Selective catalytic reduction (SCR) systems are commonly used for exhaust gas aftertreatment in many applications. For optimal NO_x reduction using the SCR technique a certain temperature must be reached. This study deals with modelling and control of the temperature inside the SCR system for optimal catalyst operation. A first principle-based model is described for the propagation of the temperature inside the catalyst. The model is described in linear parameter varying (LPV) state-space form and used for control of the temperature using a linear-quadratic-Gaussian (LQG) controller. Necessary conditions for obtaining an optimal controller without complete state information are defined. This leads to a discrete-time LQG controller for LPV systems. The results obtained for the controller are based on several assumptions to ensure the stability of the controller. The states of the proposed model are not measurable. For this purpose, a Kalman filter-based observer is designed for estimation of the states that are used for state feedback in the controller. The observer is designed for discrete-time LPV systems and necessary assumptions for the observer are derived in the work. The resulting model of the temperature gives a model fit of up to 77% for validation data and the controller requirements are met using the proposed controller applied in a simulator environment.

References

1. 1)
  - 6. Tayamon, S.: ‘Nonlinear system identification with applications to selective catalytic reduction systems’, Licentiate Thesis at Uppsala University, 2012.
2. 2)
  - 11. Cavina, N., Mancini, G., Corti, E., Moro, D.: ‘Thermal management strategies for SCR aftertreatment systems’. Tech. rep.. SAE Technical Paper 2013-24-0153, 2013.
3. 3)
  - 15. Mohammadpour, J., Scherer, C.W.: ‘Control of linear parameter varying systems with applications’ (Springer, 2012).
4. 4)
  - 27. Tóth, R., Felici, F., Heuberger, P.S.C., Van den Hof, P.M.J.: ‘Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation’. Proc. of the European Control Conf., 2007, pp. 5418–5425.
5. 5)
  - 13. Steven, H.: ‘Development of a world-wide harmonised heavy-duty engine emissions test cycle’ Tech. report. United Nations, 2001.
6. 6)
  - 2. Westerlund, C., Westerberg, B., Odenbrand, I., Egnell, R.: ‘Model predictive control of a combined EGR/SCR HD Diesel engine’, Tech. report. SAE Technical Paper 2010-36-03-06; 2010.
7. 7)
  - 9. Sluder, C.S., Storey, J.M.E., Lewis, S.A., Lewis, L.A.: ‘Low temperature urea decomposition and SCR performance’. Tech. report. SAE Paper nr 2005-01-1858, 2005.
8. 8)
  - 1. Lloyd, A.C., Cackette, T.A.: ‘Diesel engines: environmental impact and control’, J. Air Waste Manag. Assoc., 2011, 51, (6), pp. 809–847 (doi: 10.1080/10473289.2001.10464315).
9. 9)
  - 24. Katayama, T., Ohki, T., Inoue, T., Kato, T.: ‘Design of an optimal controller for a discrete-time system subject to previeable demand’, Int. J. Control, 1985, 41, pp. 677–699 (doi: 10.1080/0020718508961156).
10. 10)
  - 31. Rough, W.J.: ‘Linear system theory’ (Prentice-Hall, 1996).
11. 11)
  - 30. Kwakernaak, H., Sivan, R.: ‘Linear optimal control systems’ (Wiley Interscience, 1972).
12. 12)
  - 28. Rödönyi, G., Bokor, J., Lantos, B.: ‘LQG control of LPV systems with parameter dependent Lyapunov function’. Proc. of the 10th Mediterranean Conf., 2002.
13. 13)
  - 14. Tóth, R.: ‘Modeling and identification of linear parameter varying systems’ (Springer, 2010).
14. 14)
  - 7. Hsieh, M.F., Wang, J.: ‘A two-cell backstepping based control strategy for diesel engine selective catalytic reduction systems’, IEEE Trans. Control Syst. Tech., 2011, 19, (6), pp. 1504–1515 (doi: 10.1109/TCST.2010.2098477).
15. 15)
  - 26. Kalman, R.E.: ‘Mathematical description of linear dynamical systems’, SIAM Control, 1963, 1, (2), pp. 152–192.
16. 16)
  - 20. Westerberg, B., Künkel, C., Odenbrand, C.U.I: ‘Transient modelling of a HC-SCR catalyst for diesel exhaust aftertreatment’, Chem. Eng. J., 2003, 92, pp. 27–39 (doi: 10.1016/S1385-8947(02)00118-3).
17. 17)
  - 17. Besselmann, T., Löfberg, J., Morari, M.: ‘Explicit MPC for LPV systems: stability and optimality’, IEEE Trans. Autom. Control, 2012, 57, pp. 2322–2332 (doi: 10.1109/TAC.2012.2187400).
18. 18)
  - 5. Schär, C.M., Onder, C.H., Geering, H.P.: ‘Control of an SCR catalytic converter system for a mobile heavy-duty application’, IEEE Trans. Control Syst. Tech., 2006, 14, (4), pp. 641–653 (doi: 10.1109/TCST.2006.876634).
19. 19)
  - 25. Söderström, T.: ‘Discrete-time stochastic systems: estimation and control’ 2nd ed. (London, U.K., Springer-Verlag, 2002).
20. 20)
  - 4. Ericson, C.: ‘Model Based Optimization of a Complete Diesel Engine/SCR System’ Ph.D. thesis. Lund University. Lund, Sweden, 2009.
21. 21)
  - 19. Nova, I., Grossale, A., Tronconi, E.: ‘Nitrates and fast SCR reaction in NOx removal from diesel engine exhausts’, Chem. Today, 2009, 27, (3), pp. 17–19.
22. 22)
  - 8. Rasheed, W.A., Goyal, P., Joseph, C.: ‘Model based control for a selective catalytic reduction SCR system in exhaust gas aftertreatment system for a diesel engine’. Proc. of Int. Conf. on Energy Efficient Technologies for Sustainability (ICEETS).Nagercoil – India, 2013, pp. 744–749.
23. 23)
  - R. Tóth , P.S.C. Heuberger , P.M.J. Van den Hof . Discretisation of linear parameter-varying state-space representations. IET Control Theory Appl. , 10 , 2082 - 2096
24. 24)
  - 18. Girard, J.W., Montreuil, C., Kim, J., Cavataio, G., Lambert, C.: ‘Technical advantages of vanadium SCR systems for diesel NOx control in emerging markets’, SAE Int. J. Fuels Lubricants, 2009, 1, (1), pp. 488–494.
25. 25)
  - 22. Söderström, T., Stoica, P.: ‘System identification’. (Hemel Hempstead, UK, Prentice-Hall International, 1989).
26. 26)
  - 29. Wu, W.: ‘Time-varying feedforward and output feedback controllers for non-linear time delay processes’, Int. J. Syst. Sci., 2000, 31, pp. 315–330 (doi: 10.1080/002077200291163).
27. 27)
  - 21. Ljung, L.: ‘System identification toolbox - for use with MATLAB, User's Guide’ 5th edn. The Mathworks, Inc.Sherborn, Mass, 2000.
28. 28)
  - 16. Wu, F., Packard, A.: ‘LQG control design for LPV systems’. Proc. of American Control Conf.Seattle – WA, 1995, pp. 4440–4444.
29. 29)
  - 3. Upadhyay, D., Van-Nieuwstadt, M.: ‘Modeling of a urea SCR catalyst with automotive application’. Proc. of the ASME Int. Mechanical Engineering Congress & Exposition, 2002, pp. 707–713.
30. 30)
  - 10. Schmeisser, V., Hernando, M.W.L.S., Nova, I.: ‘Cold start effect phenomena over zeolite scr catalysts for exhaust gas aftertreatment’, SAE Int. J. Commercial Veh., 2013, 6, (1), pp. 190–199.
31. 31)
  - 12. Chen, P., Wang, J.: ‘Control-oriented model for integrated diesel engine and aftertreatment systems thermal management’, Control Eng. Pract., 2014, 22, pp. 81–93 (doi: 10.1016/j.conengprac.2013.09.009).

Model-based temperature control of a selective catalytic reduction system

References

Related content