Transient Catalytic Converter in Simulink
Updated 11 Dec 2013
Project Presentation: http://youtu.be/YOYCZeNNbsg
With the automobile becoming an ever-growing part of everyday life, air pollution and its major health impacts are becoming a growing concern. According to the World Health Organization, “urban outdoor air pollution is estimated to cause 1.3 million deaths worldwide per year.” The quality of life for infants, the elderly, and those already suffering from respiratory diseases is severely impacted when high levels of air pollution are experienced. Beyond the detrimental impacts to human health the EPA points out that, ozone, which can be created by car emissions, “is also responsible for several billion dollars of agricultural crop yield loss in the U.S. each year.” In order to potentially save millions of lives and save billions of dollars our team has endeavored to apply process control techniques to help solve the problem of excess air pollution during cold starts of an automobile. When a car starts “cold”, or at ambient temperature, it takes a while for the catalytic converter to reach its light-off temperature, the temperature at which the pollutants in the exhaust react significantly to form less harmful substances. During catalytic warm up, toxic pollutants exit with the exhaust at high rates. Our team proposes using a heating element to heat the catalytic converter up faster so that less deadly pollutants enter the atmosphere.
We modeled the catalytic converter dynamics using Simulink and a MatLab S-Function. In designing the model, we made several simplifying assumptions. First, we assumed that the catalytic converter could be modeled as a CSTR, which allowed us to treat the temperature of the converter as uniform rather than accounting for temperature change along its length. We also simplified the reaction term by assuming that the reaction was first order and that the only reaction was the conversion of carbon monoxide, the dominant pollutant, to carbon dioxide in the presence of a platinum catalyst. Conduction between the catalyst particles and the converter body was assumed to be fast such that the temperature of the catalyst and converter body would be equivalent. Heat conduction to other parts of the car from the catalytic converter was ignored, and we assumed that the total heat transfer in the catalytic converter could be modeled using approximate overall heat transfer coefficients, UAinside and UAoutside. Finally, we assumed that the electrical power being sent to the converter was converted completely into a heat source, Q. With these simplifications, we determined transient energy and species balances that describe the changes in catalytic converter temperature, TC, concentration of CO in the exiting exhaust, CCO, and exiting exhaust temperature T¬E. The balances are shown in Equations 1, 2, and 3, where q is the exhaust flow rate and V is the volume of the catalytic converter.
(∂T_C)/∂t=1/mCp[UA_inside (T_E-T_C )+UA_outside (T_A-T_C )+Q] (1)
(∂C_CO)/∂t=q/V (C_(CO,0)-C_CO )-k_0 e^(-E_a/(RT_C )) C_CO (2)
(∂T_E)/∂t=1/(ρCp_CO V)[UA_inside (T_C-T_E )+ΔH_rxn k_0 〖e^(-E_a/(RT_C )) C〗_CO V+ρCp_CO q(T_F-T_E)] (3)
We put these balances into an S-Function in Simulink to solve the differential equations. Using the Simulink model, we then did a doublet test to determine guess values for PI controller constants, which we then tuned to best follow set point changes.
John Hedengren (2023). Transient Catalytic Converter in Simulink (https://www.mathworks.com/matlabcentral/fileexchange/44677-transient-catalytic-converter-in-simulink), MATLAB Central File Exchange. Retrieved .
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