DE102005038492B4 - Method and device for determining the offset of a calculated or measured lambda value - Google Patents

Abstract

Method for determining an offset (Δ) of a lambda value upstream of a catalytic converter (18) arranged in an exhaust duct (16) of an internal combustion engine (10), wherein the lambda value is calculated or measured by means of a first lambda probe (20) arranged upstream of the catalytic converter (18) , comprising the steps of (a) registering times at which a sensor signal (Uλ) of a second lambda probe (22) connected downstream of the catalytic converter (18) crosses a nominal value corresponding to lambda = 1, (b) determination of a catalytic converter (18) accumulated oxygen mass (mO2, a) over the duration of at least one limited by the times lean phase and discharged from the catalyst cumulative oxygen mass (mO2, off) over the duration of at least one, limited by the times fat phase as a function of the calculated or measured lambda value upstream of the catalyst (18) and (c) determining the offset (Δ) for the calculated or measured Lambda value as a function of a correction oxygen mass flow, which is determined from a difference between the registered oxygen mass (mO2, on) and the discharged oxygen mass (mO2, aus) and a time interval of the determination of the cumulative oxygen masses (mO2, a, mO2, aus) ,

Description

The invention relates to a method for determining an offset of a arranged in an exhaust passage of an internal combustion engine lambda probe and a device suitable for carrying out the method.

According to the current state of the art lambda probes are used in an exhaust duct of an internal combustion engine to ensure the greatest possible pollutant conversion, which generate a signal dependent on the oxygen content of the exhaust gas. With the aid of suitable regulators, the air-fuel ratio of the engine and thus of the exhaust gas is regulated in dependence on these signals so that an exhaust gas catalytic converter operates in its optimum conversion range.

There are different configurations with different numbers and types of lambda probes and catalysts used known. A typical structure includes, for example, a first broadband lambda sensor close to the engine, which supplies a proportional voltage signal over a wide lambda range, and a catalyst arranged downstream of this broadband lambda probe, for example a 3-way catalytic converter. A second step response lambda probe located downstream of the catalyst has a steep voltage change near a stoichiometric air-fuel ratio of λ = 1. In such a configuration, a lambda pre-regulation by the first lambda probe and a fine control by the second probe can take place. For this purpose, typically exists for the probe signal downstream of the catalyst, a desired voltage value, which is adjusted for example via a PI controller. In practice, this usually happens so that the signal oscillates around this setpoint. If the signal is above the setpoint, this indicates a mixture that is too rich, and a mixture lean is requested via the controller. Conversely, a Gemischanfettung is requested when the signal is below the setpoint.

Lambda probes, in particular broadband lambda probes, are subject to age-related changes with regard to their output signals and can even become completely unsuitable.

To detect faulty probes, today's systems include algorithms for testing the electrical connections, for example for detecting short circuits in the cable guides.

The avoidance of a faulty lambda probe measurement upstream of the catalytic converter with the aid of a lambda probe downstream of the catalytic converter is disclosed in the document DE 38 37 984 A1 known.

Furthermore, programs for checking the signal plausibility of the probe signals are known (for example US 4,751,907 A ; US 5,845,624 A ) to calibrate the probes, in particular their offset, that is, the shift of their lambda characteristic in y-dimension to determine and adapt and optionally generate an error message to display a defective probe.

From the document DE 41 12 477 C2 it is disclosed to correct the offset by comparing the measured value with a simulated value.

The determination of an offset of a lambda probe downstream of a catalyst is in the document US 5 533 332 A described.

The execution of such plausibility checks is carried out according to known methods under exactly defined boundary conditions. In order to rule out that due to dynamic operating states or variations, unreasonable probe errors are detected, the malfunction must be confirmed several times until an error display is approved. In addition, various release conditions still have to be met. In particular for plausibility checks, which are based on signals of a lambda probe installed downstream of a catalytic converter, temporal decouplings are generally provided. This buffer effects, the catalysts have on the exhaust gas composition, in particular due to their ability to inject and remove oxygen, are excluded.

In order to determine an offset of a probe arranged in front of a catalyst with the aid of a probe arranged downstream of the catalytic converter, it is therefore necessary (in addition to complying with other criteria) to enforce a fixed exhaust gas mass quantity before the signal of a lambda probe arranged behind the catalytic converter is picked up. Only then can it be assumed that the catalyst is adjusted and equilibrated in its optimum conversion range and the probe is behind the catalytic converter at its desired regulation value. If the rear probe in stationary case exactly their setpoint By definition, the front lambda probe indicates by definition exactly λ = 1. However, if the probe signal of the rear probe deviates from the nominal value, this deviation is used as the offset of the front probe. If necessary, the offset thus determined is compared with defined threshold values and a maintenance signal is generated if it is exceeded. In this way, the offset of the front lambda probe is determined by the evaluation of the signal of the rear probe.

This approach has the disadvantage that relatively much time is needed in approximately constant driving operation until the release of the offset determination. Furthermore, transient operating conditions, which can never be completely ruled out, have an effect on the oxygen content of the catalytic converter and thus on the signal from the rear probe, so that the danger exists that deviations from the nominal value will be detected as an offset of the front probe, although none exists , This in turn can subsequently reduce emissions.

The object of the present invention is therefore to provide a method for determining the offset of a lambda value upstream of a catalytic converter by means of a signal of a lambda probe arranged downstream of the catalytic converter, which can also be used with high reliability in non-stationary driving mode. It is also intended to propose an arrangement suitable for carrying out the method.

This object is achieved by a method and an apparatus having the features of the independent claims. Preferred embodiments of the invention are the subject of the dependent claims.

The method according to the invention for determining an offset Δ of a lambda value upstream of a catalytic converter arranged in an exhaust duct of an internal combustion engine, wherein the lambda value is calculated or measured by means of a first lambda probe arranged upstream of the catalytic converter, comprises the steps:
Registration of times at which a sensor signal of a second lambda probe arranged downstream of the catalytic converter crosses a nominal value corresponding to lambda = 1,
Determining a cumulative oxygen mass m _{O2 introduced} into the catalyst _{, a} lean phase limited by the times and a cumulative oxygen mass m _O2 discharged from the catalyst over the duration of at least one fat phase bounded by the times as a function of the calculated value or measured lambda value upstream of the catalyst and
Determining the offset Δ for the calculated or measured lambda value as a function of a correction oxygen mass flow which is determined from a difference of the registered oxygen mass m _{O2, an} and the discharged oxygen mass m _O2, and a time interval of the determination of the cumulated oxygen masses.

The lambda value upstream of the catalytic converter, the offset of which is to be determined according to the invention, can either be calculated by means of suitable models known to the person skilled in the art, the lambda value being modeled as a function of suitable operating parameters of the internal combustion engine, for example an air-fuel pilot control.

On the other hand, it may also be a lambda value measured with a first lambda probe arranged upstream of the catalytic converter, in particular a broadband lambda probe. In this case, the offset of a measured lambda probe signal is thus determined. The invention will be explained in connection with the signal of a lambda probe connected upstream of the catalytic converter. However, the characteristics apply without restriction for a modeled lambda value.

In particular, an evaluation of the calculated amounts of input and output of oxygen into and out of the catalyst, a determination of an average correction oxygen mass flow from the difference between the input and output quantities, and with this a determination of a mean lambda deviation, which corresponds to the desired offset. The inventive method utilizes the fact that - due to a constant oxygen storage capacity - of the catalyst to the times when lean or rich exhaust gas breaks through the catalyst according to the second probe, the previously entered into the catalyst during a lean phase total oxygen mass (O ₂ -Magermasse m _{O2, a} ) equal to the in the subsequent fat phase discharged from the catalyst total oxygen mass (O ₂ -fat mass m _{O2, from} ) must be. If, in this case, the O ₂ lean mass and O ₂ fat mass are mathematically determined on the basis of the signal of the first lambda probe and it turns out that there is a difference between the thus determined lean and fat masses, this is due to an offset of the first probe, which can be calculated from this difference. If the front probe has no offset shift of its signal or if it is completely corrected, then the measured O ₂ lean and Grease masses until each crossing of the setpoint of the rear probe to be identical. The procedure according to the invention makes it possible to determine the offset value with high accuracy in a single drive even under dynamic driving style.

The determination of the cumulative oxygen mass introduced into the catalyst as well as of the discharged oxygen mass is preferably carried out at each crossing of the nominal value of the sensor signal of the second lambda probe arranged downstream of the catalytic converter. In this case, each time the setpoint is crossed, it is recorded how much oxygen has been introduced or removed since the last time the setpoint was crossed. Depending on the type of lambda control of the internal combustion engine that is being carried out, this calculation of the oxygen masses can be carried out in two ways.

1. Using the front lambda probe signal

According to this embodiment, the determination of during a lean phase (λ> 1) is carried out in the catalyst registered accumulated mass of oxygen (O ₂ -Magermasse) as well as during a fat phase (λ <1) discharged from the catalyst cumulative mass of oxygen (O ₂ -Fettmasse) in direct dependence of the lambda signal of the first lambda probe. In order to calculate an oxygen mass flow from the measured lambda value, the consideration of the current exhaust gas mass flow is necessary. Then, the oxygen mass flow can be carried out, for example, according to formula 1, wherein m. _O2 the oxygen mass flow, m. _exhaust the exhaust gas mass flow and λ means the lambda value currently measured with the front lambda probe. m. _O2 = (1 - 1 / λ) · m. _{Exhaust gas} · 64 (1)

2. Using a rear lambda probe positional intervention

According to this embodiment, the lambda control of the internal combustion engine is carried out by means of the second lambda probe by the air-fuel mixture of the internal combustion engine in accordance with a control intervention, that is, a requested lambda deviation, which is added to the lambda desired value in the direction lean or rich in case of exceeding or falling below the above target value is moved. In this case, the oxygen mass flow can be determined, for example, according to formula 2, wherein Δλ means the control intervention of the second lambda probe, and m. _O2 and m. _exhaust have the meaning given above. m. _O2 = Δλ · m. _Exhaust · 64 (2)

If the rear control is inactive - this is the case, if the lambda setpoint is not equal to 1, for example in a coasting phase - then it can be switched to the calculation formula according to formula 1 instead.

The calculation of the oxygen mass flows according to formula 1 or 2 is carried out separately for lean nominal lambda values (λ> 1) and rich desired lambda values (λ <1), that is to say for undershooting and exceeding the setpoint value of the second lambda probe, by one each To obtain value for the O ₂ masser mass flow and O ₂ -mass mass flow. By integration of the mass flows over time, the corresponding cumulative values for the total registered oxygen mass (O ₂ -mask mass) as well as the discharged total oxygen mass (O ₂ -fat mass) are obtained. As a result, it is separately summed up, which total amount of oxygen was enforced in each case if the probe signal behind the catalyst above or below the setpoint value was λ≈1.

Further, when the integration performs a calculation step, a time counter is also incremented accordingly. Preferably, the determination of the registered oxygen mass and the discharged oxygen mass is carried out at each crossing of the setpoint value for the sensor signal of the second lambda probe. Likewise, with each crossing, oxygen integration is restarted. The next time the setpoint is crossed, it is then determined which amount of oxygen was introduced or removed until this renewed crossing. The integration and the time measurement are preferably stopped when the oxygen content of the catalyst reaches its upper or lower limit, for example in a fuel cut-off phase, in which only air is enforced and the catalyst is completely filled with oxygen. The integrator value can also be reinitialized.

Since in order to be able to form a difference between the introduced and the discharged oxygen mass, at least one lean phase and at least one rich phase must have elapsed, it is provided to carry out the difference formation every second crossing of the setpoint value of the rear lambda probe or at a multiple thereof, that is, every fourth, sixth, eighth, etc. crossing.

In real driving operation, not only is the lambda signal (ie the oxygen concentration in the exhaust gas) variable in time, but also the exhaust gas mass flow. For this reason, the difference between the two oxygen masses can not be used to directly deduce the offset value of the lambda signal. Therefore, it is preferably provided to first determine a mean correction oxygen mass flow from the difference between the registered and the discharged oxygen mass. For this purpose, the difference between O ₂ -fat and O ₂ -mager mass is divided by the total time of the integration intervals. Here again, a value for the correction oxygen mass flow is usefully determined only every second crossing of the nominal value of the probe signal. According to a preferred embodiment of the method, a minimum time and / or a minimum amount of oxygen and / or a minimum number of signal cross events are predetermined for the determination of the correction oxygen mass flow, which must be exceeded before an offset mass flow is calculated from the determined oxygen masses. In this way, the process becomes more independent of dynamic scattering and thus more accurate.

After determining the correction oxygen mass flow, the offset of the front lambda probe can now be calculated. For the method according to the invention, it is assumed that the lambda offset Δ is always constant or at least approximately constant, independent of the mass flow. Furthermore, it is assumed that the exhaust gas mass flow does not move in substantially different areas after the determination of the correction oxygen mass flow. Conversely, the calculation of the offset can be suppressed, if there is obviously such a deviation of the exhaust gas mass flow. The calculation of the offset Δ of the lambda signal of the front probe can then take place, for example, according to formula 14 or - in the case of lambda control by means of control intervention of the rear lambda probe - according to formula 15. Here, λ is the lambda value currently measured with the front lambda probe, m. _exhaust the currently existing exhaust gas mass flow and C the calculated correction oxygen mass flow. The derivation of the formula 14 is explained in more detail in the embodiment.

The device according to the invention has the structure described above and a calibration algorithm for carrying out the above-described method steps, which is preferably stored in digital form in an engine control unit.

Further preferred embodiments of the invention will become apparent from the remaining, mentioned in the dependent claims characteristics.

The invention will be explained below in embodiments with reference to the accompanying drawings. Show it:

1 a schematic diagram of an internal combustion engine with downstream exhaust system and

2 time profiles of the (a) exhaust lambda before catalyst, (b) the lambda probe signal downstream of the catalyst, (c) cumulative oxygen injection or recovery mass during individual lean or rich intervals, (d) and (e) cumulative oxygen injection or recovery mass during several lean or fat intervals.

1 shows a schematic diagram of an internal combustion engine 10 , which can be a gasoline or diesel engine, with downstream exhaust system. The internal combustion engine 10 is via an intake pipe 12 supplied with air. In the intake pipe 12 there is a throttle 14 which one Control of the air mass flow allowed. The internal combustion engine 10 also has a fuel supply, not shown here, which includes a direct injection or port injection.

One from the internal combustion engine 10 generated exhaust gas is via an exhaust passage 16 passed, which is an exhaust gas catalyst 18 which may be a 3-way catalyst, for example. Optionally, the catalyst 18 be followed by other catalysts. In the exhaust duct 16 is also in a position close to the engine upstream of the catalyst 18 a first lambda probe 20 arranged, which is for example a broadband lambda probe. Wideband lambda probes have over wide lambda ranges a voltage signal proportional to the oxygen content of the exhaust gas, which enables them for the lambda control even in the very lean region at λ> 1. A second lambda probe 22 is the catalyst 18 downstream. This is typically a step response lambda probe which has a steep voltage characteristic in the region around λ = 1, thereby enabling a particularly accurate lambda control in the stoichiometric range.

The probe signals of the lambda probes 20 . 22 go into a motor control 24 which makes an air-fuel control in response to them. In particular, the engine control affects 24 the air mass flow via position of the throttle 14 and / or an amount of fuel supplied via influencing the fuel supply. The engine control 24 includes, among other things, a calibration algorithm 26 , which the inventive method for determining an offset of the front lambdasonde 20 performs. This will be described in more detail below.

In 2 (a) show the lines 100 and 102 typical curves of the front lambda probe 20 measured lambda signal. The curve represents 100 the signal of a fully offset-corrected lambda probe (or the true lambda curve), while the curve 102 represents the shifted by an offset Δ in the λ-dimension course. While the surfaces of the curve 100 without offset in each case below λ = 1 (fat phases) are equal to the areas above λ = 1 (lean phases), is at 102 to see a clear shift in favor of the lean side. Thus, the signal λ of the lambda probe with offset (history 102 ) from a lambda lambda λ _b + the offset Δ corresponding to the true lambda value. (This representation is chosen here for better comprehension.) In practice, an offset in the front lambda will have an effect in different times Δt, since usually with a lambda curve according to curve 100 is regulated.)

In 2 B) the course of the sensor signal U _{λ is} the downstream of the catalyst 18 arranged lambda probe 22 shown. In this case, signal values above the setpoint value of a rich exhaust gas atmosphere (λ <1) corresponding to λ = 1 and values below the setpoint value correspond to lean exhaust gas compositions (λ> 1). According to the illustrated embodiment, the air-fuel control of the internal combustion engine takes place 10 based on the signal U _{λ of} the lambda probe 22 , This is at a fall below the setpoint, that is, at a breakthrough lean exhaust gas through the catalyst 18 , the air-fuel mixture of the internal combustion engine 10 shifted in the direction of bold. Conversely, when the nominal value is exceeded, that is to say the breakthrough of rich exhaust gas through the catalyst 18 , the air-fuel mixture shifted toward lean. In each case, a control intervention Δλ with a corresponding sign is added to the lambda setpoint. According to the method according to the invention, the times are registered at which the sensor signal U _λ crosses the setpoint value corresponding to a lambda value of 1, ie exceeds or falls below it.

These times are marked in the present representation with t0 to t4. According to the method according to the invention, each time the setpoint is crossed, that is to say at the times t0, t1, t2, t3 and t4, the determination of the temperature in the catalyst begins 18 registered oxygen masses or the discharged oxygen masses according to the lambda signal of the front lambda probe 20 (Curve 100 respectively. 102 ). For this purpose, starting with the exceeding of the setpoint of the rear lambda probe 22 (Curve 104 ) at t0 as a function of the lambda signal of the front lambda probe 20 (Curve 100 respectively. 102 ) calculated in accordance with formula 1a, the registered oxygen mass flow and integrated to below the setpoint value at time t1. From time t1, that is to say at lambda values <1, a separate calculation of the discharged oxygen mass flow according to formula 1b starts. In the formulas 1a and 1b, the exhaust gas mass flow m. _exhaust the unit kg / h and the oxygen mass flow m. _O2 mg / s.

As in the present case, the air-fuel control by means of the rear lambda probe 22 takes place here, alternatively, the calculation of the oxygen mass flows via the control intervention Δλ the rear lambda probe 22 take place according to the formulas 2a and 2b. m. _{O2, a} = Δλ · m. _{Exhaust gas} · 64 for λ> 1 (2a) m. _{O2, from} ⁼ Δλ · m. _{Exhaust gas} · 64 for λ <1 (2b)

According to formula 3, by integrating the mass flows calculated in one way or the other over the time intervals limited by the corresponding crossing times, the accumulated registered oxygen mass m _{O2, an} (O ₂ lean mass) and the cumulated discharged oxygen mass m _{O2, from} (O ₂ - Fat mass). These are in picture 2 (c) shown, the gradients 106 . 108 the result at an offset-corrected lambda probe (curve 100 ) and the curves 110 and 112 the lean or rich masses according to non-offset-corrected lambda curve 102 , While the amounts 106 and 108 are identical, differ significantly with existing offset, the O ₂ -mask mass and the O ₂ fat mass.

2 (d) and (e) show the courses of the oxygen lean and fat masses according to FIG 2 (c) if they are integrated over several intervals. In this case, during a fat phase, the value for the O ₂ -mask mass m O _{2 , one} each constant and increases only during the lean phases (curves 114 . 118 ). Accordingly, the value for the O ₂ fat mass m _{O2, from} during the lean phases is constant and grows only in fat phases (curves 116 . 120 ). At every second crossing or a multiple thereof, the set value of the probe signal of the rear probe 22 According to formula 4, a correction oxygen mass flow Δm. _O2 determined from the difference between the cumulative O ₂ fat mass and the cumulated O ₂ -mager mass divided by the total time .DELTA.t of the integration time. In 2 Thus, for example, Δt results at time t2 at t2-t0 or at time t4 at t4-t0.

From the thus determined correction O ₂ mass flow is now the offset Δ of the front lambda probe 20 calculated, it being assumed that the exhaust gas mass flow in the following calculation period does not differ significantly and the lambda offset Δ is largely independent of the exhaust gas mass flow, so that the consideration of an averaged calculation step is allowed. The calculation of the offset is performed according to equation 14 for each time step according to the following derivation.

From (9) and (7) follows:

From (10) and (5) follows:

If the amount of oxygen is not determined directly via the lambda signal, but by means of adjustment intervention Δλ the rear lambdasond 22 , so the calculation of the offset with a small error according to formula 15 is simplified.

In order to minimize the influence of dynamic fluctuations, it is preferably provided to sum up the thus determined offset Δ of the individual partial steps and to determine an average value with the aid of the simultaneously recorded summation time. An evaluation of this average should preferably take place when the summation time has exceeded a predetermined minimum time and / or a simultaneously determined amount of exhaust gas has exceeded a predetermined minimum amount. This mean value corresponds to the offset Δ of the front lambda probe according to FIG 2 (a) ,

The offset, in addition to its actual use to correct the measured lambda signal, may also be used to generate a maintenance signal when the offset exceeds a predetermined threshold. It can also supplement a conventional adaptation value for the offset (this is usually the I-part of the second lambda control loop behind the catalyst), for example by adding it.

LIST OF REFERENCE NUMBERS

10

Internal combustion engine

12

intake

14

throttle

16

exhaust duct

18

catalyst

20

first lambda probe

22

second lambda probe

24

motor control

26

calibration algorithm

Δ

offset

Δm. _O2

Correction oxygen mass flow

λ

Lambda, currently measured

λ _b

base lambda

Δλ

control intervention

m _{O2, a}

cumulative registered oxygen mass, O ₂ -magermasse

m _{O2, out}

Cumulated discharged oxygen mass, O ₂ fat mass

m. _{O2, a}

registered oxygen mass flow

m. _{O2, from}

discharged oxygen mass flow

m. _exhaust

Exhaust gas mass flow

U _λ

sensor signal

A

calculated oxygen mass

D

Differential oxygen mass

Claims (8)

Method for determining an offset (Δ) of a lambda value upstream of one in an exhaust gas duct ( 16 ) an internal combustion engine ( 10 ) arranged catalyst ( 18 ), wherein the lambda value is calculated or by means of an upstream of the catalyst ( 18 ) arranged first lambda probe ( 20 ) is measured, with the steps (a) registration of times at which a sensor signal (U _λ ) of a second, the catalyst ( 18 ) downstream lambda probe ( 22 ) crosses a setpoint value corresponding to lambda = 1, (b) determining a value in the catalyst ( 18 ) accumulated oxygen mass (m _{O2, a} ) over the duration of at least one limited by the time lean phase and discharged from the catalyst cumulative oxygen mass (m _{O2, off} ) over the duration of at least one limited by the time fat phase in dependence of the calculated or measured lambda value upstream of the catalyst ( 18 ) and (c) determining the offset (Δ) for the calculated or measured lambda value as a function of a correction oxygen mass flow, which consists of a difference between the registered oxygen mass (m _{o2, in} ) and the discharged oxygen mass (m _{o2, aus} ) and a Time interval of the determination of the cumulative oxygen masses (m _{O2, a} , m _{O2, off} ) is determined. A method according to claim 1, characterized in that an air-fuel regulation of the internal combustion engine ( 10 ) by means of the first lambda probe ( 22 ) and the determination of the catalyst ( 18 ) Registered cumulative oxygen mass (m _{O2, a)} and the catalyst discharged from the accumulated mass of oxygen _{(O2 m, (off)} in the immediate response to the signal from the first lambda probe 20 ) he follows. A method according to claim 1, characterized in that an air-fuel regulation of the internal combustion engine ( 10 ) by means of the second lambda probe ( 22 ) is carried out by the air-fuel mixture of the internal combustion engine when an above or below the setpoint ( 10 ) corresponding to a control intervention (Δλ) of the second lambda probe ( 22 ) is shifted in the direction of lean or rich in direction, and the determination of the catalyst ( 18 ) registered cumulative oxygen mass (m _{O2, a} ) and from the catalyst discharged cumulative oxygen mass (m _{O2, out} ) as a function of a control engagement (Δλ) of the second lambda probe ( 22 ) he follows. Method according to one of the preceding claims, characterized in that the determination of the in the catalyst ( 18 ) accumulated oxygen mass (m _{O2, a} ) and discharged from the catalyst cumulative oxygen mass (m _{O2, out} ) at each crossing of the setpoint value of the sensor signal (U _λ ) of the second lambda probe ( 22 ) is carried out. Method according to one of the preceding claims, characterized in that the determination of the difference of the registered oxygen mass (m _{O2, a} ) and the discharged oxygen mass (m _O2, OFF) and the offset (Δ) at every second crossing of the setpoint value of the sensor signal (U _λ ) of the second lambda probe ( 22 ) or at a multiple thereof. Method according to one of the preceding claims, characterized in that the time interval of the determination of the cumulative oxygen masses (m _{O2, a} , m _{O2, off} ) is recorded. Method according to one of the preceding claims, characterized in that the upstream of the catalyst ( 18 ) arranged lambda probe ( 20 ) is a broadband lambda probe. Device for determining an offset (Δ) of a lambda value upstream of one in an exhaust gas duct ( 16 ) an internal combustion engine ( 10 ) arranged catalyst ( 18 ), wherein the lambda value is calculated or by means of an upstream of the catalyst ( 18 ) arranged first lambda probe ( 20 ), comprising a calibration algorithm ( 26 ) for carrying out the steps: (a) registering times at which a sensor signal (U _λ ) of a second, the catalyst (U 18 ) downstream lambda probe ( 22 ) crosses a setpoint value corresponding to lambda = 1, (b) determining a value in the catalyst ( 18 ) accumulated oxygen mass (m _{O2, a} ) over the duration of at least one limited by the time lean phase and discharged from the catalyst cumulative oxygen mass (m _{O2, off} ) over the duration of at least one limited by the time fat phase in dependence of the calculated or measured lambda value upstream of the catalyst ( 18 ) and (c) determining the offset (Δ) for the calculated or measured lambda value as a function of a correction oxygen mass flow, which consists of a difference between the registered oxygen mass (m _{o2, in} ) and the discharged oxygen mass (m _{o2, aus} ) and a time interval of the determination of the total mass of oxygen _(O2 m _a, m _{O2, off)} is determined.

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