Method for operating a drive device for a motor vehicle, corresponding drive device and computer program product

The method calculates the convertible nitrogen oxide content using the carbon monoxide and oxygen contents to determine the nitrogen oxide output content with high accuracy and low computational effort, addressing the inaccuracies and resource-intensive challenges of existing methods.

DE102024114196B3Active Publication Date: 2025-06-26AUDI AG
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Patent Information

Application Number
DE102024114196
Authority / Receiving Office
DE · DE
Patent Type
Patents
Current Assignee / Owner
Filing Date
2024-05-21
Publication Date
2025-06-26
Estimated Expiration
2044-05-21

AI Technical Summary

Technical Problem

Existing methods for determining the initial content of nitrogen oxide in exhaust gases of motor vehicles are not accurate enough and require significant computational resources.

Method used

A method that calculates the convertible nitrogen oxide content based on the carbon monoxide and oxygen contents upstream of the vehicle catalytic converter, using the relationship y NO,c = |y CO - 2 · y O2|, to determine the output content of nitrogen oxide with high accuracy and low computational effort.

Benefits of technology

The method allows for precise determination of the nitrogen oxide output content with minimal computational resources, ensuring reliable compliance with exhaust emission limit values.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to a method for operating a drive device (1) for a motor vehicle, which drive unit (2) has an exhaust gas-generating drive unit (2) and an exhaust gas aftertreatment device (12) designed as a vehicle catalytic converter for aftertreating the exhaust gas, wherein an output content of the exhaust gas component present downstream of the vehicle catalytic converter is determined at least temporarily by means of a computer model from an input content of an exhaust gas component of the exhaust gas present upstream of the vehicle catalytic converter. It is provided that nitrogen oxide is used as the exhaust gas component and that the output content is determined based on a carbon monoxide content and an oxygen content upstream of the vehicle catalytic converter. The invention further relates to a drive device (1) for a motor vehicle and to a computer program product.
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Description

[0001] The invention relates to a method for operating a drive device for a motor vehicle, which has a drive unit generating exhaust gas and an exhaust gas aftertreatment device designed as a vehicle catalytic converter for aftertreating the exhaust gas, wherein an output content of the exhaust gas component present downstream of the vehicle catalytic converter is determined at least temporarily by means of a computer model from an input content of an exhaust gas component of the exhaust gas present upstream of the vehicle catalytic converter, wherein nitrogen oxide is used as the exhaust gas component and the output content is determined based on a carbon monoxide content and an oxygen content upstream of the vehicle catalytic converter. The invention further relates to a drive device for a motor vehicle and a computer program product.

[0002] For example, the prior art document DE 10 2015 215 504 A1 describes a method for determining NO x -Conversion rate of an SCR catalyst, which is part of a regenerable NO x storage catalyst. It is intended that with regard to a first regeneration phase of the NO x storage catalyst, the NH3 quantity in the exhaust gas flow upstream of the catalyst box is determined and in a lean phase immediately following the regeneration phase, a first value for a NO x -Conversion of the catalyst box is determined, with regard to a second regeneration phase of the NO x-storage catalyst, the NH3 quantity is determined, at least if the NH3 quantity determined during the second regeneration phase differs from the NH3 quantity determined during the first regeneration phase, in a lean phase immediately following the second regeneration phase, a second value for a NO x -Conversion of the catalyst box and depending on the difference between the first value and the second value of the NO x -Conversion the NO converted in the SCR catalyst x -amount is determined.

[0003] Document WO 2024 / 084654 A1 describes a control device for an internal combustion engine, comprising: an exhaust gas flow rate calculation unit; an exhaust gas temperature detection unit; a catalyst upstream state variable estimation unit that detects an upstream catalyst air-fuel ratio, an exhaust gas flow rate, and an exhaust gas temperature, and estimates an upstream catalyst NOx discharge amount, an upstream catalyst HC discharge amount, and an upstream catalyst CO discharge amount as the catalyst upstream state variables;a downstream catalyst state quantity estimation unit that inputs the upstream catalyst air-fuel ratio, the exhaust gas flow rate, the exhaust gas temperature, and the upstream catalyst state quantities, and estimates the catalyst temperature of a three-way catalyst, an oxygen storage capacity, a downstream catalyst air-fuel ratio, a downstream catalyst NOx discharge amount, a downstream catalyst HC discharge amount, and a downstream catalyst CO discharge amount as downstream catalyst state quantities; and a correction unit that corrects the downstream NOx discharge amount, the downstream HC discharge amount, and the downstream CO discharge amount using the NOx sensor value detected by a downstream NOx sensor.

[0004] The prior art also includes the documents DE 10 2020 100 158 B4 and JP 2008 - 069 708 A.

[0005] It is an object of the invention to propose a method for operating a drive device for a motor vehicle, which has advantages over known methods, in particular implementing the determination of the initial content with high accuracy and low expenditure.

[0006] This is achieved according to the invention with a method for operating a drive device for a motor vehicle having the features of claim 1. It is provided that the initial content is determined from a convertible nitrogen oxide content calculated from the carbon monoxide content and the oxygen content, wherein the convertible nitrogen oxide content is determined using the relationship y NO,c = | y CO - 2 · y O2 | is calculated, where 0y NO,c is the convertible nitrogen oxide content, yco is the carbon monoxide content and y O2 the oxygen content is.

[0007] In principle, it is intended that nitrogen oxide is used as the exhaust gas component and that the initial content is determined based on a carbon monoxide content and an oxygen content upstream of the vehicle catalytic converter.

[0008] Advantageous embodiments with useful further developments of the invention are specified in the dependent claims. It should be noted that the exemplary embodiments explained in the description are not limiting; rather, any variations of the features disclosed in the description, the claims, and the figures are feasible.

[0009] The drive device serves to drive the motor vehicle, thus providing a drive torque directed toward driving the motor vehicle. The drive unit provides the drive torque. The drive unit is preferably an internal combustion engine, in particular a gasoline internal combustion engine or a diesel internal combustion engine. During operation of the drive device, fuel and fresh gas are supplied to the drive unit at least temporarily, with the fresh gas containing fresh air at least temporarily.

[0010] Additionally, the fresh gas may contain exhaust gas, provided exhaust gas recirculation is implemented, in which the exhaust gas generated by the drive unit is at least partially recirculated back into the drive unit, namely as a component of the fresh gas. The fuel and the fresh gas supplied to the drive unit form a fuel-fresh gas mixture with a specific composition, which is reacted in the drive unit.

[0011] During operation of the drive unit, the chemical reaction between fuel and fresh gas produces exhaust gas, which is discharged towards the outside environment of the drive system or motor vehicle. Since the exhaust gas produced by the drive unit contains pollutants, the exhaust gas is first fed to the exhaust gas aftertreatment system before being released into the outside environment. In the exhaust gas aftertreatment system, the pollutants are at least partially converted into less hazardous products. Only after passing through the exhaust gas aftertreatment system is the exhaust gas discharged into the outside environment, in particular through a tailpipe of the drive system.

[0012] The exhaust gas aftertreatment device is available as a vehicle catalyst, in particular as a three-way catalyst, oxidation catalyst, NO xStorage catalyst or as an SCR catalyst. The vehicle catalyst is particularly preferably integrated into a particulate filter, in particular a gasoline particulate filter or a diesel particulate filter. For this purpose, the particulate filter is provided with a catalytic coating, for example. The conversion rate and thus the conversion performance of the exhaust gas aftertreatment system, with which the pollutants are converted into less hazardous products, depend in particular on the composition of the exhaust gas supplied to the exhaust gas aftertreatment system, the temperature of the exhaust gas aftertreatment system, and the condition of the exhaust gas aftertreatment system.

[0013] The components of the exhaust gas produced by the drive unit are also referred to as raw emissions. Raw emissions describe the composition of the exhaust gas upstream of the exhaust gas aftertreatment device, or in terms of flow between the drive unit and the exhaust gas aftertreatment device. The substances contained in the exhaust gas are partially converted as the exhaust gas passes through the exhaust gas aftertreatment device, changing the composition of the exhaust gas. The substances present in the exhaust gas downstream of the exhaust gas aftertreatment device, which make up the exhaust gas, are also referred to as tailpipe emissions, since the exhaust gas with this composition is released into the outside environment through the tailpipe of the drive direction.

[0014] The quantity of pollutants contained in the exhaust gas downstream of the exhaust aftertreatment device, particularly in the tailpipe emissions, depends, as already mentioned, on the raw emissions, but also on the conversion efficiency of the exhaust aftertreatment device. This is temperature-dependent. In particular, the further the temperature of the exhaust aftertreatment device is from the operating temperature of the exhaust aftertreatment device, i.e., the greater the absolute value of the difference between the temperatures, the lower the conversion efficiency. The temperature of the exhaust aftertreatment device is understood to mean, in particular, the temperature of a ceramic honeycomb body provided with the catalytic coating.In addition, the conversion performance depends on the condition of the exhaust gas aftertreatment system, which results in particular from the age or operating time of the exhaust gas aftertreatment system.

[0015] Due to the ever-stricter regulations for exhaust emissions, these must be monitored with increasing precision. Since the content of all exhaust gas components cannot be measured, or a sensor cannot be provided for each exhaust gas component, a mathematical model is used to calculate the output content for the exhaust gas component from the input content. The input content and the output content are content values ​​and each indicate the content of the exhaust gas component in the exhaust gas. The content values ​​are given, for example, as mass fractions, mole fractions, or volume fractions. However, they can also be given as mass concentrations, mole concentrations, or volume concentrations.

[0016] Several chemical reactions take place in the exhaust aftertreatment system or vehicle catalytic converter, which can be roughly divided into oxidation reactions and reduction reactions. Oxidation reactions include one or more of the following reactions: H2 + 0.5 O 2 ↔ H2O CO + 0.5 O2 ↔ CO2 C3H6 + 4.5 O2 → 3 CO2 + 3 H2O C3H8 + 5 O2 → 3 CO2 + 4 H2O CH4 + 2 O2 → CO2 + 2 H2O

[0017] Reduction reactions, on the other hand, include one or more of the following reactions: NO + H2 → H2O + 0.5 N2 NO + CO → CO2 + 0.5 N2 9 NO + C3H6 → 3 CO2 + 3 H2O + 4.5 N2 10 NO + C3H8 → 3 CO2+4 H2O + 5 N2

[0018] The exhaust gas component whose initial content is to be determined is nitrogen oxide, specifically nitrogen monoxide (NO). The conversion performance of the exhaust gas aftertreatment system for nitrogen oxide is usually better when there is a lack of oxygen than when there is an excess of oxygen. If λ < 1 applies to the raw emissions, the conversion performance is better than for λ > 1. The excess oxygen is determined on the one hand by the nitrogen oxide and on the other hand by the oxygen content, specifically the content of molecular oxygen, in the exhaust gas or the raw emissions. If, for example, λ = 1.01 is present in the raw emissions, this means that there is a one percent excess oxygen. With an oxygen concentration of molecular oxygen in the fresh air of 21%, this means that the exhaust gas has a residual oxygen content of 0.21% O2. This corresponds to 2,100 ppm.

[0019] The applicant has surprisingly discovered that the initial nitrogen oxide content can be determined with high accuracy based on the carbon monoxide content and the oxygen content of the raw emissions, i.e., upstream of the vehicle's catalytic converter. If one roughly assumes that the exhaust gas aftertreatment system first reduces the residual oxygen content in the exhaust gas before the reduction of the nitrogen oxide begins, it follows that the initial nitrogen oxide content depends solely on the initial nitrogen oxide content, the carbon monoxide content, and the oxygen content. Therefore, the initial content is preferably determined solely based on the initial content, the carbon monoxide content, and the oxygen content.

[0020] For example, if we assume raw emissions in the exhaust gas with 10,000 ppm CO, 2,500 ppm O2 and 9,200 ppm NO, 5,000 ppm carbon monoxide remain after the reaction of carbon monoxide with oxygen. With these 5,000 ppm carbon monoxide, 5,000 ppm nitrogen oxide can be converted; 4,200 ppm nitrogen oxide cannot be reduced. This results in a conversion efficiency for the nitrogen oxide of 5,000 ppm / 9,200 ppm ≈ 54%. With a raw emission composition of 10,000 ppm CO, 5,000 ppm O2 and 4,200 ppm NO, however, all of the available carbon monoxide would be used up for the reaction with the oxygen, meaning that no reduction of the nitrogen oxide would be possible.

[0021] Using the described procedure for determining the initial nitrogen oxide content from the input nitrogen oxide content, the carbon monoxide content, and the oxygen content, preferably exclusively, the initial content can be determined with low computing power yet high accuracy. The oxygen content upstream of the vehicle's catalytic converter is measured, in particular, using a lambda sensor.

[0022] Preferably, the initial content determined using the computational model is monitored and, if the initial content exceeds a threshold value, a malfunction of the drive system is detected. Likewise, the initial content can be used to determine and accumulate a quantity of the exhaust gas component downstream of the exhaust gas aftertreatment device. For example, if a limit value is exceeded, the cumulative quantity of the exhaust gas component based on a distance traveled by the motor vehicle is used to detect a malfunction of the drive system. The quantity is understood to mean, in particular, a mass or volume of the exhaust gas component.

[0023] If the malfunction is detected, faulty operation of the drive system is preferably initiated, in particular the drive device is operated in such a way that, despite the malfunction, the initial concentration is lower than the threshold value or the cumulative amount based on the distance traveled by the motor vehicle is within a permissible range. In more general terms, the drive device is operated depending on the initial concentration, or the drive unit is controlled depending on the initial concentration. This ensures reliable compliance with the limit values ​​for the motor vehicle's exhaust emissions.

[0024] The invention provides that the output content is determined from a convertible nitrogen oxide content calculated from the carbon monoxide content and the oxygen content. The convertible nitrogen oxide content is understood to be the nitrogen oxide content that can be converted in the exhaust gas aftertreatment system, namely taking into account the carbon monoxide content and the oxygen content. The convertible nitrogen oxide content is higher the higher the carbon monoxide content and lower the higher the oxygen content. The output content corresponds to the input nitrogen oxide content minus the convertible nitrogen oxide content. Accordingly, the output content can be known with sufficiently high accuracy with extremely little computational effort.

[0025] A further development of the invention provides that the convertible nitrogen oxide content is calculated from the difference between the carbon monoxide content and the oxygen content. Preferably, the convertible nitrogen oxide content corresponds to the carbon monoxide content minus an integer multiple of the oxygen content, in particular twice the oxygen content. Once again, the aforementioned advantages are achieved in the manner described.

[0026] The invention provides that the convertible nitrogen oxide content is determined using the relationship y NO,c = | y CO - 2 · y O2 | is calculated, where y NO,c is the convertible nitrogen oxide content, yco is the carbon monoxide content and y O2The convertible nitrogen oxide content thus corresponds to the absolute value of the difference between the carbon monoxide content and twice the oxygen content, i.e., the sign-corrected difference. The conversion efficiency of the exhaust gas aftertreatment system can be calculated from the convertible nitrogen oxide content, namely by relating it to the input nitrogen oxide content. The relationship for the conversion efficiency is therefore xNO=|yCO−2⋅yO2| / yNO,1 where x NO the conversion performance in percent and y NO,1 the input nitrogen oxide content. This calculation rule can also be implemented easily and with low computing power in the drive system or a control unit of the drive system.

[0027] A further development of the invention provides that the initial content is calculated from the input content present upstream of the vehicle catalyst and the convertible nitrogen oxide content. In other words, the initial content is y NO,2 = y NO,1 - y NO,c , where y NO,1 the starting salary and y NO,2 the initial nitrogen oxide content. Here, too, the calculation is extremely simple.

[0028] A further development of the invention provides that when calculating the convertible nitrogen oxide content, at least one of the following variables is additionally taken into account: hydrogen content, propene content, propane content, and methane content, each upstream of the vehicle catalytic converter. These contents describe the raw emissions of the respective substance. Only one of the variables mentioned, several of the variables mentioned, or all of the variables mentioned can be additionally included in the calculation of the convertible nitrogen oxide content.

[0029] If all variables are taken into account, the following relationship results: yNO,c=|yCO+yH2+9 yC3H6+10 yC3H8+4 yCH4−2⋅yO2 Here y H2 the hydrogen content, y C3H6 the propene content, y C3H8 the propane content and y CH4the methane content. If one of the variables is not to be considered, it can simply be deleted from the relationship. It should be emphasized that the mentioned contents are considered with different integer weightings. The conversion performance of the exhaust gas aftertreatment system when considering the mentioned variables can be expressed as xNO=|yCO+yH2+9 yC3H6+10 yC3H8+4 yCH4−2⋅yO2| / yNO,1 The use of at least one of the above-mentioned quantities results in a further improvement in the accuracy of determining the initial content without significantly increasing the computational effort.

[0030] A further development of the invention provides that the drive unit is controlled at least temporarily based on the initial concentration. This has already been mentioned. In particular, the control is carried out such that the initial concentration is less than the aforementioned threshold value. Additionally or alternatively, the control is carried out such that a quantity of the exhaust gas component related to the distance traveled, which is calculated from the initial concentration, is less than a corresponding threshold value. This ensures reliable compliance with emission limits.

[0031] A further development of the invention provides for the use of nitrogen monoxide as the nitrogen oxide. This has also been mentioned above. Monitoring the nitrogen monoxide emissions of the drive system is particularly important, since nitrogen monoxide is a particular consideration when examining the exhaust gases of the drive system. The described procedure provides a simple yet effective way to reliably monitor nitrogen monoxide emissions.

[0032] The invention further relates to a drive device for a motor vehicle, in particular for carrying out the method according to the embodiments in the context of this description, wherein the drive device has a drive unit generating exhaust gas and an exhaust gas aftertreatment device designed as a vehicle catalytic converter for aftertreating the exhaust gas, wherein the drive device is provided and designed to use a computer model to at least temporarily determine an output content of the exhaust gas component present downstream of the vehicle catalytic converter from an input content of an exhaust gas component of the exhaust gas present upstream of the vehicle catalytic converter. The drive device is further provided and designed to use nitrogen oxide as the exhaust gas component and to determine the output content based on a carbon monoxide content and an oxygen content upstream of the vehicle catalytic converter.It is further provided that the initial content is determined from a convertible nitrogen oxide content calculated from the carbon monoxide content and the oxygen content, the convertible nitrogen oxide content being determined using the relationship y. NO,c = | y CO - 2 · y O2 | is calculated, where y NO,c the convertible nitrogen oxide content, y CO the carbon monoxide content and y O2 the oxygen content is.

[0033] The advantages of such a design of the drive device or such a procedure have already been pointed out. Both the drive device and the method for its operation can be further developed according to the explanations in this description, so reference is made to these in this regard.

[0034] The invention also relates to a computer program product comprising instructions that cause the drive device to execute the described method according to the embodiments of this description. Regarding the advantages and possible advantageous developments, reference is made to the entire description.

[0035] The features and feature combinations described in the description, in particular the features and feature combinations described in the following description of the figures and / or shown in the figures, can be used not only in the respective combination specified, but also in other combinations or on their own, without departing from the scope of the invention. Thus, embodiments are also to be considered encompassed by the invention that are not explicitly shown or explained in the description and / or the figures, but which emerge from or can be derived from the explained embodiments.

[0036] The invention will be explained in more detail below with reference to the exemplary embodiments shown in the drawing, without limiting the invention. The only Fig. 1 a schematic representation of a drive device for a motor vehicle.

[0037] The Fig.Figure 1 shows a schematic representation of a drive device 1 comprising a drive unit 2, which here takes the form of an internal combustion engine, and an exhaust tract 3. In the illustrated embodiment, the drive unit 2 has a plurality of cylinders 4, each with a combustion chamber. Each of the cylinders 4 has at least one intake valve 5 and at least one exhaust valve 6. Fresh gas from a fresh gas tract 7 can be supplied to the respective cylinder 4 via each of the intake valves 5, whereas exhaust gas from the corresponding cylinder 4 can be discharged through each of the exhaust valves 6, namely in the direction of the exhaust tract 3.

[0038] The fresh gas is provided to the intake valves 5 by means of a compressor 8, which is part of an exhaust gas turbocharger 9. In addition to the compressor 8, the exhaust gas turbocharger 9 has a turbine 10, which is fluidly connected to the exhaust valves 6 via an exhaust line 11, which is part of the exhaust tract 3. Downstream of the turbine 10 is an exhaust gas aftertreatment device 12, which here is designed as a vehicle catalytic converter, in particular as a three-way catalytic converter. Downstream of the exhaust gas aftertreatment device 12, the exhaust tract 3 opens into an external environment of the drive device 1, for example via a tailpipe. It should be noted that the exhaust gas turbocharger 9 is purely optional. It can also be omitted accordingly.

[0039] Upstream of the exhaust gas aftertreatment device 12, a first lambda probe 13 is located to determine a first residual oxygen content and, accordingly, a first combustion air ratio of the exhaust gas at this location. Downstream of the exhaust gas aftertreatment device 12, a second lambda probe 14 is used to determine a second residual oxygen content and, accordingly, a second combustion ratio of the exhaust gas.

[0040] It is intended to determine an input nitrogen oxide content and a carbon monoxide content, each upstream of the exhaust gas aftertreatment device 12, during operation of the drive system 1. This is done, for example, mathematically from a quantity of fresh gas supplied to the drive unit 2 and a quantity of fuel, thus the composition of a fuel-air mixture used to operate the drive unit 2.

[0041] Furthermore, the oxygen content is measured using the first lambda probe 13. The initial nitrogen oxide content downstream of the exhaust gas aftertreatment device 12 is calculated from the initial content, the carbon monoxide content, and the oxygen content. The drive unit 2 is preferably controlled based on the initial content. This procedure is characterized by low computing power requirements while still maintaining high accuracy. LIST OF REFERENCE SYMBOLS: 1 drive device 2 drive unit 3 Exhaust system 4 cylinders 5 Inlet valve 6 exhaust valve 7 Fresh gas tract 8 compressors 9 exhaust gas turbocharger 10 turbines 11 Exhaust pipe 12 Exhaust aftertreatment system 13 1. Lambda sensor 14 2. Lambda sensor

Claims

[1] Method for operating a drive device (1) for a motor vehicle, which has a drive unit (2) generating exhaust gas and an exhaust gas aftertreatment device (12) designed as a vehicle catalyst for aftertreating the exhaust gas, wherein by means of a computer model, at least temporarily, an output content of the exhaust gas component present downstream of the vehicle catalyst is determined from an input content of an exhaust gas component of the exhaust gas present upstream of the vehicle catalyst, wherein nitrogen oxide is used as the exhaust gas component and the output content is determined on the basis of a carbon monoxide content and an oxygen content upstream of the vehicle catalyst, characterized by that the initial content is determined from a convertible nitrogen oxide content calculated from the carbon monoxide content and the oxygen content, the convertible nitrogen oxide content being determined using the relationship y NO,c = | y CO - 2 · yO2 | is calculated, where y NO,c is the convertible nitrogen oxide content, yco is the carbon monoxide content and y O2 the oxygen content is. [2] Method according to claim 1, characterized by that the convertible nitrogen oxide content is calculated from a difference between the carbon monoxide content and the oxygen content. [3] Method according to one of the preceding claims, characterized by that the output content is calculated from the input content present upstream of the vehicle catalyst and the convertible nitrogen oxide content. [4] Method according to one of the preceding claims, characterized by that when calculating the convertible nitrogen oxide content, at least one of the following variables is additionally taken into account: hydrogen content, propene content, propane content and methane content, each upstream of the vehicle catalytic converter. [5] Method according to one of the preceding claims, characterized by that the drive unit (2) is controlled at least temporarily based on the initial content. [6] Method according to one of the preceding claims, characterized by that nitric oxide is used as nitrogen oxide. [7] Drive device (1) for a motor vehicle, in particular for carrying out the method according to one or more of the preceding claims, wherein the drive device (1) has a drive unit (2) generating exhaust gas and an exhaust gas aftertreatment device (12) designed as a vehicle catalyst for aftertreating the exhaust gas, wherein the drive device (1) is provided and designed to determine, by means of a computer model, at least temporarily from an input content of an exhaust gas component of the exhaust gas present upstream of the vehicle catalyst, an output content of the exhaust gas component present downstream of the vehicle catalyst, wherein the drive device (1) is further provided and designed to use nitrogen oxide as the exhaust gas component and to determine the output content based on a carbon monoxide content and an oxygen content upstream of the vehicle catalyst characterized bythat the initial content is determined from a convertible nitrogen oxide content calculated from the carbon monoxide content and the oxygen content, the convertible nitrogen oxide content being determined using the relationship y NO,c = | y CO - 2 · y O2 | is calculated, where y NO,c the convertible nitrogen oxide content, y CO the carbon monoxide content and y O2 the oxygen content is. [8] Computer program product comprising instructions which cause the drive device (1) according to claim 7 to carry out the method according to one or more of claims 1 to 6.

Citation Information

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