs. (35) and (38), which are as follows:

381

 e1  f1 (e1 )  g1 (e1 )   e2      e2  f 2 (e1 ,  )  g 2  u  

382

As a result, the Lyapunov function can be augmented as:

383

1 1 V2  e12 + e22 2 2

384

The derivative of V2 is expressed after integration of Eqs. (37) and (40) as:

(41)

(42)

V2  e1e1 +e2 e2  1e12  g1 (e1 )  e1e2  e2   f 2 (e1 ,  )  g 2  u   

385

  e   e  0 2 1 1

(43)

2 2 2

386

Thus, V2 is the negative semi-definite type. What's more, the ammonia coverage ratio

387

asymptotically converges to its corresponding desired value in accordance to the MRAC law (Eq.

388

(37)). 18

ACCEPTED MANUSCRIPT 389 390

4. Results and discussion

391

4.1 Validation of the SCR model

392

The SCR model shall be first verified prior to the simulation study by means of a validation

393

experiment. It shall be accurate enough to predict the NOx emissions and NH3 leakage at the tailpipe.

394

An AC electrical dynamometer was experimentally applied for operation of the diesel engine under

395

ETC so that the transient operation conditions of a heavy-duty vehicle can be simulated.

396

The experimental setup shown in Figure 5 is primarily made up of an AVL PUMA OPEN test

397

bench, a six-cylinder YC6J-42 diesel engine, 13.5L V2O5/WO3-TiO2 catalyst (active phase:

398

V2O5/WO3-TiO2, cell density: 400cpsi, surface area: 61.67m2/g), the urea dosing control unit, the

399

electronic control unit and related measuring equipment. Its after-treatment system is equipped with

400

SEMTECH-EFM2, temperature sensors, AVL DiGas 4000 lights and LDS6. SEMTECH-EFM2 is to

401

measure the exhaust flow rate. The temperature sensors and AVL DiGas 4000 lights located at the

402

upstream and downstream of the catalyst converter are to measure the exhaust temperature and NOx

403

concentration, respectively. The NOx sensor at downstream of catalyst converter is to measure the

404

NOx concentration. The LDS6 is to measure NH3 concentration at the tailpipe. Other parameters such

405

as the urea dosage and the fuel supply per cycle are directly got by means of the CAN bus. The main

406

specifications of the diesel engine and the measuring equipment are presented in Tables 1 and 2,

407

respectively.

19

ACCEPTED MANUSCRIPT

408 409

Figure 5 Schematic diagram of the experimental setup

410 411

Table 1 Engine specification Feature

Parameter

Engine model

Inline 6-cylinder, YC6J-42

Displacement

6.6L

Rated power

132kW

Maximum torque

660N∙m (1200-1700 rpm)

Idle speed

650±50 rpm

20

ACCEPTED MANUSCRIPT 413

Table 2 Measuring and monitoring devices Device

Application AC

Unit

electrical Controlling speed or torque of Speed: rpm

dynamometer and the dynamometer to change Torque: Nm AVL

its control system

PUMA

Accuracy Speed: ±1 rpm Torque: ±0.2%

the engine load Regulating

the

engine /

/

thermodynamic /

/

Throttle actuator OPEN

operating conditions

test

Thermodynamic

Monitoring

bench

parameter

parameters such as cooling

monitoring

water temperature, and intake

system

and exhaust pressures Measuring the exhaust flow kg/h

≤ ±2.5%

SEMTECH-EFM2 rate Measuring AVL DiGas 4000 light

the

NOx ppm

≤ ±0.5%

concentration at the upstream and the downstream pipe

NOx sensor

Measuring

the

concentration

at

NOx ppm

≤ ±0.5%

the

downstream pipe LDS6

Measuring the NH3 Leakage

ppm

Temperature sensor

Measuring the upstream and ℃

≤ ±2% ≤ ±0.9%

the downstream temperature 414 415

Figure 6 shows some major variables such as the exhaust mass flow rates, the urea dosages and

416

temperatures at both sides of the catalyst convertor for an ETC test. The downstream NOx and NH3 21

ACCEPTED MANUSCRIPT 417

emissions can be simulated by means of the SCR model in accordance with major variables for a

418

transient state test.

419 420

Figure 6 Major variables in a transient test cycle

421

Comparison of the measured and simulated results of NOx and NH3 concentrations at the tailpipe

422

is given in Figure 7. Figure 7a indicates that the both results are roughly consistent, and the mean

423

relative and absolute prediction errors are 258.57% and 85.44ppm for the NOx emissions,

424

respectively. It is found that the relative prediction errors are above 100% for 23.7% of total operating

425

points and the corresponding mean relative prediction error is 40.3% except these large relative

426

prediction errors for NOx emissions. Figure 7b shows the NH3 leakage can be predicted well by

427

means of the SCR model and the corresponding mean absolute prediction error is only 0.96ppm.

428

Overall, predicted errors of NOx emissions are relatively large due to three factors:

429

1. Several assumptions were applied to simplify the SCR model.

430

2. The operating conditions fluctuate violently over some periods so that the corresponding NOx

431

and NH3 emissions may be difficultly predicted accurately.

432

3. The performance of EKF observer didn’t work well in such intensive nonlinear process.

433

Although the predicted errors of NOx and NH3 emissions are slightly large under several

434

operating conditions, their trends on simulation are fortunately similar to their corresponding

435

measurements. Thus, our SCR model can be utilized to predict the NOx and NH3 emissions at the

436

tailpipe. 22

ACCEPTED MANUSCRIPT

437 438

(a)

439 440

(b)

441

Figure 7 Comparison of measured and simulated values

442

4.2 SCR performances vs. hydrothermal aging

443

For investigating SCR performances of vanadium catalyst under different aging degrees based

444

on the SCR aging model, simulation was carried out under ESC and ETC to the NOx concentration,

445

NH3 leakage and ammonia coverage ratio based on various aging factors by means of

446

Matlab/Simulink. As for an ESC test, it consists of 13 operating conditions, namely, one idle

447

operating condition and other 12 operating conditions corresponding to four loads (25%, 50%, 75%

448

and 100%) at three different speeds (1325 rpm,1750 rpm and 2175 rpm). As for an ETC test, its

449

duration is 1800 seconds and the duration per operation condition is only 1 second. It is made up of

450

three parts: 23

ACCEPTED MANUSCRIPT 451

The 1st part (0-600s): it is designed to simulate the urban driving cycle.

452

The 2nd part (600-1200s): it is designed to simulate the suburban driving cycle.

453

The 3rd part (1200-1800s): it is designed to simulate the highway driving cycle.

454

Diesel engine operating conditions (including speed and load) for ETC and ESC test are

455

illustrated in Figures 8(a) and 8(b), respectively. These data are taken as simulation inputs in

456

Matlab/Simulink. The exhaust flow rate and temperature profiles under ETC and ESC tests are shown

457

in Figures 9(a) and 9(b).

458 459

(a)

460 461

(b)

462

Figure 8 Diesel engine operating conditions for simulation (a: ETC and b: ESC)

24

ACCEPTED MANUSCRIPT

463 464

(a)

465 466

(b)

467

Figure 9 The exhaust flow rate and temperature profiles (a: ETC and b: ESC)

468

469 470

(a)

25

ACCEPTED MANUSCRIPT

471 472

(b)

473

Figure 10 Urea dosage under various aging degrees (a: ETC and b: ESC)

474 475

(a)

476 477

(b)

478

Figure 11 Ammonia coverage ratio under various aging degrees (a: ETC and b: ESC) 26

ACCEPTED MANUSCRIPT

479 480

(a)

481 482

(b)

483

Figure 12 NOx conversion efficiency under various aging degrees (a: ETC and b: ESC)

484 485

(a)

27

ACCEPTED MANUSCRIPT

486 487

(b)

488

Figure 13 Ammonia leakage under various aging degrees (a: ETC and b: ESC)

489

Table 3 SCR performances in different aging factors

Aging factor

Mean NOx conversion

Mean NH3 leakage

Peak NH3 leakage

efficiency [%]

[ppm]

[ppm]

ETC

ESC

ETC

ESC

ETC

ESC

1

76.76

86.52

2.31

2.53

5.61

5.82

0.8

72.73

83.85

2.68

2.87

5.80

6.62

0.6

66.92

79.81

3.22

3.41

6.75

7.86

490 491

Figure 10 illustrates urea dosage in ETC and ESC tests while the aging factor are among 0.6 to

492

1 at a step of 0.2. Figures 10a and 10b indicate that the urea dosage declines along with the growth

493

of the aging factor in both ETC and ESC test. It is possibly because the urea dosage necessarily

494

reduces to control ammonia coverage ratio tracking the desired value, owing to the fact that the

495

ammonia storage capability of the SCR catalyst decreases with the growth of the aging factor.

496

Figure 11 illustrates ammonia coverage ratio in ETC and ESC tests under various aging factors.

497

Figures 11a and 11b show that ammonia coverage ratio can be under control to track the desired

498

value under various aging degrees. It indicates that the control of ammonia coverage ratio is not

499

remarkably impacted by SCR catalyst hydrothermal aging. 28

ACCEPTED MANUSCRIPT 500

Figure 12 shows the NOx conversion efficiency in ETC and ESC tests under different aging

501

factors. Figures 12a and 12b noticeably show that the NOx conversion efficiency rises along with the

502

growth of the aging factor. Moreover, the relationship between the mean NOx conversion efficiency

503

and the aging factor is presented in Table 3. It indicates that the former falls along with the growth

504

of the latter but there is not a linear relationship between the catalyst aging degree and NOx emissions,

505

and the NOx conversion efficiency in ESC test is slightly less affected by SCR catalyst hydrothermal

506

aging than that in ETC test.

507

Figure 13 illustrates the ammonia leakage under various aging degrees in ETC and ESC test.

508

Figures 13a and 13b both show that the ammonia leakage from the tailpipe is minimal as for the

509

fresh catalyst but the worst aged catalyst would lead to the maximum ammonia leakage. In contrast

510

to Figure 10, the ammonia leakage still increases remarkably in spite of the urea dosage falling along

511

with the growth of the aging factor. It is possibly because the decline of urea dosage can’t offset the

512

negative impact of decreasing the ammonia storage capability on ammonia leakage. For more visual

513

demonstration of the control effect on the NH3 leakage, the evaluation indexes of NH3 leakage are

514

given in Table 3. It indicates that the mean NH3 leakage and the peak NH3 leakage increase faster

515

along with the growth of the catalyst aging degree in ETC and ESC tests although they are still within

516

the emission limits. Especially, it is noted that they conform to the same law as that for the mean NOx

517

conversion efficiency along with the growth of the aging factor.

518

Obviously, the SCR performances are not only worsened but also deteriorated faster along with

519

the growth of the catalyst aging degree and the same results were reported in our previous work [55].

520

4.3 Failure-diagnosis and tolerant control performances of a hydrothermally aged SCR system

521

As discussed above, SCR performances are significantly affected by means of the catalyst aging

522

degree. For the sake of monitoring the catalyst aging degree, precise diagnosis of the catalyst

523

hydrothermal aging degree shall be necessary. Quantitative estimation is performed here under

524

various hydrothermal aging conditions by means of the EKF-based observer. The measurement noises

525

are taken into account in actual cases and the measurements of the downstream NOx and NH3 29

ACCEPTED MANUSCRIPT 526

concentrations regarded as the observer vector in the EKF are subject to a band-limited white noise.

527

Figure 14 and Figure 15 show the relationship between diagnosis performances under various

528

aging factors (range: 0.6-1, step size: 0.2) in ETC and ESC tests, respectively. Figures 14(a), 14(b)

529

and 14(c) illustrate that the observed aging factor can track the actual value in about 0.3s in ETC test.

530

In addition, Figures 15(a), 15(b) and 15(c) show that the observed value can follow the actual one

531

within 0.2s in ESC test. Comparison of Figures 14 and 15 clearly indicates that diagnosis

532

performance in ESC test is slightly better than that in ETC test. But the actual aging factor can

533

generally be accurately and rapidly tracked by means of our observer in spite of the catalyst aging

534

degree in both ETC and ESC tests. Thus, there is no doubt that the catalyst aging factor can be

535

estimated accurately by means of our qualified EKF-based observer. In addition, while the observed

536

aging factor satisfy the stability judgment principles for estimation of processes of the EKF (Section

537

3.1), the diagnosis information can be thought to be valid to the failure-tolerant controller.

538 539

(a)

30

ACCEPTED MANUSCRIPT

540 541

(b)

542 543

(c)

544

Figure 14 Diagnosis performances vs. the aging factor in ETC test

545 546

(a)

31

ACCEPTED MANUSCRIPT

547 548

(b)

549 550

(c)

551

Figure 15 Diagnosis performances vs. the aging factor in ESC test

552 553

(a)

32

ACCEPTED MANUSCRIPT

554 555

(b)

556

Figure 16 Urea dosage vs. the aging factor under failure-tolerant control (a: ETC and b: ESC)

557 558

(a)

559 560

(b)

561

Figure 17 Ammonia coverage ratio vs. the aging factor under failure-tolerant control (a: ETC and

562

b: ESC) 33

ACCEPTED MANUSCRIPT

563 564

(a)

565 566

(b)

567

Figure 18 NOx conversion efficiency vs. the aging factor under failure-tolerant control (a: ETC and

568

b: ESC)

569 570

(a)

34

ACCEPTED MANUSCRIPT

571 572

(b)

573

Figure 19 Ammonia leakage vs. the aging factor under failure-tolerant control (a: ETC and b: ESC)

574

Table 4 SCR performances in various aging factors for the failure-tolerant controller

Aging factor

Mean NOx conversion

Mean NH3 leakage

Peak NH3 leakage

efficiency [%]

[ppm]

[ppm]

ETC

ESC

ETC

ESC

ETC

ESC

1

76.91

86.63

2.32

2.53

5.73

5.59

0.8

76.89

86.62

3.05

3.21

7.76

7.07

0.6

76.85

86.59

4.48

4.40

12.30

9.62

575 576

The urea dosage can be corrected by means of the MRAC based on the diagnosis information

577

from the EKF-based observer to ensure the ammonia coverage ratio approaching its target value. As

578

shown in Figure 16, the urea dosages are regulated to almost the same level regardless of catalyst

579

aging degrees in ETC and ESC tests. As illustrated in Figure 17, the ammonia coverage ratio is

580

controlled to track the new ammonia coverage ratio reference under various aging conditions in ETC

581

and ESC tests. Figure 18 illustrates the relationship between the NOx conversion efficiency and the

582

aging factor (range: 0.6-1, step size: 0.2) under the hydrothermal aging failure-tolerant control mode

583

in ETC and ESC tests. Figures 18(a) and 18(b) show that the NOx conversion efficiency is insensitive

584

to the catalyst aging degree in ETC and ETC respectively. It rises by 0.15%, 4.16% and 9.93% in 35

ACCEPTED MANUSCRIPT 585

ETC, and 0.11%, 2.77% and 6.78% in ESC under the aging failure-tolerant control mode, respectively,

586

in comparison with those (Tables 4 and 3) under the corresponding aging conditions. Thus, the higher

587

the SCR catalyst aging degree is the more remarkable the fault-tolerant control effect is. Figure 19

588

obviously shows that the NH3 leakage still falls along with the growth of the aging factor (set values:

589

1, 0.8 and 0.6) under the aging failure-tolerant control mode although the ammonia input is almost

590

the same in spite of catalyst aging conditions in ETC and ESC tests respectively. It may because that

591

the net adsorption capability of SCR catalyst declines with the growth of catalyst aging degree.

592

Moreover, the mean and peak NH3 leakages in Table 4 are mostly more than those in Table 3 under

593

the corresponding aging conditions, respectively. Although the NH3 leakage of the failure-tolerant

594

control system is more than that of the baseline control system, it rises only slightly and it still not

595

exceeds the emission limit while the aging degree increases. Thus, the failure-tolerant control effects

596

of MRAC shall be better than those of any PID controller against the catalyst aging effect in both

597

ETC and ESC test.

598 599

5 Conclusions

600

The quantitative identification of the vanadium catalyst hydrothermal aging degree was carried

601

out here on the basis of our EKF-based observer, based on whose diagnosis information an MRAC

602

based on the Lyapunov stability principles was designed to achieve the SCR aging failure-tolerant

603

control mode. Modeling and simulation was performed in Matlab/Simulink and various aspects were

604

discussed in detail.

605

Our work comes to the conclusions as follow:

606

1. The ammonia-coverage-ratio-based closed-loop control strategy was applied to our SCR

607

model and the transient test results were verified so that the NOx emissions and NH3 leakage out of

608

the catalyst convertor could be predicted by means of our SCR model. Then, the SCR aging model

609

was established based on the definition of the aging factor (α) and the aging degree was primarily

610

affected by the concentration of active atoms with respect to the volume of SCR catalyst (Cs). 36

ACCEPTED MANUSCRIPT 611

2. The relationship between the aging effect and the performances of a SCR system under the

612

ammonia-coverage-ratio-based closed-loop control was studied by means of the SCR aging model

613

under various aging factors (α), and the transient and steady-state test results indicate that

614

performances of the SCR control system are significantly deteriorated due to the SCR catalyst aging

615

effect.

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3. The catalyst aging states were diagnosed rapidly and precisely by means of our EKF-based

617

observer in ETC and ESC tests. Moreover, the stability judgment principles for estimation of EKF

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processes in the beginning phase were put forward to guarantee the stabilization of diagnosis

619

information.

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4. A MRAC was designed based on the Lyapunov stability principle to achieve the SCR aging

621

failure-tolerant control strategy in accordance with the diagnosis information from the EKF-based

622

observer. The simulation results indicated that in comparison with that under baseline control mode,

623

the NOx conversion efficiency improved by 0.15%, 4.16% and 9.93% in ETC, and 0.11%, 2.77% and

624

6.78% in ESC respectively when the aging factor is 1, 0.8 and 0.6 respectively; meanwhile, NH3

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leakage just slightly increased and didn’t exceed the emission limit under the aging failure-tolerant

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control mode. It proved that SCR aging failure-tolerant control system performed well against SCR

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catalyst aging effect.

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This paper provides an original idea to investigate the deactivation of SCR catalyst, which is

629

beneficial to save research cost and time. Meanwhile, it is the theoretical basis for practical

630

engineering application of SCR catalyst failure diagnosis and tolerant control system. In the future’s

631

work, we will focus on optimizing the urea injection control strategy, SCR catalyst failure diagnosis

632

method and failure-tolerant control method to improve control accuracy and stability of the SCR

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system. Furthermore, we will validate effectivity of SCR catalyst failure diagnosis and tolerant

634

control method by means of engine bench test.

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37

ACCEPTED MANUSCRIPT 636

Acknowledgments

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The authors wish to gratefully acknowledge the Hubei Key Laboratory of Advanced Technology

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for Automotive Components (Wuhan University of Technology). This study was financially

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supported by the National Key R & D Program of China (Grant No. 2017YFC0211203), National

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Natural Science Foundation (Grant No. 51406140), National Engineering Laboratory for Mobile

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Source Emission Control Technology (Grant No. NELMS2017A08), Natural Science Foundation of

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Hubei Province (Grant No. 2018CFB592) and 111 Project (Grant No. B17034).

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ACCEPTED MANUSCRIPT Highlights research 1.

The aging effect on the performance of SCR control system was studied

2.

EKF observer was designed to quantitatively diagnose SCR catalyst aging

condition 3.

The Lyapunov-based MRAC controller was proposed against SCR catalyst aging