DE102015203458B3 - Method and device for operating an internal combustion engine - Google Patents

Abstract

An internal combustion engine has a plurality of cylinders, to each of which an injection valve is assigned and which are each assigned to a common exhaust gas probe, which is arranged in or upstream of an exhaust gas catalytic converter in an exhaust gas tract and provides a measurement signal (MS_A). Furthermore, the engine is associated with a crankshaft angle sensor whose measurement signal (MS_N) is representative of a curve of a crankshaft angle of a crankshaft. For operating the internal combustion engine, a noise characteristic value (RM) is determined as a function of a course of the measurement signal (MS_A) of the respective exhaust gas probe, which is representative of a measure of a noise of the measurement signal (MS_A) of the respective exhaust gas probe. Depending on a course of the measuring signal (MS_N) of the crankshaft angle sensor, an uneven running characteristic value (LU) assigned to the respective cylinder is determined. Dependent on the respective unrestricted rolling index characteristic value (LU) and the noise characteristic value (RM), respective control signals (SG_INJ) for controlling the respective injection valves are adapted in the sense of equalizing an air / fuel ratio in the individual cylinders.

Description

A contribution to keeping pollutant emissions as low as possible during operation of an internal combustion engine can be achieved by minimizing pollutant emissions that occur during the combustion of the air / fuel mixture in the respective cylinders. On the other hand, exhaust gas aftertreatment systems are used in internal combustion engines, which convert the pollutant emissions which are generated during the combustion process of the air / fuel mixture in the respective cylinder into harmless substances.

For this purpose, catalytic converters are used which convert carbon monoxide, hydrocarbons and optionally nitrogen oxides into harmless substances.

Both the targeted influencing of the generation of pollutant emissions during combustion, as well as the conversion of the pollutant components with a high efficiency by an exhaust gas catalyst require a very precisely adjusted air / fuel ratio in the respective cylinder.

From the DE 10 2005 009 101 B3 a cylinder-specific lambda control is known, wherein a cylinder-individual air / fuel ratio deviation is determined, which then fed to a controller whose output is a regulator value for influencing the air / fuel ratio in the respective cylinder. The controller comprises an integral component.

From the DE 10 2006 026 390 A1 an electronic control device for controlling the internal combustion engine in a motor vehicle is known with a Laufunruheermittlungseinheit and with a Einspritzmengenkorrektureinheit, wherein a defined group of cylinders is associated with a lambda probe. The injection amount correcting unit is configured such that the injection quantity of a cylinder of the defined group to be examined is adjustable in the lean direction by a difference adjustment value assigned to a running disturbance difference value and the injection quantity of at least one of the remaining cylinders is correspondingly adjustable in the direction of grease, so that overall a predetermined lambda value is achieved. It is furthermore designed such that a cylinder-individual Differenzverstellwert for each cylinder is adjustable in this way and that cylinder-individual correction values can be determined by the cylinder-individual Differenzverstellwerte be set in relation to each other.

From the DE 10 2012 223 129 B3 a method for operating an injection device for an internal combustion engine is described in which a profile of a value of a rotational speed of a crankshaft within a predetermined period of time for each combustion chamber of the plurality of combustion chambers is determined. Furthermore, the respective courses are compared with a predetermined comparison course in order to determine a deviation between the respective power output of the combustion chambers from a predetermined power output. Furthermore, a differential is determined in each case and / or an integral of the course determined within the predetermined period. In addition, the respective determined differentials are compared with a differential of the predetermined comparison profile and / or the respective determined integral with an integral of the predetermined comparison profile.

From the DE 10 2009 027 822 A1 a method is known for determining a trimming of at least one cylinder of an internal combustion engine, wherein the at least one cylinder is operated in succession in at least one lean phase and at least one rich phase to provide on average exhaust neutrality, wherein a run disturbance signal in a lean phase is evaluated to be a cylinder individual Feature regarding the trim.

DE 10 2005 047 829 B3 describes a method for controlling the running noise of reciprocating engines. A Fourier series is used with Z-1 summands a _n , b _n ..., where n = 2, 3, ... to Z, where Z is the number of cylinders of the engine, as a series representation of average speed values the engine speed. The order n is chosen so that at least an odd multiple of half the camshaft frequency is taken into account in the series representation for generating a control deviation e _n . An individual contribution to the control deviation for each addend of the series representation is calculated by means of a predetermined value k = k (n), k (n) originating from a preliminary investigation and being the value at which the maximum expression of the effect of the last ignition of the cylinder, which will ignite next, is measured. A total deviation e _{Z is formed} from the individual contributions.

In the DE 3314225 C2 is a control device for an internal combustion engine described with a signal train from an exhaust gas sensor to an input of a control device for the rough running. The string comprises a signal processing unit and an averaging stage connected in parallel with each other. The output of an exhaust probe is fed to the averaging stage. It is also fed to the signal processing unit which is a high pass or bandpass.

From the DE 10 2005 049 069 A1 it is known, a lambda signal by means of a Filter bandpass filter, whereby a filtered lambda signal is obtained. Subsequently, a diagnostic statement regarding a component of the internal combustion engine which influences the formation of the air / fuel mixture is made as a function of the filtered lambda signal. Further, for differentiation between different errors, a running noise signal is determined based on a respectively considered cylinder.

In the DE 10 2008 031 713 A1 a mixture control for an internal combustion engine is described, wherein the internal combustion engine comprises a first cylinder bank with a first exhaust gas line and a second cylinder bank with a second exhaust gas line. Each exhaust gas line is assigned a lambda probe which measures a respective residual oxygen concentration. Furthermore, measuring devices are provided for determining first and second running noise values associated with the respective cylinder banks.

A mixture error is detected from a frequency analysis of the first residual oxygen concentration and / or a frequency analysis of the second residual oxygen concentration.

From the DE 10 2007 024 416 A1 It is known to perform misfire detection based on a comparison of successive segment times, the raw signals for which are provided by a speed sensor system. To achieve a higher accuracy, describes the DE 10 2007 024 416 A1 to additionally use a lambda signal for misfire detection.

The object on which the invention is based is to provide a method and a device for operating an internal combustion engine having a plurality of cylinders, which makes a contribution to a low-emission operation in a simple and reliable manner.

The object is solved by the features of the independent claims. Advantageous embodiments are characterized in the subclaims.

An embodiment of the invention is characterized by a method and a corresponding apparatus for operating an internal combustion engine having a plurality of cylinders, each associated with an injection valve and each associated with a common exhaust probe, which is arranged in an exhaust tract in or upstream of an exhaust gas catalyst. The exhaust gas probe provides a measurement signal. Furthermore, a crankshaft angle sensor is provided, whose measurement signal is representative of a curve of a crankshaft angle of a crankshaft.

Depending on a profile of the measurement signal of the respective exhaust gas probe, a noise characteristic value is determined, which is representative of a measure of a noise of the measurement signal of the respective exhaust gas probe. Depending on a course of the measurement signal of the crankshaft angle sensor, an uneven running characteristic associated with the respective cylinder is determined. Depending on the respective unimportant cylinder uneven running characteristic and the noise characteristic value, respective control signals for controlling the respective injection valves are adapted in the sense of equalizing an air / fuel ratio in the individual cylinders.

In this way, the insight is used that the noise characteristic is characteristic of an uneven metering of fuel to the individual cylinders. By additionally taking into account the respective uneven running characteristic which is representative of a similarity measure of segment times of the respective cylinder compared to the segment times of the other cylinders, an assignment to the individual cylinders is then possible in a suitable manner and thus a simple and reliable matching of the air / fuel ratio. Fuel ratio in each cylinder possible.

Thus, this procedure does not necessarily require an exact knowledge of a phase position or a point in time of the measurement signal of the exhaust gas probe that is decisive for the respective cylinder, which is otherwise determined empirically and can be corrected by a subsequent adaptation. This adaptation represents a particular challenge in particular in the case of special exhaust gas configurations, for example with an exhaust gas turbocharger, with strongly changing points in time of the measurement signal at the exhaust gas probe.

According to an advantageous embodiment, the determination of the noise characteristic value comprises a Fourier transformation. In particular, this may include a fast Fourier transform. This enables a particularly efficient calculation.

According to a further advantageous embodiment, the respective uneven running parameter is indicative of a direction of a similarity measure of segment times of the respective cylinder in comparison to the segment times of the other cylinders. The direction is in particular represented by a sign.

According to a further advantageous embodiment, the respective uneven running characteristic characterizes a relevance of adapting the respective actuating signal to trigger the respective injection valve. In particular, the relevance has either a relevance value, for example a neutral value, such as 1, or an irrelevance value, such as a blanking value, such as 0.

In this context, it is particularly advantageous if the uneven running characteristic value is determined in such a way that its relevance has an irrelevance value within a predetermined range of the degree of similarity of segment time durations of the respective cylinder compared to segment periods of the other cylinders. In this way, the control signal for a respective cylinder can not be adjusted within the suitably predetermined range, which can be determined for example by appropriate tests or can be determined by simulations, while it is adjusted accordingly if the relevance value is present.

According to a further advantageous embodiment, the noise characteristic value is fed on the input side to a PI controller. By providing the PI controller, a particularly efficient and effective adaptation of the respective actuating signal can take place.

In this context, it is advantageous if a degree of taking into account a regulator control signal of the PI controller for adjusting the respective control signal for controlling the respective injection valve is determined, depending on the rough running characteristic value taking into account the similarity measure of segment durations of the respective cylinder compared to segment periods of the other Cylinder. In this way, a particularly effective adaptation in the sense of equalizing the air / fuel ratios in the individual cylinders can take place.

Segment durations here denote durations of a respective cylinder segment, wherein a cylinder segment results from the crankshaft angle of a working cycle divided by the number of cylinders of the internal combustion engine. For example, in a four-stroke internal combustion engine with four cylinders, a crankshaft angle of 720 ° results: 4, ie 180 °.

Embodiments of the invention are explained in more detail below with reference to the schematic drawings.

Show it:

1 an internal combustion engine with a control device,

2 a block diagram of the control device,

3A and 3B first signal curves,

3C a frequency spectrum associated with the first signal progressions,

4A and 4B second waveforms and

4C a frequency spectrum associated with the second waveforms.

Elements of the same construction or function are identified across the figures with the same reference numerals.

An internal combustion engine ( 1 ) comprises an intake tract 1 , an engine block 2 , a cylinder head 3 and an exhaust tract 4 , The intake tract 1 preferably includes a throttle 11 and a collector 12 and a suction tube 13 leading to a cylinder Z1 via an inlet passage in the engine block 2 is guided. The engine block 2 further comprises a crankshaft 21 , which has a connecting rod 25 with the piston 24 of the cylinder Z1 is coupled.

The cylinder head 3 includes a valvetrain with a gas inlet valve 30 , a gas outlet valve 31 and valve actuators 32 . 33 , The cylinder head 3 further comprises an injection valve 34 and a spark plug 35 , Alternatively, the injection valve 34 also in the intake tract 1 be arranged.

The exhaust tract 4 includes an exhaust gas catalyst 40 , which is preferably designed as a three-way catalyst.

A control device 6 is provided, the sensors are assigned, which detect different parameters and determine the measured values of the measured variable. Operating variables include not only the measured variables but also derived from these variables. The control device 6 controls depending on at least one of the operating variables, the actuators, which are assigned to the internal combustion engine, and which each corresponding actuators are assigned, by generating control signals for the actuators. The control device 6 may also be referred to as a device for operating the internal combustion engine.

The sensors are a pedal position transmitter 71 , which indicates the position of an accelerator pedal 7 captured, an air mass meter 14 , which is an air mass flow upstream of the throttle 11 detected, a temperature sensor 15 , which detects an intake air temperature, a pressure sensor 16 , which detects the intake manifold pressure, a crankshaft angle sensor 22 , which detects a crankshaft angle, which is then assigned a speed, a torque sensor 23 , which is a torque of the crankshaft 21 captured, one Camshaft angle sensor 36a which detects a camshaft angle and an exhaust gas probe 41 , which detects a residual oxygen content of the exhaust gas and whose measurement signal MS_A is characteristic of the air / fuel ratio in the cylinder Z1 in the combustion of the air / fuel mixture. The exhaust gas probe 41 is for example designed as a lambda probe, in particular as a linear lambda probe, and generates, if it is designed as a linear lambda probe, over a wide relevant range of the air / fuel ratio, a proportional to this measurement signal.

The measurement signal MS_N of the crankshaft angle sensor 22 is thus representative of a curve of the crankshaft angle of the crankshaft 21 , Preferred is a donor gear with teeth on the crankshaft 21 arranged and the crankshaft angle sensor 22 assigned, so that depending on the measurement signal of the crankshaft angle sensor 22 Tooth periods can be determined.

Depending on the embodiment, any subset of said sensors may be present or additional sensors may also be present.

The actuators are, for example, the throttle 11 , the gas inlet and outlet valves 30 . 31 , the injection valve 34 or the spark plug 35 ,

In addition to the cylinder Z1 also more cylinders Z2 to Z4 are provided, which then also corresponding actuators are assigned. Preferably, each exhaust bank on cylinders, which can also be referred to as a cylinder bank, in each case an exhaust gas line of the exhaust gas tract 4 assigned and the respective exhaust line each an exhaust gas probe 41 assigned accordingly.

The control device 6 preferably comprises a computing unit and a memory for storing data and programs. To operate the internal combustion engine is in the control device 6 stored a program for operating the internal combustion engine, which can be processed during operation in the computing unit. The software implemented the program below using the 2 described block diagram. The program for operating the internal combustion engine is in particular started promptly to an engine start of the internal combustion engine.

A block B1 ( 2 ), the measuring signal MS_A of the exhaust gas probe is supplied on the input side. Depending on the course of the measuring signal MS_A of the exhaust gas probe 41 In the block B1, a noise parameter RM is determined, which is representative of a measure of a noise of the measurement signal MS_A of the respective exhaust gas probe 41 ,

In a particularly simple manner, the noise characteristic can be calculated, for example, taking into account a summation of jumps in the measurement signal MS_A of the exhaust gas probe 41 be determined over a given period of time.

The noise characteristic value RM can be determined particularly well by means of a Fourier transformation, whereby a fast Fourier transformation, also abbreviated as FFT, is preferably used. In this context, a filter is preferably used, which is formed for example in the form of a bandpass. The filter is preferably designed such that it includes a frequency which correlates to the respective current rotational speed, in particular a frequency which correlates to a current frequency, in particular approximately in the middle of the segment. In particular, it comprises the fundamental frequency assigned to the respective average segment time duration.

The noise characteristic value is thus taking into account the frequency spectrum of the measurement signal MS_A of the exhaust gas probe 41 determined.

In this context, in particular the recognition is used that an amplitude in the range of the above-mentioned fundamental frequency of the Fourier-transformed at unequal air / fuel ratios in the respective cylinders Z1 to Z4 exceeds a predetermined threshold. Thus, the amplitude in the region of the fundamental frequency can be used, for example, in particular decisively for determining the noise characteristic value RM.

The noise characteristic RM is in turn fed to the input side of a block B3, in which a controller, in particular a PI controller, is formed. The controller in the block B3 is also supplied in particular also a desired value, which is suitably predetermined in advance. In particular, a control difference is determined from the difference of the setpoint value and the noise characteristic value RM and then supplied to the controller, in particular to the PI controller. On the output side, the controller generates in block B3 a regulator control signal R_SG, which is supplied to a block B5, which in particular comprises a multiplier.

A block B7 is the measurement signal MS_N of the crankshaft angle sensor 22 supplied on the input side.

The block B7 is designed to be dependent on a course of the measurement signal MS_N of the crankshaft angle sensor 22 to determine a rolling index characteristic LU assigned to the respective cylinder Z1 to Z4. The uneven running characteristic LU is in particular representative of a similarity measure of segment durations which correspond to the respective cylinder in the Compared to segment durations of other cylinders. In this context, for example, so-called tooth times can be analyzed or a speed gradient can also be analyzed.

For example, the rough running characteristic value LU is determined in such a way that is characteristic for a direction of a similarity measure of segment time durations of the respective cylinder Z1 to Z4 in comparison to segment time periods of the other cylinders Z1 to Z4. The direction is here represented in particular by a sign, ie plus or minus.

In addition, the rough running characteristic value LU is determined, for example, in such a way that it is indicative of a relevance of adapting the respective actuating signal SG_INJ for driving the respective injection valve. In particular, the relevance has either a relevance value, for example a neutral value, such as 1, or an irrelevance value, for example a blanking value, such as 0.

In addition, the rough running value is determined, for example, in such a way that its relevance has an irrelevance value within a predetermined range of the similarity measure of segment durations of the respective cylinder Z1 to Z4 in comparison to segment periods of the other cylinders Z1 to Z4.

For example, the smooth running characteristic may have the discrete values +1, 0 and -1.

According to another embodiment, a degree of considering a servo control signal of the PI controller for adjusting the respective control signal SG_INJ for driving the respective injector becomes 34 determines, as a function of the rough running value LU, taking into account the similarity measure of segment time durations of the respective cylinder Z1 to Z4 in comparison to the segment periods of the other cylinders. In this case, the rough running value potentially has further values apart from the above-mentioned values +1, 0 and -1.

In the block B5, the controller control signal R_SG is then multiplied by the running noise characteristic value LU by means of the multiplier, and a corresponding adaptation of the respective actuating signal SG_INJ of the respective injection valve takes place depending on this product. The respective actuating signal is determined, for example, primarily as a function of an air mass flow and a rotational speed value, for example with the aid of a characteristic map which was determined in advance.

In a further embodiment, the running noise value LU and the noise characteristic RM are linked, for example multiplicatively, and then linked on the input side to the block B3, in particular as an actual value. In this case, if necessary, it is possible to dispense with multiplying the control signal R_SG in the block B5 by the running noise characteristic LU, and thus possibly omit the rough running characteristic LU from the block B5.

In the 3A and 3B are curves of the measurement signal MS_A shown, the 3B a first window area F1 of the signal according to 3A represents time resolved in more detail. The waveforms in the 3A and 3B are plotted over time t. The ordinate in the 3A and 3B is each a voltage.

In 3C is a frequency spectrum of the first window area F1 shown, wherein the abscissa is the frequency and the ordinate is in particular a voltage or may be a signal power. The ordinate may also represent a current.

In the first window area F1, there is no relevant unequal distribution of the air / fuel mixture in the respective cylinders. The basic oscillation corresponding to the current segment duration is in this case in the range of approximately 15 Hz and the amplitude of the frequency spectrum in this region is for example 12 × 10 ^-4 V.

In the 4A is again the course of the measuring signal MS_A the exhaust gas probe 41 represented and in the 4B the one within a second window area F2 (see also 4A ) temporally higher-resolution signal waveform shown.

In the 4C is the frequency spectrum with respect to the second window area F2 of the measuring signal MS_A of the exhaust gas probe 41 according to the 3C applied. In this example too, the fundamental frequency which corresponds to the respective current segment duration is in the range of 15 Hz. However, in the region of the second window region, the injection has been canceled so that there is an unequal distribution of the air / fuel ratio in the individual cylinders is. The fundamental frequency also corresponds in each case to the ignition frequency.

It can be clearly seen that the amplitude of the frequency spectrum in the range of the fundamental frequency in the case of 4C is significantly higher and that is about the factor 50 in comparison to 3C Here, for example, an unequal distribution of 10% between the cylinders was set. Thus, for example, one cylinder is adjusted by -10% and the other by + 10% with respect to its air / fuel ratio.

In a particularly simple embodiment, the noise characteristic value RM is determined, for example, as a function of the amplitude of the frequency spectrum in the region of the fundamental frequency.

It has been shown that in particular in internal combustion engines which are operated with gasoline and in particular in a homogeneous operation, ie in particular with an air / fuel ratio, are operated in the vicinity of the value λ = 1, by combining the consideration of the regulator control signal R_SG and the uneven running characteristic LU a particularly precise adjustment of the control signal SG_INJ for the injection into the respective cylinder Z1 to Z4 can be achieved, especially there in an internal combustion engine, which is operated with gasoline and operated in the vicinity of the stoichiometric air / fuel ratio is the relationship between fuel mass and torque in the vicinity of the stoichiometric air-fuel ratio is not particularly pronounced. In addition, when using a linear lambda probe as an exhaust gas probe 41 there is no jumping around the stoichiometric air-fuel ratio, and thus a signal difference of the measurement signal MS_A is not very pronounced in an unequal distribution of the air-fuel ratio.

By the above procedure, there is the possibility of the measurement signal MS_A the exhaust gas probe 41 to use for the determination of the unequal distribution of the air / fuel ratio, without having to determine the exact assignment to cylinder injection or cylinder filling exactly. Thus, if appropriate, an active adjustment as in the so-called Cybl_Hom method, for example, in the DE 10 2006 026 390 A1 is described, or to dispense with an adaptation of the phase shift. Furthermore, a cylinder-specific lambda control is also very precisely possible in the case of unfavorable exhaust-gas configurations, for example with an exhaust-gas turbocharger.

LIST OF REFERENCE NUMBERS

1

intake system

11

throttle

12

collector

13

suction tube

14

Air mass sensor

15

temperature sensor

16

intake manifold pressure sensor

2

block

21

crankshaft

22

Crank angle sensor

23

torque sensor

24

piston

25

connecting rod

3

cylinder head

30

Gas inlet valve

31

gas outlet

32, 33

valve drive

34

Injector

35

spark plug

36

camshaft

36a

Camshaft angle sensor

4

exhaust tract

40

catalytic converter

41

gas probe

6

control device

7

accelerator

71

Pedal position sensor

Z1-Z4

cylinder

KW

crankshaft angle

SG_INJ

Control signal for controlling the respective injection valve

MS_A

Measuring signal of the exhaust gas probe

MS_N

Measuring signal of the crankshaft angle sensor

RM

Noise characteristic value

LU

Uneven running characteristic

B1-B7

block

R_SG

Controller output signal

F1

first window area

F2

second window area

t

Time

f

frequency

Claims (8)

Method for operating an internal combustion engine having a plurality of cylinders (Z1, Z2, Z3, Z4), each of which has an injection valve ( 34 ) and each of a common exhaust gas probe ( 41 ) in or upstream of a catalytic converter ( 40 ) in an exhaust tract ( 4 ) and a measurement signal (MS_A) is provided, and with a crankshaft angle sensor ( 22 ) whose measurement signal (MS_N) is representative of a curve of a crankshaft angle of a crankshaft ( 21 ), wherein - depending on a course of the measurement signal (MS_A) of the respective exhaust gas probe a noise characteristic value (RM) is determined which is representative of a measure of a noise of the measurement signal (MS_A) of the respective exhaust gas probe ( 41 ), - depending on a course of the measuring signal (MS_N) of the crankshaft angle sensor ( 22 ) an uneven running characteristic value (LU) assigned to the respective cylinder (Z1, Z2, Z3, Z4) is determined, depending on the uneven running characteristic value (LU) assigned to the respective cylinder (Z1, Z2, Z3, Z4) and the noise characteristic value (RM) Control signals (SG_INJ) for controlling the respective injection valves ( 34 ) are adapted in the sense of a Aligning an air / fuel ratio in the individual cylinders (Z1, Z2, Z3, Z4). Method according to claim 1, wherein the determination of the noise characteristic value (RM) comprises a Fourier transformation. Method according to one of the preceding claims, in which the respective uneven running characteristic value (LU) is indicative of a direction of a similarity measure of segment time durations of the respective cylinder (Z1, Z2, Z3, Z4) compared to segment time periods of the other cylinders (Z1, Z2, Z3, Z4). Method according to one of the preceding claims, in which the respective uneven running characteristic value (LU) is indicative of a relevance of adapting the respective actuating signal (SG_INJ) for driving the respective injection valve ( 34 ). Method according to Claim 4, in which the uneven running characteristic value (LU) is determined such that within a predetermined range of the similarity measure of segment time durations of the respective cylinder (Z1, Z2, Z3, Z4) compared to the segment times of the other cylinders (Z1, Z2, Z3 , Z4) its relevance has an irrelevance value. Method according to one of the preceding claims, in which the noise characteristic value (RM) is fed on the input side to a PI controller. Method according to Claim 6, in which a degree of consideration of a control actuating signal of the PI controller for adapting the respective actuating signal (SG_INJ) for actuating the respective injection valve ( 34 ) is determined as a function of the uneven running characteristic value (LU) taking into account the similarity measure of segment time durations of the respective cylinder (Z1, Z2, Z3, Z4) compared to segment time periods of the other cylinders (Z1, Z2, Z3, Z4). Device for operating an internal combustion engine with a plurality of cylinders (Z1, Z2, Z3, Z4), each of which has an injection valve ( 34 ) and each of a common exhaust gas probe ( 41 ) in or upstream of a catalytic converter ( 40 ) in an exhaust tract ( 4 ) and a measurement signal (MS_A) is provided, and with a crankshaft angle sensor ( 22 ) whose measurement signal (MS_N) is representative of a curve of a crankshaft angle of a crankshaft ( 21 ), the apparatus being adapted to carry out a method according to one of the preceding claims.

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