SCIENCE CHINA Information Sciences, Volume 62, Issue 6: 062201(2019) https://doi.org/10.1007/s11432-018-9638-7

An ammonia coverage ratio observing and tracking controller: stability analysis and simulation evaluation

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  • ReceivedFeb 6, 2018
  • AcceptedOct 31, 2018
  • PublishedApr 23, 2019


In urea selective catalytic reduction (urea-SCR) systems, theammonia coverage ratio is an important parameter for satisfyingemission regulations. However, this parameter cannot be directly measured byonboard sensors. Most of observersand tracking controllers for the ammonia coverage ratio in theexisting literature were designed separately and lacked an overallrobustness analysis. In this paper, an observing and tracking controller (AOTC), along with its overall design andstability analysis, is proposed under input-to-state stability (ISS)theory. The proposed AOTC strategy consists of a sliding modeobserver based on ${\rm~NH}_3$ concentration dynamics and a trackingcontroller based on the observer dynamics. The stability is discussed considering theuncertainties about the conversion of urea to ${\rm~NH}_3$ and the cross-sensitivityof the ${\rm~NO}_x$ sensor, and the principle for adjusting the control parameters is provided. A few transientsimulations are conducted to evaluate the effectiveness of theproposed AOTC strategy.


This work was supported by National Nature Science Foundation of China (Grant Nos. 61773009, U1864201, 61703177) and Jilin Province Science and Technology Development Plan (Grant Nos. 20180101067JC, 201903021 05GX, JJKH20180144KJ, JJKH20190999KJ).


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  • Figure 1

    (Color online) Schematic diagram of urea-SCR reactions.

  • Figure 2

    Block diagram of the proposed AOTC strategy.

  • Figure 3

    (Color online) Transient operating conditions of ETC.

  • Figure 4

    Input data for modeling of urea-SCR system. (a) Engine out NO$_{~x}$; (b) AdBlue inlet mass; (c) engine out temperature; (d) exhaust flow.

  • Figure 5

    Output data for modeling of urea-SCR system. (a) Urea-SCR out NH$_{3}$; (b) urea-SCR out NO$_{~x}$.

  • Figure 6

    (Color online) Transient simulation test platform.

  • Figure 7

    (Color online) Result of validation. (a) Validation of urea-SCR out NH$_{3}$; (b) validation of urea-SCR out NO$_{~x}$.

  • Figure 8

    (Color online) Part of the operating conditions of FTP75.

  • Figure 9

    (Color online) Effect comparison of estimator under the nominal condition (FTP75).

  • Figure 10

    (Color online) Error rate comparison of estimator under the nominal condition (FTP75).

  • Figure 11

    (Color online) The curve of $\eta$ under environment and conditions of FTP75.

  • Figure 12

    (Color online) Error rate of mechanism observer under nominal and non-nominal conditions of FTP75.

  • Figure 13

    (Color online) Error rate of ISS sliding mode observer under nominal and non-nominal conditions of FTP75.

  • Figure 14

    (Color online) Ammonia coverage ratio control in the FTP75 cycle.

  • Figure 15

    (Color online) Comparison results of before and after considering parameter uncertainties and measurement disturbance (FTP75). (a) Comparison of urea-SCR out NH$_{3}$; (b) comparison of NO$_{~x}$ conversion.

  • Figure 16

    (Color online) Comparison results of before and after considering parameter uncertainties and measurement disturbance (ETC). (a) The curve of $\eta~$; (b) comparison of urea-SCR out NH$_3$; (c) comparison of NO$_x$ conversion.

  • Table 1   Nomenclature of constants
    Symbol Description Value Unit
    $S_c$ The area of one mole of active surface atoms 581 m$^2$/mol
    $\alpha_{\rm~prob}$ Sticking probability 1.11E$-$3
    $c_s$ Concentration of active surface atoms with respect to gas volume in converter 7.30 mol/m$^3$
    $c_{\rm~p,EG}~$ Specific heat at constant pressure of exhaust gas 1060 J/kgK
    $c_{\rm~p,c}~~$ Specific heat of the catalysts 1054 J/kgK
    $M_{\rm~NH_3}~$ Molar mass of ${\rm~NH}_3$ 17 g/mol
    $R$ Universal gas constant 8.3145 J/molK
    $R_{\rm~S,EG}$ Gas constant of engine 288 J/kgK
    $P_{\rm~amb}$ Ambient pressure 101325 Pa
    $V_c~$ Total volume of the urea-SCR system 0.01 m$^3$
    $m_c$ Mass of catalytic converter 19 kg
    $\varepsilon~$ Ratio of gas to total converter volume 0.81
    $\varepsilon_{\rm~rad,scr}$ Radiation coefficient of silencer0.507
    $\sigma_{\rm~sb}$ Radiation constant5.67E$-$8
    $A_{\rm~rad,scr}~$ Radiating surface area of the silencer0.9044 m$^2$
    $M_{\rm~Adblue}$ Molar mass of urea 60 g/mol
    $C_{\rm~Adblue}~$ Urea solution concentration32.5%
    $k_{\rm~Des}$ Pre-exponential factor of desorption $^*$1/s
    $k_{\rm~SCR}$ Pre-exponential factor of urea-SCR $^*$m$^2$/s
    $k_{{\rm~O}_x}~$ Pre-exponential factor of ${\rm~NH}_3$ oxidation$^*$1/s
    $E_{a,\rm~Des}$ Activation energy of desorption $^*$J/mol
    $E_{a,\rm~SCR}$ Activation energy of urea-SCR $^*$J/mol
    $E_{a,~{\rm~O}_x}$ Activation energy of ${\rm~NH}_3$ oxidation $^*$J/mol


  • Table 2   Nomenclature of variables
    Symbol Description Unit
    $C_{x}$ Molar concentration of species $x$ mol/m$^3$
    $n^\ast_{x}$ Molar mass flow of species $x$ mol/s
    $m^\ast_{\rm~EG}$ Exhaust gas mass flow kg/s
    $T$ Internal temperature of SCR systems K
    $T_{\rm~in}$ Exhaust gas temperature of engine K
    $T_{\rm~amb}~$ Ambient temperature K
    $\Theta_{\rm~NH_3}$ Scaled surface coverage with ${\rm~NH}_3$ in an SCR cell
  • Table 3   Parameter identification results
    Symbol Value Unit Symbol Value Unit
    $k_{\rm~des,1}$ 0.72 1/s $E_{a,\rm~Des,1}$ 14.34 J/mol
    $k_{\rm~des,2}$ 0.63 1/s $E_{a,\rm~Des,2}$ 15.43 J/mol
    $k_{\rm~des,3}$ 0.51 1/s $E_{a,\rm~Des,3}$ 16.22 J/mol
    $k_{\rm~des,4}$ 0.45 1/s $E_{a,\rm~Des,4}$ 17.14 J/mol
    $k_{\rm~SCR,1}$ 3.30 m$^2$/s $E_{a,\rm~SCR,1}$ 26324 J/mol
    $k_{\rm~SCR,2}$ 2.71 m$^2$/s $E_{a,\rm~SCR,2}$ 28115 J/mol
    $k_{\rm~SCR,3}$ 2.55 m$^2$/s $E_{a,\rm~SCR,3}$ 30108 J/mol
    $k_{\rm~SCR,4}$ 2.14 m$^2$/s $E_{a,\rm~SCR,4}$ 32034 J/mol
    $k_{{\rm~O}_x,1}~$ 5.21 1/s $E_{a,{\rm~O}_x,1}$ 0.71 J/mol
    $k_{{\rm~O}_x,2}~$ 4.43 1/s $E_{a,{\rm~O}_x,2}$ 1.03 J/mol
    $k_{{\rm~O}_x,3}~$ 3.26 1/s $E_{a,{\rm~O}_x,3}$ 1.25 J/mol
    $k_{{\rm~O}_x,4}~$ 2.64 1/s $E_{a,{\rm~O}_x,4}$ 1.51 J/mol

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