Three-Way Catalytic Converter Modeling: Specific Heat Capacity and Reaction Rates, Study Guides, Projects, Research of Automobile Engineering

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Modelling and Control of Three-Way Catalytic Converters

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contact: theophil.auckenthaler@alumni.ethz.ch

ISBN 3-906483-08-

IMRT Press c/o Institut für Mess- und Regeltechnik ETH Zentrum 8092 Zürich Schweiz

07/

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“Nothing shocks me. I’m a scientist.”

(Harrison Ford, as Indiana Jones)

To Anna-Lena, Benjamin and Julian

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Acknowledgements

This thesis was written at the Measurement and Control Laboratory of the Swiss Federal Institute of Technology (ETH) in Zürich from 1999 to 2005. It was carried out with the support of the Robert Bosch GmbH, Germany. I would like to thank my supervisor, Prof. Dr. H.P. Geering for his support, trust, and for generously overlooking minor deficiencies in the planning of the schedule during the whole project. Furthermore I would like to thank Prof. Dr. A. Baiker and Prof. Dr. Ph. Rudolf von Rohr for accepting to be my co-examiners. Very special thanks go to Dr. Chris Onder for his immense support, the many fruitful discussions and inputs during the entire project. I would like to thank everybody of the Robert Bosch GmbH, who contributed to the project, especially E. Schnaibel, Dr. J. Frauhammer and Dr. R. Hotzel for their patience, the many rewarding discussions, for introducing me to the secrets of engine control in the real world, and last but not least, for the unbu- reaucratic and generous support during the entire project. Many thanks go to Dr. M. Votsmeier of the Umicore AG for all the discus- sions, his support and the generous contribution of the five TRI/X5 catalytic converters. Special thanks go to the technical staff of the laboratory, Dani Matter, Jan Prikryl, Oskar Brachs and of course Hansueli Honegger, who contributed, apart from his support, a lot to the great atmosphere and the fun in the catacombs of the laboratory. It was always a big pleasure to meet my coworkers in the field, Dr. Mario Balenovic and Dr. James Peyton-Jones, who contributed a lot to the project with their openness, the many fruitful discussions, and feedbacks. For their search for the many errors and typos in the thesis I would like to thank Roman Möller, Brigitte Rohrbach, Delia Ajtay, and of course Jenny Johansson and Mikaela Waller of the Linköping University, Sweden. Many thanks go to Prof. Dr. Eigenberger of the Institute for Chemical Processes Engineering of the University of Stuttgart for providing the PDEX solver. In the context of this thesis, I had to learn a lot about chemical engineering. I would like to thank Dr. Esther Hammerschmied and Dr. Stefan Menzi for

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opening some doors to the cryptic world of chemical engineering. The time at the Measurement and Control Laboratory was particularly funny and entertaining thanks to the gang of the F-floor, especially Dr. Marzio Lo- catelli, Dr. Michael Simons, and Dr. Simon Frei. It was their contribution, which lead to the solution of many open questions vital for the welfare of mankind. These range from the development of the OB-Space and the hier- archy in the Swiss Army to the fine details regarding the formulation of high- performance lubricants. The period at the Measurement and Control Laboratory was both instructive and entertaining. I would like to thank everybody at the IMRT for the great atmosphere, the good humour, support, and cooperation during the last five years. The education of a student with sometimes extravagant ideas about the plan- ning of his career can be costly and nerve wracking. I would like to thank my parents who spared no effort to make my education possible. Last but not least, I would like to express my sincerest gratitude to my wife Anna-Lena for all her constant support, her care, her encouragement, and pa- tience, especially during the last part of the project.

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means of a detailed process model, including diffusion effects and reaction kinetics both on the electrodes and the electrolyte. It has been found that under rich engine operation, the sensor response is mainly driven by the chemical potential of the hydrogen and carbon monoxide oxidation, rather than by a shortage of oxygen in the exhaust. From the process models, a simplified control-oriented model for the TWC and the λ sensors has been deduced, which accounts for the deactivation and oxygen storage dynamics, the temperatures, and the concentrations of oxygen, carbon monoxide, and hydrogen with their influence on the switch-type λ sen- sor. The model very well reflects the behaviour of both the TWC and the sensor in a wide range of operating points and ageing levels. A procedure has been developed which allows an automated calibration of the model using measure- ments obtained from an engine with standard production-type sensor equip- ment. The control-oriented model has been incorporated in an extended Kalman filter. This filter allows the online estimation of the oxygen storage levels and the storage capacity, the latter being used for diagnosis purposes. Thus, it is persistently adapted to the changing dynamics of the TWC due to ageing. The filter performed robustly and reliably, such that storage capacities of differently aged converters could be identified within a few hundred seconds with arbitrary initial values. An LQ regulator with an integrator extension has been designed to control the levels of the stored oxygen. The regulator can be tuned with mainly two parameters, by means of which the balance between the conversion rates of oxidising and reducing species can be adjusted and the signal energy of the control signal can be altered, the latter being closely related to the conversion rates of carbon monoxide and nitric oxide. The controller has been tested in FTP cycles with frequent fuel cut-offs. As compared to a simple λ control con- cept, the conversion rates of the species limited by legislation were improved and stabilised for ageing levels ranging from considerably aged to fresh. The integrating extension of the controller was demonstrated to master the estima- tion of the offset of the wide-range λ sensor located in the raw exhaust, which is valuable for the diagnosis of this device.

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Zusammenfassung

Dreiwegekatalysatoren für die Abgasnachbehandlung von Ottomotoren werden nun seit über 20 Jahren eingesetzt. Während dieser Zeit wurden die Emissions- grenzwerte innerhalb und ausserhalb Europas ungefähr alle fünf Jahre halbiert. Neben den Grenzwerten wurden auch Vorschriften erlassen, welche die per- manente Überwachung des Abgasnachbehandlungssystems und die Anzeige allfälliger Fehlfunktionen zwingend erfordern. Um den strengen Anforderungen gerecht zu werden, wurden Konzepte ent- wickelt, welche neben der Regelung des Luft/Brennstoffgemisches am Eingang des Katalysators auch dessen interne Zustände, wie zum Beispiel den Füllstand des Sauerstoffspeichers einbeziehen. Normalerweise wird die Menge des ge- speicherten Sauerstoffs aus den Lambda-Sensorsignalen vor und nach dem Ka- talysator berechnet. Oft ergeben sich jedoch Probleme, weil die Sensoren durch den Einfluss des Wasserstoffs stark gestört werden. Die Wasserstoffkonzentra- tion im Rohabgas des Motors kann relativ genau mit statischen Funktionen oder Kennfeldern bestimmt werden. Die Oxidation bzw. Produktion im Katalysator ist jedoch ein dynamischer Prozess, welcher sich sowohl in Abhängigkeit des Motorbetriebspunktes als auch der Katalysatoralterung ändert. Im Rahmen dieser Abhandlung wurde ein Konzept für die Regelung und Diagnose von Dreiwegekatalysatoren entwickelt, welches nicht nur die Sauer- stoffspeicherdynamik einbezieht, sondern auch die Wasserstoffkonzentration und deren Einfluss auf die Lambdasonden berücksichtigt. Um die Mechanismen zu identifizieren, welche die Zusammensetzung der wichtigsten Abgaskomponenten in Bezug auf die Gesetzgebung und den Ein- fluss auf die Sensorsignale beeinflussen, wurde ein detailliertes 1-D Modell eines Dreiwegekatalysators hergeleitet, welches das dynamische Verhalten wäh- rend tieffrequenter Anregungen durch das Luft/Brennstoffverhältnis sehr gut abbildet. Es hat sich herausgestellt, dass der Dreiwegekatalysator durch die Adsorption von Kohlenwasserstoffen beim fetten Betrieb, d.h. mit Brennstoff- überschuss, deaktiviert wird. Dadurch wird die Aktivität der Wasser-Gas-Shift- und der Steam-Reforming-Reaktionen stark reduziert, was einen erheblichen Einfluss auf das Verhältnis zwischen Wasserstoff, Kohlenmonoxid und Koh- lenwasserstoffe zur Folge hat. Dieser Effekt verstärkt sich mit zunehmender Alterung des Katalysators.

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Contents

Acknowledgements vii

Abstract ix

Zusammenfassung xi

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Nomenclature

Symbols

Variable Unit Description

A s−^1 Pre-exponential factor (Langmuir-Hinshelwood) A s−^1 /(molm−^3 )Pre-exponential factor (Eley-Rideal) Acat m^2 /m^3 Specific catalytic active surface Acs m^2 Catalyst cross-sectional area Aelectrode m^2 Electrode surface Ageo m^2 /m^3 Specific geometric catalyst surface Asensor m^2 /m^3 Specific diffusion cross-sectional area AT W C m^2 Outer TWC surface Aλst... Fλst V, 1/ppm Coefficients switch-type sensor model D m Diameter Di m/s Convection mass transfer coefficient of i DiN 2 cm^2 /s Binary diffusion coefficient of i in N 2 Def f kg/(ms) Gas dispersion coefficient E kJ/mol Activation energy Fλ - Signal of the λ feedback-controller G(s) Plant transfer function J mol/(m^2 s) Mole flux J - Quadratic cost function K(s) Controller transfer function L mol/m^2 Adsorption capacity Le(s) Loop gain transfer function M kg/mol Molar mass N uD - Nusselt Number Q J Thermal energy SC mol/m^3 Storage capacity ShD - Sherwood number R J/(kgK) Specific gas constant R mol/(m^2 s) Production rate T K Temperature Tsensor K Sensor temperature

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λ W/(mK) Heat conductivity ν - Stoichiometric coefficient ν O2+ - Positive vacancy in electrolyte ̺ kg/m^3 Density φH 2 /CO - H 2 /CO ratio (raw exhaust)

Vectors and Matrices

Variable Description

f Dynamics function of state-space system h Measurement function of state-space system u Control vector x State vector y Measurement vector v, w Uncorrelated white noise process

A System dynamics matrix B Control matrix C Measurement matrix D Feedthrough matrix G State feedback gain matrix (LQ regulator) H Observer gain matrix (Kalman filter) H Measurement matrix I Identity matrix K Kalman Gain matrix P Covariance matrix of the estimate error Q Covariance matrix of process white noise (Kalman Filter) Q Weighting matrix for the state vector (LQ cost function) R Covariance matrix of measurement white noise (Kalman Filter) R Weighting matrix for the control vector (LQ cost function) Φ Fundamental matrix

Constants

Constant Value/Unit Description

F 96485 C/mol Faraday number ℜ 8.31451 J/molK Universal gas constant

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Subscripts

Subscript Description

Cer Ceria KF Kalman filter N M Noble metal T emp Temperature T W C Three-way catalyst V Vacant surface

a Backward reaction ads Adsorption amb Ambient calc Calculated ch Channel (outer gas phase) chan Channel chem Chemical des Desorption el Electrostatic eng Engine eq Equilibrium exh Exhaust gas (upstream of TWC) f Forward reaction g Gas phase meas Measured ref Reference tp Tailpipe (downstream of TWC) wc Washcoat (inner gas phase) reac Reaction s Solid phase, surface stst Steady-state λst Switch-type λ sensor

Acronyms

BIBO Bounded Input, Bounded Output ECE Economic Commision for Europe EKF Extended Kalman Filter EUDC Extra Urban Driving Cycle FTP Federal Test Procedure GUI Graphical User Interface

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