Solución analítica de un filtro de Kalman estacionario para la observación de deriva en modelos de emisiones de NOx en motores diesel de automoción

C. Guardiola, S. Hoyas, B. Pla, D. Blanco Rodríguez

Resumen

En los algoritmos de control y diagnóstico de los motores diesel la precisión en la estimación de las variables resulta crítica. En el caso de las emisiones de óxidos de nitrógeno (NOx) recientemente se han desarrollado sensores con una buena precisión de medida estacionaria pero que, debido a su lentitud y a la existencia de un retraso significativo, presentan unas características dinámicas insuficientes para el control. Por otro lado, existen diferentes tipos de modelos capaces de reproducir con mayor o menor precisión la respuesta dinámica de los NOx; sin embargo, ninguno de ellos está exento de deriva asociada al envejecimiento del motor y de los diferentes sensores que suministran las entradas al modelo. La combinación de un modelo de emisiones con un sensor de NOx permite proporcionar una estimación que combina las características dinámicas del modelo con la precisión del sensor. En este trabajo se combina la información a través de un modelo en espacio de estados que permite la observación y corrección de la deriva del modelo de NOx. El vector de estado que describe la salida objetivo se aumenta con un estado extra que define la deriva o error estacionario entre el modelo derivado y la referencia de medida del sensor. El vector de estado es observado mediante un filtro de Kalman. Dicho modelo es lineal invariante en el tiempo y las covarianzas de los ruidos que afectan a los estados son consideradas como constantes. Bajo estas hipótesis, el filtro es estacionario, es decir, la ecuación de Riccati que estima la ganancia del filtro converge tras un número determinado de iteraciones. El presente artículo resuelve la ecuación iterativa de Riccati para dichas condiciones y deriva la solución analítica del filtro. Asimismo, dicho algoritmo es usado para la estimación de NOx en un motor diesel y en el nuevo ciclo Europeo de conducción (NEDC).

Palabras clave

Filtro de Kalman; fusión de datos; corrección de derivas; automoción; NOx; diesel

Texto completo:

PDF

Referencias

Alberer, D., del Re, L., 2009. Fast oxygen based transient diesel engine operation. SAE Technical Paper 2009-01-0622.

Andersson, M., Hultqvist, A., Johansson, B., Nohre, C., 2006. ¨ Fast physical NOx prediction in diesel engines. In: The Diesel Engine: The Low CO2 and Emissions Reduction Challenge (Conference Proceedings), Lyon.

Arsie, I., Pianese, C., Sorrentino, M., 2010. Development of recurrent neural networks for virtual sensing of NOx emissions in internal combustion engines. SAE International Journal of Fuels and Lubricants 2 (2), 354–361.

Benaicha, F., Bencherif, K., Sorine, M., Vivalda, J., 2011. Model based mass soot observer of diesel particle filter. In: IFAC Proceedings Volumes (IFACPapersOnline). Vol. 18. pp. 10647–10652.

Chauvin, J., Moulin, P., Corde, G., Petit, N., Rouchon, P., 2006. Kalman filtering for real-time individual cylinder air fuel ratio observer on a diesel engine test bench. In: Proceedings of the American Control Conference. Vol. 2006. pp. 1886–1891.

Desantes, J., Lopez, J., Red ´ on, ´ P., Arregle, J., 2012. ` Evaluation of the thermal no formation mechanism under low-temperature diesel combustion conditions. International Journal of Engine Research 13 (6), 531–539.

Ekstrand, B., 1983. Analytical steady state solution for a kalman tracking filter. IEEE Transactions On Aerospace and Electronic Systems AES-19 6.

EU, 2009. Regulation (EC) No 443/2009 of the European Parliament and of the Council of 23 April 2009 setting emission performance standards for new passenger cars as part of the Community’s integrated approach to reduce CO2 emissions from light-duty vehicles. Official Journal of the European Union.

Faouzi, N.-E., Leung, H., Kurian, A., 2011. Data fusion in intelligent transportation systems: Progress and challenges - a survey. Information Fusion 12 (1), 4–10.

Galindo, J., Lujan, J., Climent, H., Guardiola, C., 2007. ´ Turbocharging system design of a sequentially turbocharged diesel engine by means of a wave action model. SAE Technical Paper 2007-01-1564.

Galindo, J., Serrano, J., Guardiola, C., Blanco Rodríguez, D., Cuadrado, I., 2011. An on-engine method for dynamic characterisation of NOx concentrations sensors. Experimental Thermal and Fluid Science 35 (3), 470-476.

Gao, J., Harris, C., 2002. Some remarks on kalman filters for the multisensor fusion. Information Fusion 3, 191–201.

Geupel, A., Kubinski, D., Mulla, S., Ballinger, T., Chen, H., Visser, J., Moos, R., 2011. Integrating NOx sensor for automotive exhausts - a novel concept. Sensor Letters 9 (1), 311–315.

Grünbacher E., Kefer, P., del Re, L., 2005. Estimation of the mean value engine torque using an extended kalman filter. SAE Technical Paper 2005-01-0063. DOI: 10.4271/2005-01-0063

Guardiola, C., Climent, H., Pla, B., Blanco-Rodriguez, D., 2014a. Ecu oriented models for NOx prediction. part 2: adaptive estimation by using an nox sensor. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering Online. DOI: 10.1177/0954407014561278

Guardiola, C., Pla, B., Blanco-Rodriguez, D., Calendini, P., 2014b. Ecu oriented models for NOx prediction. part 1: A mean value engine model for NOx prediction. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering Online. DOI: 10.1177/0954407014550191

Guardiola, C., Pla, B., Blanco-Rodriguez, D., Eriksson, L., 2013a. A computationally efficient kalman filter based estimator for updating look-up tables applied to NOx estimation in diesel engines. Control Engineering Practice 21 (11), 1455–1468.

Guardiola, C., Pla, B., Blanco-Rodriguez, D., Mazer, A., Hayat, O., 2013b. A bias correction method for fast fuel-to-air ratio estimation in diesel engines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 227 (8), 1099–1111.

Hewer, G., 1973. Analysis of a discrete matrix riccati equation of linear control and kalman filtering. Journal of Mathematical Analysis and Applications 42, 226–236.

Höckerdal, E., Frisk, E., Eriksson, L., 2009. Observ ¨ er design and model augmentation for bias compensation with a truck engine application. Control Engineering Practice 17 (3), 408–417.

HORIBA, August 2001. Horiba MEXA-7000DEGR instruction manual.

Hsieh, M.-F., Wang, J., 2011. Design and experimental validation of an extended kalman filter-based NOx concentration estimator in selective catalytic reduction system applications. Control Engineering Practice 19 (4), 346– 353.

Johnson, T., 2012. Vehicular emissions in review. SAE Technical Paper 2012- 01-0368 5 (2).

Kalman, R., 1960. A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82 (35-45).

Kalman, R., Bucy, R., 1961. New results in linear filtering and prediction theory. Journal of Basic Engineering, 95–108.

Karlsson, M., Ekholm, K., Strandh, P., Tunestål, P., Johansson, R., 2010. Dynamic mapping of diesel engine through system identification. In: Proc. American Control Conference. Baltimore, MD.

Kato, N., Nakagaki, K., Ina, N., 1996. Thick film ZrO2 NOx sensor. SAE Technical Paper 960334.

Khaleghi, B., Khamis, A., Karray, F., Razavi, S., 2013. Multisensor data fusion: A review of the state-of-the-art. Information Fusion 14 (1), 28 – 44.

Lainiotis, D., Assimakis, N., Katsikas, S., 1994. A new computationally effective algorithm for solving the discrete riccati equation. Journal of Mathematical Analysis and Applications 3, 868–895.

Nash Jr., R., 1967. The general solution to a second order optimal filtering problem. Proceedings of the IEEE 55, 93–94.

Payri, F., Lujan, J., Guardiola, C., Pla, B., 2012. ´ A challenging future for the ic engine: New technologies and the control role. Keynote in ECOSM 2012 Workshop on Engine and Powertrain Control, Simulation and Modeling.

Poloni, ´ T., Rohal’-Ilkiv, B., Alberer, D., del Re, L., Johansen, T., 2012. Comparison of Sensor Configurations for Mass Flow Estimation of Turbocharged Diesel Engines. Vol. 418 of Lecture Notes in Control and Information Sciences.

Schilling, A., 2008. Model-based detection and isolation of faults in the air and fuel paths of common-rail di diesel engines equipped with a lambda and a nitrogen oxides sensor. Ph.D. thesis, ETH-Zurich.

Schilling, A., Amstutz, A., Onder, C., Guzzella, L., 2006. A real-time model for the prediction of the NOx emissions in DI diesel engines. In: Proceedings of the 2006 IEEE International Conference on Control Applications. Munich, Germany.

Simon, D., 2001. Kalman filtering. Embedded Systems Programming 14, no. 6, 72–79.

Smith, J., 2000. Demonstration of a fast response on-board NOx sensor for heavy-duty diesel vehicles. swri project no. 03-02256 contract no. 98-302. Tech. rep., Southwest Research Institute Engine and Vehicle Research Division P.O. Box 28510 San Antonio, Texas 78228-0510.

Sudano, J., 1995. Analytical solution for a steady-state kalman filter tracker with random power spectral density process noise. In: Aerospace and Electronics Conference. NAECON 1995., Proceedings of the IEEE National 748-751 vol.2.

Surenahalli, H., Parker, G., Johnson, J., Devarakonda, M., 2012. A kalman filter estimator for a diesel oxidation catalyst during active regeneration of a cpf. In: Proceedings of the American Control Conference. pp. 4969–4974.

Trimboli, S., Di Cairano, S., Bemporad, A., Kolmanovsky, I., 2012. Model Predictive Control with Delay Compensation for Air-to-Fuel Ratio Control. Vol. 423 of Lecture Notes in Control and Information Sciences. Springer-Verlag Berlin Heidelberg 2012.

Tschanz, F., Amstutz, A., Onder, C., Guzzella, L., 2012. Feedback control of particulate matter and nitrogen oxide emissions in diesel engines. Control Engineering PracticeIn Press.

Westlund, A., Åmstrong, H., 2009. ¨ Fast physical prediction of no and soot in diesel engines. SAE Technical Paper 2009-01-1121.

Winkler-Ebner, B., Hirsch, M., del Re, L., Klinger, H., Mistelberger, W., 2010. Comparison of virtual and physical NOx-sensors for heavy duty diesel engine application. SAE International Journal of Engines 3 (1), 1124–1139. DOI: 10.4271/2010-01-1296

Yan, F., Wang, J., 2012. Pressure-based transient intake manifold temperature reconstruction in diesel engines. Control Engineering Practice 20 (5), 531– 538.

Zhou, G., Jørgensen, J., Duwig, C., Huusom, J., 2012. State estimation in the automotive scr deNOx process. In: IFAC Proceedings Volumes. Vol. 8. pp. 501–506.

Abstract Views

631
Metrics Loading ...

Metrics powered by PLOS ALM




Creative Commons License

Esta revista se publica bajo una Licencia Creative Commons Attribution-NonCommercial-CompartirIgual 4.0 International (CC BY-NC-SA 4.0)

Universitat Politècnica de València     https://doi.org/10.4995/riai

e-ISSN: 1697-7920     ISSN: 1697-7912