Technical scope

The present invention relates to a method for determining and utilizing pressure in an exhaust gas pipe in accordance with the recitals for patent claim 1 and a system for determining and utilizing pressure in an exhaust gas pipe in accordance with the recitals for patent claim 26.

The present invention also relates to a computer program and a computer software product which implements the method

according to the invention.

Background

The following background description represents a description of the background to the present invention, though not

necessarily constituting the previously known art.

In order to meet current requirements for exhaust gas

purification and exhaust emissions, present-day motor vehicles are usually fitted with an aftertreatment device that purifies exhaust gases given off by the engine before they are

discharged from the vehicle. This also applies to other devices and craft including combustion engines, such as ships, vessels and aeroplanes.

In an exhaust gas pipe from an engine, catalytic converters are arranged so as to effect the catalytic conversion of environmentally hazardous constituents in the exhaust gases to less environmentally hazardous substances. One method used to bring about effective catalytic conversion is based on the injection of a reducing agent into the exhaust gases upstream of a catalytic converter in the exhaust gas pipe. Such a reduction catalytic converter can be of the SCR (Selective Catalytic Reduction) type, for example. An SCR catalytic converter selectively reduces the concentration of nitrogen oxides N0 _X in the exhaust gases. For an SCR catalytic

converter, a reduction agent in the form of urea or ammonia is normally injected into the exhaust gases upstream of the catalytic converter. When urea is injected into the exhaust gases, ammonia is formed, and it is this ammonia which

constitutes the reductant that contributes to the catalytic conversion in the SCR catalytic converter. The ammonia

accumulates in the catalytic converter through adsorption on active seats of the catalytic converter, converting the nitrogen oxides N0 _X occurring in the exhaust gases into nitrogen and water when these are in the catalytic converter and come into contact with this accumulating ammonia on the active seats of the catalytic converter.

Using an SCR catalytic converter in combination with dosing reduction agent in the form of urea or ammonia, it is

important to control injection of the reductant so as to achieve the desired conversion of the relevant exhaust gas substance without overly large volumes of unspent ammonia accompanying the exhaust gases out of the catalytic converter and thereby being discharged to the surroundings. From the known art a system for controlling reductant injection is known to use the calculation values from a computational model which, taking into account the anticipated reactions in the catalytic converter under the prevailing operating conditions, continuously determines the current state in the catalytic converter. Also previously known is a method for measuring pressure in an aftertreatment system, such as the method described in FR2893979. Brief description of the invention

One of the initial values often used in a computational model to control the injection of reductant is the concentration of nitrogen oxides N0 _X in the exhaust gases upstream of the catalytic converter. This concentration can be determined with the aid of a N0 _X sensor located upstream of the catalytic converter. Ά conventional N0 _X sensor is pressure sensitive, and the measurement signals from the sensor have to be

corrected for the prevailing pressure around the sensor in order to yield correct values for the N0 _X concentration being measured.

The pressure in the part of the exhaust gas pipe upstream of the SCR catalytic converter where the N0 _X sensor is located varies according to prevailing operating conditions, and the prevailing pressure drop across the SCR catalytic converter and the pressure drop across other exhaust gas aftertreatment units located between the N0 _X sensor and the exhaust gas outlet. One way of determining this pressure is to measure it with the aid of a pressure transmitter. However, such a supplementary pressure transmitter involves additional costs which it is desirable to avoid. Alternatively, the relevant pressure can be determined with the aid of a computational model that depends on prevailing operating conditions.

However, such a computational model is associated with sources of error which can become relatively great over time.

In order to solve this, in FR2893979 it has been proposed to utilize pressure dependence in a first oxygen sensor located in a first position in the exhaust gas pipe upstream of the aftertreatment device and pressure dependence in a second oxygen sensor located in a second position in the exhaust gas pipe downstream of the aftertreatment device to determine a pressure differential between the first and second positions. The first and second sensors can be connected to a control unit. In accordance with this proposed solution, the

concentrations of oxygen are identical in the first and second positions in certain specific instances, for example in the case of low exhaust gas flows following engine start-up.

Since the oxygen concentrations in certain specific instances are assumed to be identical in the first and second positions, in accordance with FR2893979 introductory initialization is performed in such specific instances, which entails resetting the differential values produced for the two sensors.

Following this initialization, based on the pressure

dependences for the two sensors and on an assumption that the second sensor is exposed to atmospheric pressure plus a pressure loss dependent on the second sensor's location in relation to the exhaust gas pipe outlet, the pressure in the first position is calculated on the basis of the two

measurement values for the oxygen concentrations provided by the first and second gas sensors. By this means, therefore, the pressure at the first position can be determined without needing to install an extra pressure sensor in the exhaust gas pipe at the first position.

However, the solution described in FR2893979 provides only relatively rough determination, which is to say non-exact determination of the pressure. In keeping with FR2893979, the initialization required in accordance with FR2893979 in order to be able to apply the method can only be carried out in certain specific instances and presupposes that the oxygen concentrations in the first and second positions are equal in size. Such instances can be produced where, for example, there are low exhaust gas flows in the exhaust gas pipe or in the event of retardation. The solution described in FR2893979 provides only one

opportunity for determining a single parameter on which a difference between the first and second gas sensors'

measurement values can depend. In accordance with FR2893979, therefore, two or more parameters affecting this difference cannot be determined. The solution can determine a quotient, for example, between the sensitivity of the two gas sensors. Alternatively, a quotient between the two sensors' constant deviation can be determined. FR2893979 further presupposes a particular pressure sensitivity for the gas sensors and a particular flow dependence y for the pressure at the position of the sensors, which means that the solution can provide only relatively rough, unreliable pressure determination.

One aim of the present invention, therefore, is to provide determination of the pressure in the exhaust gas pipe that is precise and reliable, and for which no preliminary

initialization is required. There is also a need for pressure determination that does not require the second gas sensor always to be exposed to pressure equivalent to atmospheric pressure plus a well-defined pressure loss dependent on sensor siting .

This purpose is achieved through the above-mentioned method in accordance with the characteristic part of patent claim 1. The purpose is also achieved by the above-mentioned system in accordance with the characteristic part of patent claim 26. The purpose is also achieved through the above-mentioned computer program and computer software product .

According to the present invention, at least two

characteristic properties are estimated. These at least two characteristic properties include a first pressure sensitivity x for the first gas sensor at a first position and a first flow dependence for a first pressure P _x at this first position, which are estimated therefore. The first pressure P _x is then determined on the basis of at least this estimated first pressure sensitivity a _lr on the estimated first flow

dependence, and on first y and second y ₂ measurement values for a concentration for a substance at the first and second gas sensors, respectively. The first pressure P ₁ established is then utilized, for example, in a vehicle.

Thus, according to the present invention, the first pressure sensitivity is estimated, enabling the determination of the first pressure P _x according to the present invention to be utilized on essentially all types of gas sensors, since the estimation denotes the way in which the sensors depend on the pressure. This is a great advantage compared with previously known solutions, which assume that sensors' pressure

sensitivities are known. The sensors' pressure sensitivity can vary with time and operating mode; as a result, previously known solutions either cannot be used or provide poor accuracy with older sensors and/or multiple operating modes. Since the present invention estimates the first pressure sensitivity a and the first flow dependence for the first pressure P at the first sensor, a knowledge of these

parameters is obtained, which can be used to determine the first pressure Ρ . According to one embodiment, the second pressure sensitivity a ₂ and the second flow dependence are also estimated for the second pressure P ₂ at the second sensor, thereby providing a knowledge of the individual properties of the second sensor, which can be used to determine the second pressure P ₂ . The knowledge of the second sensor's individual properties can also be used to increase the accuracy for determining the first pressure P _x if the second sensor is pressure sensitive and is positioned such that the pressure varies. Thus the individual properties are estimated for the first and/or second sensors, which are used to increase the accuracy for determining the first P ₁ and/or second P ₂

pressure. This exploits a weakness identified by the inventors in the previously known solutions for enhancing the accuracy of the present invention.

By estimating the individual properties for the first and/or second sensors, the restrictive preliminary initialization steps in previously known solutions can also be avoided. Since the previously known solutions lack any knowledge of these individual properties, they have to ensure that the system is set up for these solutions to provide an acceptable result.

By estimating and utilizing the pressure sensitivity and the flow dependence, the present invention can estimate the first P ₁ and/or second P ₂ pressure for essentially all operating modes and essentially all types of sensor, and for different ageing of these sensors. Highly accurate determination of the first Ρ and/or second P ₂ pressure is therefore provided, which to all intents and purposes can be performed continuously, if so desired, or when values for the first P ₁ and/or second P ₂ pressures are needed by other systems in, say, a vehicle.

This means that the present invention has universal

applicability and is not dependent on particular operating modes that occur relatively rarely. Since a correlation between pressure and flow in the exhaust gas pipe is

determined by estimating pressure sensitivity and flow

dependence by means of the present invention, therefore, this offers the option of determining the pressure in essentially every position in the exhaust gas pipe with great precision without having a specific measurement value for the pressure in these positions. The present invention does not reguire the second sensor to experience atmospheric pressure plus a well- defined loss of pressure dependent on the location of the sensor, making the invention generally applicable in a great many different positions in exhaust gas pipes.

In addition, the present invention can be implemented with a low addition of complexity, particularly as pre-existing gas sensors are used to determine the pressure.

Brief list of figures

The invention will be elucidated in more detail below, based on the drawings attached, using similar reference terms for similar parts, where:

Figure 1 shows an engine and exhaust gas purification system,

Figure 2a shows a flow chart for the present invention,

Figure 2b shows a flow chart for one embodiment of the present invention, and

Figure 3 shows a control unit. Description of preferred embodiments

As mentioned above, contemporary motor vehicles and other devices and craft containing combustion engines, such as ships, vessels and planes, are usually fitted with an

aftertreatment device arranged to purify exhaust gases given off by the engine. This document describes the invention exemplified in a motor vehicle, but the skilled person will realize that the invention can also be applied to essentially all other devices and craft containing combustion engines. Figure 1 shows a schematic representation of an engine and exhaust gas purification system 1 fitted with a combustion engine 2 and an exhaust gas pipe 3. Exhaust gases leaving the combustion engine 2 move around an exhaust gas pipe 3 in the form of exhaust gas flows 21, 22, 23 in the various parts of the exhaust gas pipe and exit to the surroundings via an exhaust gas outlet 30. The exhaust gas pipe 3 houses an exhaust gas aftertreatment device 4.

The exhaust gas aftertreatment device 4 can be comprised of a separate exhaust gas aftertreatment unit or a set of two or more exhaust gas aftertreatment units connected in series and/or parallel, in which the respective exhaust gas

aftertreatment unit, for example, is made up of a catalytic converter or a particle filter. In the example illustrated, the aftertreatment device 4 includes an oxidation catalytic converter DOC (Diesel Oxidation Catalyst) 5, a particle filter DPF (Diesel Particle Filter) 6 and a reduction catalytic converter 7, for example, of the SCR typ (SCR = Selective Catalytic Reduction) , interconnected in series with the particle filter DPF 6 located between the oxidation catalytic converter DOC 5 and the reduction catalytic converter 7. As mentioned above, however, the aftertreatment device 4 need not include each and every one of the oxidation catalytic

converter DOC 5, the particle filter DPF 6 and the reduction catalytic converter 7, but in different embodiments can include one or more of an oxidation catalytic converter, a particle filter and a reduction catalytic converter. The aftertreatment device 4 can also include an ammonia slip catalyst (ASC) , which will eliminate an excess of ammonia.

The present invention can be used to determine pressure in an exhaust gas pipe 3 connected to a combustion engine 2. As described above, the first gas sensor 11 is arranged so as to provide a first measurement value y corresponding to a first concentration of a substance in a first position 3a in the exhaust gas pipe 3 upstream of an aftertreatment device 4 in the exhaust gas pipe. The aftertreatment device 4 can include one or more of an oxidation catalytic converter DOC 5, a particle filter DPF 6, a reduction catalytic converter 7, for example an SCR, or some other applicable aftertreatment device. The first gas sensor 11 is pressure dependent, as mentioned above.

A second gas sensor 12 is arranged to provide a second

measurement value y ₂ corresponding to a second concentration of the substance, which is also measured by the first gas sensor 11. The second gas sensor 12 is arranged in a different position 3b downstream of the aftertreatment device 4.

The method for determining and utilizing the pressure in the exhaust gas pipe is subsequently described with the aid of the flow chart in Figure 2a.

In a first step 201 of the method, an estimation is made of a first pressure sensitivity α _χ for the first gas sensor 11. A first flow dependence for a first pressure P _x at the first position 3a is also estimated. In the first step 201, then, an estimation is made of the two characteristic properties, which comprise the first pressure sensitivity ₁ and the first flow dependence .

A second step 202 of the method establishes the first pressure Pi at the first position 3a, based at least on the first pressure sensitivity a _{l f} on the first flow dependence and on the first y _i and second y ₂ measurement values, where the first y _x and second y ₂ measurement values are provided by the first 11 and second 12 gas sensors, respectively. This determination is described in more detail below.

In a third step 203 of the method the first pressure P

established is used. According to one embodiment the

established first pressure P ₁ is used to correct the first measurement value y ₁ provided by the first sensor 11, thereby obtaining a more exact measurement value. According to one embodiment the established first pressure P ₁ is used to determine an amount of soot in the particle filter DPF 6, where the quantity of soot determined, for example, can be used to determine when regeneration of the particle filter DPF is to be carried out. According to one embodiment the

established first pressure P _x is determined in order to also correct the second pressure dependent on measurement signals, for example measurement signals for both nitrogen oxides N0 _X and oxygen 0 ₂ , provided by the first sensor 11, as both these measurement values are pressure sensitive and require

correction .

The method according to the invention can be performed

continuously while operating the combustion engine 2 normally, which is to say during the time when a vehicle is being driven. In the case of continuous estimation, for example, a Kalman filter can be utilized for estimation purposes.

According to one embodiment the estimation is made more robust by performing it quickly, utilizing the Kalman filter in an initial step of the estimation for the more significant parameters, and more slowly during the ensuing steps for other parameters, something which is described further below.

The method according to the invention allows for the fact that the differences in measurement value between the first 11 and second 12 sensor may be due to a number of different things. This may entail multiple parameters having to be estimated. Some of these have a big impact on the sensors, i.e. are more significant, while others have less impact; for example, the pressure sensitivity and the flow dependence for the first sensor 11 have a great impact, while the pressure sensitivity 2 and the flow dependence for the second sensor 12 have less impact on the sensors.

By dividing the estimation into two steps, the most

significant parameters can be determined first during the first step, then the less significant parameters determined in the second step. Fast and slow estimation, respectively, refer to the speed with which the- estimation converges, i.e. how quickly the optimal parameter values are achieved by

estimation. In practical terms, this means that fewer

measurement values are required before the estimation

converges for a quick estimation, but at the same time the fast estimation becomes more sensitive to noise.

The method according to the present invention can also be preceded by collecting data during normal running of the combustion engine 2, on which the estimation is performed based on these collected data through regression analysis.

According to one embodiment the estimation is made more robust here by the fact that during an initial step the estimation collects a suitably smaller number of measurement value samples and performs regression analysis on these, following which a suitably larger number of measurement value samples are collected, which are then analyzed in regression analysis.

According to one embodiment estimated coefficients are saved when the engine is switched off. When the engine is then started again, the estimations can be begun again by carrying on from the coefficient values most recently saved. This produces a more effective estimation, which more quickly results in correct values, as the estimated coefficients are not expected to change appreciably during the time the engine is off. Therefore, the pressure can then be determined with essentially the same accuracy as before the engine was

switched off.

According to one embodiment of the present invention, a second pressure sensitivity a ₂ is also estimated for the second gas sensor 12 in the second position 3b, as well-as a second flow dependence for a second pressure P ₂ at the second position 3b. The second pressure P ₂ is then established, based, apart from the first pressure sensitivity a _lr on the first flow dependence and on the first y _x and second y ₂ measurement values, also on this second pressure sensitivity a ₂ for the second gas sensor 12 and on the second flow dependence for the second pressure P ₂ at the second position 3b. Both the first pressure P ₁ and the second pressure P ₂ are established by this means, therefore. The established second pressure P , according to one

embodiment, is used to correct the second measurement value y ₂ provided by the second gas sensor 12, obtaining a more exact measurement value in the method.

The present invention exploits the fact that gas sensors

11,12, which measure e.g. the content of nitrogen oxides N0 _X , oxygen 0 _2r nitrogen N ₂ , carbon dioxide C0 ₂ or water H ₂ 0 , are generally pressure sensitive. As a consequence, measurement values provided by these sensors also depend, in addition to the content of the substance being measured, on the total pressure in the gas of which the substance forms part. In order to obtain the correct value for the content of the substance, the measurement value therefore needs to be

corrected with regard to the total pressure of the gas. A typical relation between a measurement value and the correct, i.e. corrected, content of the substance can be described using the following equation: y _c = y[( -l)a + l], (equ. 1) where y is the measurement signal and y _c is the corrected measurement value, corresponding to the correct content of the substance. P is the total pressure of the gas, P ₀ the air pressure of the surroundings and a the sensor' s pressure sensitivity. The sensors/transmitters therefore display pressure

sensitivity. In general this pressure sensitivity is

relatively well-known; for instance, it may be stated in the supplier's specifications.

According to the present invention the estimation of the first pressure sensitivity _r for the first gas sensor 11 and/or the estimation of the second pressure sensitivity a ₂ for the second gas sensor 12 is intended to determine a more precise value for the pressure sensitivity in question than that provided by the specifications/supplier. This more precise pressure sensitivity determination is valuable since the pressure sensitivity can vary, depending on the individual level for the sensors/transmitters. Greater precision in determining the pressure can therefore be achieved by estimating the first pressure sensitivity for the first gas sensor 11 and/or estimating the second pressure sensitivity a ₂ for the second gas sensor 12 according to the present invention.

According to the present invention, in other words, the estimation of the first pressure sensitivity <x _x for the first gas sensor 11 and/or the estimation of the second pressure sensitivity a ₂ for the second gas sensor 12 can be seen as an improvement, i.e. an increase in accuracy, for a value

provided/predetermined for pressure sensitivity.

It should be noted here that the pressure sensitivity can be expected to be relatively constant over time, for which reason this estimation need not necessarily be carried out often, making for a low utilization rate for the system's processor power .

Sensors generally have a degree of accuracy, which can also change as they age. As a result, with time they reproduce the measured magnitude with some deviation. There are at least two types of deviation. One type of deviation is dependent on the size of the measurement signal, which is to say that the deviation is proportional to the measurement signal, and another type of deviation is dependent on the size of the measurement signal, which is to say that the deviation is constant. The relation between the corrected correct

measurement value and the sensor' s uncorrected measurement value can be described using the equation: x _c = k · x + d , (equ . 2 ) in which x is the sensor's uncorrected measurement value, x _c the corrected correct measurement value, k is the correction factor for the sensor's proportional deviation 1/fc and d is the correction factor for the sensor's constant deviation — d . In this document, therefore, the correction d for the sensor and the sensor's constant deviation have the same value,

permanently with the opposite sign ±d , since the correction d has to correct for the constant deviation — d . According to one embodiment of the present invention, the method includes an estimation of at least one additional characteristic feature for one or more of the first 11 and second 12 sensors. This at least one additional characteristic feature includes the proportional error 1/k for the first 11 or second 12 gas sensor, respectively, and/or the constant deviation —d for the first 11 or second 12 gas sensor,

respectively. Determination of one or more of the first pressure P ₁ and the second pressure P ₂ is then performed based, apart from on the first ₁ and/or second a ₂ pressure

sensitivity, on the first and/or the flow dependence, and on the first y ₁ and second y ₂ measurement value, also on the one (at least) additional characteristic feature, thereby

obtaining more exact determination of the first pressure P _x and/or the second pressure P ₂ .

The pressure flow dependence, i.e. the first flow dependence for the first pressure P ₁ and/or the second flow dependence for the second pressure P ₂ , is also relatively well-known, since the design of the exhaust gas system and the siting of

sensors/transmitters is known. The purpose of estimating the flow dependence according to the present invention with [is to achieve??] greater accuracy, by virtue of the fact that account is taken of the individual variations for exhaust gas systems. For the sensor/transmitter in the first position 3a allowance can also be made for the way the flow dependence changes over time. In the first position 3a changes occur primarily to the linear flow dependence of the pressure over time, due to the fact that soot and ash accumulate in the exhaust gas treatment system's particle filter (DPF) . In the event of a great accumulation of ash and soot in the particle filter (DPF) , the quadratic dependence will also be affected, meaning that the quadratic flow dependence is an effect that changes relatively slowly as a result of accumulations. In other words, a big change in ash and soot accumulations is required for the quadratic flow dependence to change. The linear and quadratic flow dependence is described in more detail below.

For the sensor/transmitter in the second position 3b the pressure flow dependence changes marginally over time, since the second sensor/transmitter 12 is located near the outlet and has no filter fitted downstream of it. For the second transmitter position 3b, therefore, the pressure flow

dependence can be assumed to be essentially constant over time. Due to the siting 3b of the second sensor/transmitter 1 the difference in pressure between its position 3b and the surroundings should also be slight. In other words, the secon sensor/transmitter 12 in the second position 3b may be

significantly exposed to atmospheric pressure.

According to one embodiment of the present invention each of the first pressure P _x at the first position 3a and the second pressure P ₂ at the second position depends on a exhaust gas flow velocity v in the exhaust gas pipe 3 with a linear term v and a quadratic term a ₂ v ² . The pressure in the exhaust gas pipe 3 depends on the surrounding air pressure and the flow resistance in the exhaust gas system. The flow resistance depends on the extent to which the flow is laminar or

turbulent. The flow resistance also depends on changes in the cross-section area of the exhaust gas system in the direction of flow. Weighing all the effects together, the pressure in each position in the exhaust gas system can be described with the equation:

P = P _Q + a · v + a ₂ ^■ v ² , (equ. 3) where P is the pressure in the current position in the exhaust gas system, P ₀ is the air pressure of the surroundings, v is the exhaust gas flow's average velocity in the cross-section of the flow in the current position, and a and a ₂ are

coefficients for the linear or quadratic dependence,

respectively, of the flow velocity in the current position.

According to one embodiment of the present invention, each of the first pressure P _x at the first position 3a and the second pressure P ₂ at the second position depends on a mass flow rh in the exhaust gas pipe 3 with a linear term b^m and a quadratic term b ₂ m ² , where the dependence of the mass flow rh may depend on a temperature T in the exhaust gases passing through the exhaust gas pipe 3.

Since the cross-section area generally varies along the exhaust gas system's direction of flow, it is an advantage to use the volumetric or mass flow in the equation for the pressure's flow dependence (equation 3). The flow velocity relates to the volumetric flow through the cross-section area and the volumetric flow to the mass flow through the density in accordance with the following equation:

_ q _ m _ RT

A A-p PM' (equ. 4) where q is the volumetric flow, A is the cross-section area, rh is the mass flow, p is the density, P is the pressure, M is the average molar mass of the exhaust gases, R is the general gas constant and T is the temperature. The dependence of pressure on the mass flow can thus be expressed as:

P = P ₀ + b · rh + b ₂ ^■ rh ² , (equ. 5) where b ₁ and b ₂ are coefficients for the linear or quadratic dependence, respectively, on the mass flow. These coefficients are temperature dependent by virtue of the density' s

temperature dependence. Since the first coefficient b^

describes the laminar part of the flow resistance, it

additionally has a temperature dependence from the temperature dependence of the viscosity, with an exponent between 0.7 and 0.75, b _x ~[T ⁰ , Γ ^{0 75} ] , depending on the composition of the gas. In the aggregate this results in the first coefficient b _x

depending on the temperature with the exponent 1.7-1.75,

ό ₁ ~[Γ ¹ · ⁷ , ^1-75 ] , and the second coefficient b ₂ depending on the temperature with the exponent 2, b ₂ ~T ² .

The estimation of the first pressure sensitivity a for the first gas sensor 11 and/or the second pressure sensitivity a ₂ for the second gas sensor 12, and the first flow dependence for the first pressure P _x and/or the second flow dependence for the second pressure P ₂ may, according to one embodiment of the present invention, involve the following steps, as illustrated in the flow chart in Figure 2b. In an initial step 210 an estimation of a proportional and static correction is performed for the first gas sensor 11 and/or the second gas sensor 12. The sensors' /transmitters' proportional and static deviation always affect the sensors' measurement values regardless of operating mode. A

satisfactory estimation of corrections for these deviations should be made first, therefore. Low flows, which produce a slight effect on the pressure effect on the

sensors/transmitters, and variation in measurement value (0 ₂ ) will enable the proportional and static correction to be estimated here, termed ki, k ₂ , di and d ₂ , for example, in equation 13 below. In a second step 220 an accurate estimation of values for the first pressure sensitivity a for the first gas sensor 11 is carried out based on relatively well-known values provided for the pressure sensitivity and for respective flow pressure dependence as described above. Therefore, the relatively well- known value for the pressure sensitivity for the gas sensor 12 in the second position 3b and relatively well-known values for the pressure's flow dependence can be exploited to estimate a more exact/precise value for the pressure sensitivity for the first sensor 11.

In a third step 230 an accurate estimation of values for the flow dependence for the first position 3a is performed, estimating first a linear then a quadratic flow dependence, as described above. In a fourth step 240 accurate estimation of values for the second pressure sensitivity ct ₂ for the second gas sensor 12 is performed, based on relatively well-known values provided for the pressure sensitivity and flow pressure dependence, and based on the properties for the first sensor 11 accurately estimated in the second 220 and third 230 steps.

In a fifth step 250 an accurate estimation of values for the flow dependence for the second position 3b is performed, estimating first a linear then a quadratic flow dependence, as described above. In a sixth step 260 the change over time for the pressure's flow dependence for the first position 3a can then be

estimated with great accuracy, based on the values estimated in the second 220, third 230, fourth 240 and fifth 250 steps, which present a high degree of accuracy. To summarize, this can be described as estimating the

proportional and static correction for the first 11 and second 12 gas sensor/transmitter. Then, based on a relatively well- known pressure sensitivity and the pressure dependence of the flow, a more precise value can be estimated for the pressure sensitivity. Following this, the pressure's flow dependence is then estimated: first the linear dependence, then the

quadratic one. This procedure is done first for the first gas sensor 11 in the first position 3a then for the second gas sensor 12 in the second position 3b, where relevant.

The skilled person will realize that the order of the method can also be changed so as to carry out the method for the second gas sensor in the second position 3b first, then for the first gas sensor 11 in the first position. Hence the method can be carried out sequentially for the first 11 and second 12 gas sensors, in arbitrary order.

Including the gas sensor' s pressure sensitivity , the

correction k for its proportional deviation 1/k and the correction d for its constant deviation and pressure flow dependence in the same equation gives: y _c = fe · V \( _n ^P ₂ -l) + l]+d (equ. 6)

Dividing the quota for the pressure by the ambient air

pressure P ₀ in both numerator and denominator, and simplifying the equation gives the following expression: where c _t and c ₂ are the coefficients b ₁ and b ₂ divided by the ambient air pressure P ₀ . According to one embodiment of the invention the first

measurement value measured by the first gas sensor 11 and the second measurement value y ₂ measured by the second gas sensor 12, respectively, are related to a substance or

compound in which a concentration of the substance or compound in transit through the aftertreatment device 4 remains

essentially unchanged. When this is the case, determination of the pressure in the exhaust gas pipe can be based on an assumption that a first corrected measurement value y _cl ,

corresponding to this first measurement value y _{l r} and a second corrected measurement value y _c2 , corresponding to this second measurement value y ₂ , are equal in size.

For two gas sensors, therefore, the first gas sensor 11 sited in the first position 3a and the second gas sensor 12 sited in the second position 3b in the exhaust gas system, which measure a substance that is unaffected by the exhaust gas system's components, the corrected measurement values for the two gas sensors 11, 12 must be equal to each other, which is to say: c,i= _C ,2 (equ. 8) which, applying equation 7, is equivalent to: k _i ⁱ _y ^J _i ⁱ [Ll - a, ^c "* ^+c »* ² I + _{dl =} k ₂ y ₂ [i - a ₂ ^c »* ^+c »* ² I + d ₂ (equ. 9)

1 l+c^rh+c^m ² ] ¹ tJt y l+c ₂₁ m+c ₂₂ m ² J ^Δ ^ ' where the first position 3a is matched by index 1 and the second position 3b by index 2, which for the coefficients c dindc ₂ matches the first figure in the index.

Equation 9 can be rewritten in accordance with:

(equ. 10)

Subtracting the correction d for the first constant deviation — d ₁ from both sides and multiplying both sides by their respective denominator gives: kiyitl + (1 - ai)ciim + (1 - a c^m ² ^! + c ₂₁ rh + c ₂₂ rh ² )

= k ₂ y ₂ [ + (1 - a ₂ )c ₂₁ rh + (1 - a ₂ )c ₂₂ rh ² ](l + c^rh + c ₁₂ rh ² )

+ (d ₂ - dJCl + Cum + c ₁₂ rn ² )(l + c ₂₁ rh + c ₂₂ rh ² )

(equ. 11)

The equation can be rewritten so that the respective side is expressed as a polynomial of the mass flow rh in accordance with : friyi + [(1 - + c ₂₁ ]rh + [(1 - aJCc^ + c _n c ₂₁ ) + c ₂₂ ]m ²

= k ₂ y ₂ {l + [(1 - «2)c ₂ i + Cn]m + [(1 - a ₂ )(c ₂₂ + c ₂₁ c _1:L ) + c ₁₂ ]rh ²

+ (1 - a ₂ )(c ₂₁ c ₁₂ + c^Cn)™ ³ + (1 - a ₂ )c ₂₂ c ₁₂ m ⁴ }

+ (^2 - <*_.){! + (en + c ₂₁ )m + (c ₁₂ + c ₂₂ + c _1:L c ₂₁ )?n ²

+ (cuc ₂₂ + c ₁₂ c ₂₁ )m ³ + c ₁₂ c ₂₂ m ⁴ }

(equ. 12)

From equation 12 the gas sensors' 11, 12 pressure

dependence/pressure sensitivity a _x , a ₂ , the correction factors k _{l r} k ₂ for proportional deviation l/k _{l r} l/k ₂ and corrections d _{l r} d ₂ for constant deviation — d _{l r} —d ₂ and respective pressure flow dependence can then be estimated. Therefore, the first pressure Ρ- and the second pressure P ₂ can be determined on the basis of 12.

According to one embodiment of the invention the size of the respective gas sensor' s pressure dependence is assumed to be relatively equal, ₁ » a ₂ . Also, in accordance with the

embodiment, the correction factors k _{l r} k ₂ for the respective gas sensor' s proportional deviation can be expected to be relatively equal, k _x « k ₂ . This means that the terms with the product of respective measurement value and the powers 3 and 4 of the mass flow rh cancel each other out in principle. Since the flow resistance is greater for the upstream gas sensor 11 in the first position 3a, all coefficients ¾ for the upstream gas sensor 11 are resultantly greater than the corresponding coefficient c ₂ j for gas sensor 12 located in the second position 3b downstream. These assumptions made in keeping with the invention simplify estimation according to the invention.

With these simplifications, the estimation problem is reduced to:

Ύ2 = i-ydl + [(1 - + c ₂₁ ]rh + [(1 - a _t c ₁₂ + c _ll( : ₂₁ ) + c ₂₂ ]rh ² }

^K 2

- - «2 c ₂ i + Cn]m + [(1 - a ₂ )(c ₂₂ + c ₂₁ c ) + c ₁₂ ]rh ² }

(equ. 13)

Equation 13 can be written as: 2 = ydPw + βιιτ + β ₁₂ τ ^η2 ] - γ ₂ [β ₂₁ τ ^η + β ₂₂ τη ² ] - [γ ₀ + γ τη + γ ₂ πι \

(equ. 15) where the respective coefficient and γι are an expression of the original coefficients k _lr k ₂ , CC _\ , ct ₂ , c _llf c ₁₂ , c ₂₁ , c ₂₂ , d and d ₂ in accordance with: β ^ι ° ⁼ ¾ ^;

(equ. 16)

(equ. 17)

012 ^{+ C} ll ^C 2l) + C22] ; ( ^eC 3 ^U -

18) β ₂₁ = (1 - a ₂ )c ₂₁ + c _u ; (equ

19)

0 ₂₂ = (l-a ₂ )(¾ ₂ + ¾iCii) + ₁₂ ; (equ.

20)

(equ. 21)

Yi = - di) ^{Cll +C¾1} ; and (equ.

22)

K2 = (rf2- rfi) ^{Cl2+C2 ilC21} - (equ.

23) According to one embodiment of the invention only the size of the first measurement value y _x of the first pressure mentioned P _x is affected, i.e. only the first gas sensor 11 in the first position 3a is pressure dependent. If the second gas sensor 12 in the second downstream position 3b is independent of the pressure, all terms containing c ₂ i, c ₂₂ or 1— a ₂ , respectively, are omitted, simplifying the expression considerably.

According to one embodiment of the invention the size of the first measurement value y ₁ or the second measurement value y ₂ , respectively, of the first pressure P _t or the second pressure P ₂ , respectively, is affected; that is to say, both the first 11 and the second 12 gas sensors are pressure dependent.

According to one embodiment of the invention the estimation is performed in at least two steps, since both the first 11 and the second 12 gas sensor are pressure dependent. In the first step the coefficients -^, a _lf c _xl and c ₁₂ are then estimated with

2

assumed values for the coefficients a ₂ , c ₂₁ , c ₂₂ , d _lr and d ₂ , respectively. In the second step new values are estimated for these coefficients, using the coefficients estimated in the first step as knowns . When additional new values are estimated for the coefficients after the second step, these coefficients estimated in the second step can then be used for a subsequent additional first step. In other words, the first step here estimates the most significant coefficients, which have the greatest effect on the correlation. The remaining coefficients are estimated in the second step.

According to one embodiment of the invention the estimation of the pressure sensitivity and flow dependence for the first gas sensor 11 is paused in the first position 3a, and for the second gas sensor 12 in the second position 3b, if the first y _x and second y ₂ measurement values are expected to be of equal size, i.e. because the measured gas concentration can be expected to be different at the first position 3a for the first gas sensor 11 located upstream and at the second

position 3b for the second gas sensor 12 located downstream. In this application, pausing the estimation entails terminating the estimation in order to resume it later on, moving the estimation into a temporary holding position, or temporarily interrupting the estimation in some other way.

Pausing the estimation avoids inexact estimations, increasing the accuracy and robustness of the method according to the present invention. However, determination of the first P ₁ and/or second P ₂ pressure can still continue since the first y ₁ and second y ₂ measurement values are expected to be equal in size if determination is then based on flow dependence values already estimated.

The first y and second y ₂ measurement values are expected to differ substantially with operating mode, as the measured gas concentration is affected by reactions in the exhaust gas system' s components between the position of the two gas sensors, for example, in the event of a quick change in the desired engine torque and/or speed, i.e. in the event of a quick change in power take-off from the engine. Owing to the volume in the exhaust gas system between the first 11 and second 12 sensors, there is some time lag between the exhaust gases passing the first sensor 11 and passing the second 12. This time depends on the volume and velocity of the gas, which in turn depend on the mass flow, pressure and temperature.

Since these are relatively well-known, it is possible to compensate for this time lag, though usually not altogether perfectly. In the case of stationary operating mode and slow changes, this will not give rise to any major deviation. In the case of quick changes, however, this can lead to

significant deviations. In that situation, therefore, the estimation should be paused in accordance with the method according to the invention. The first y ₁ and second y ₂ measurement values are also expected to differ substantially when regeneration of the particle filter DPF 6 is in progress. During regeneration, hydrocarbons are dosed, which oxidize in the oxidation catalytic converter DOC 5, affecting the oxygen content so as to reduce it, and affecting the carbon dioxide and water contents so as to increase both. According to one embodiment of the invention, therefore, the estimation must be temporarily paused in connection with such regeneration, for example, by pausing the estimation while regeneration is in progress, resuming it once regeneration has finished, thereby enabling new parameter values to be determined as soon as possible after

regeneration. The pressure calculated at the first gas sensor 11 located in first position 3a upstream can be expected to be somewhat overestimated/elevated for a while after regeneration has been carried out, until it has been managed to estimate new values for the pressure flow dependence coefficients.

According to one embodiment of the present invention, the estimation is based on an assumption that the first corrected measurement value y _cl , corresponding to the first measurement value y _x , differs from the second corrected measurement value y _c2 , corresponding to the second measurement value y ₂ . The difference between these corrected measurement values depends here on the quantity of the measured substance consumed between the first 3a and second 3b positions. A slight change in the measured gas concentration of the substance between the first 3a and second 3b position of the gas sensors occurs with relative frequency. In the oxidation catalytic converter DOC 5 oxygen is consumed at the same time as carbon dioxide and water are formed. The same reactions take place in the

particle filter DPF 6, though to a considerably lesser extent. In the catalytic converter SCR 7 oxygen is consumed. The magnitude of these changes can be determined from models for the respective component in the exhaust gas system. In order to improve the accuracy of the estimation, therefore, and in accordance with this embodiment of the invention the

measurement value for the second gas sensor 12 located in the second position 3b downstream is compensated for this change in the gas concentration for the substance.

Furthermore, the method for determining and utilizing pressure in an exhaust gas pipe according to the present invention can be implemented in a computer program, which when executed in a computer causes the computer to carry out the method. The computer program usually constitutes part of a computer software product 303, in which the computer software contains a suitable digital storage medium on which the computer program is stored. Said computer-readable medium consists of a suitable memory, such as: ROM (Read-Only Memory), PROM

(Programmable Read-Only Memory), EPROM (Erasable PROM), Flash memory, EEPROM (Electrically Erasable PROM) , a hard disk unit etc.

In accordance with one aspect of the present invention a system is provided for determining and utilizing pressure in an exhaust gas pipe connected to a combustion engine. The system comprises the first 11 and second 12 gas sensors described above. The system also includes an estimation unit 131 configured to estimate at least two characteristic

properties, including where the estimation involves estimating a first pressure sensitivity a ₁ for the first gas sensor 11 and estimating a first flow dependence for a first pressure P ₁ at the first position 3a. The system further includes a

determination unit 132, configured to determine the first pressure P ₁ based at least on the first pressure sensitivity a _lr on the first flow dependence and on the first y _x and second y ₂ measurement values. The system also includes a utilization unit 133 configured to exploit the established first pressure

Figure 3 is a schematic illustration of a control unit 300 which constitutes a schematic description of the control unit 13 in Figure 1 connected to the first 11 and second 12 gas sensors. The control unit 300 comprises a calculation unit 301, which can be made up of essentially some suitable type of processor or microcomputer, e.g. a circuit for digital signal processing (Digital Signal Processor, DSP) , or a circuit with a pre-determined specific function (Application Specific

Integrated Circuit, ASIC) . The calculation unit 301 is

connected to a memory unit 302 (placed in the control unit 300), which provides the calculation unit 301 with e.g. the stored program code and/or stored data which the calculation unit 301 requires in order to be able to perform calculations. The calculation unit 301 is also configured to store the partial or final result of calculations in the memory unit 302. Furthermore, the control unit 300 is provided with devices 311, 312, 313, 314 for the respective reception and

transmission of input and output signals, respectively, for example measurement signals from the first 11 and second 12 gas sensors. These input and output signals can contain wave forms, impulses or other attributes which can be detected as information by the devices 311, 313 for receiving input signals and can be transformed into signals which can be processed by the calculation unit 301. These signals are then supplied to the calculation unit 301. The devices 312, 314

[are] for transmitting calculation results from the

calculation unit 301 to output signals for transfer to other parts of the vehicle's control system and/or the component (s) for which the signals are intended, e.g. to other parts of the system' s engine and exhaust gas purification system, or to other parts of, say, a vehicle.

Every single one of the connections to the devices for

receiving or, respectively, transmitting input and output signals can be made up of one or more of: a cable, a data bus, such as a CAN bus (Controller Area Network bus) , a MOST bus (Media Orientated Systems Transport bus) or some other bus configuration, or a wireless connection.

A person skilled in the art will realize that the above computer can be made up of the calculation unit 301 and that the above memory can be made up of the memory unit 302.

In general, control systems in modern vehicles consist of a communications bus system consisting of one or more

communications buses for interconnecting a number of

electronic control units (ECUs) or controllers, and various on-board components. Such a control system can include a large number of control units, and responsibility for a specific function can be shared between more than one control unit. Vehicles of the type shown, therefore, often contain

considerably more control units than shown in Figures 1 and 3, which will be familiar to the person skilled in the art.

In the embodiment shown the present invention is implemented in the control unit 300. However, the invention can also be partly or wholly implemented in one or more other control units already found on the vehicle or in some dedicated control unit for the present invention.

The skilled person will also realize that the above system can be modified in accordance with the various embodiments of the method according to the invention, which is also indicated in the independent patent claims for the system. In addition, the invention relates to a motor vehicle, for example a lorry or a bus, and other devices and craft containing combustion

engines, such as a ship, vessel or aeroplane, containing at least one system for determining exhaust gas back pressure according to the invention.

The present invention is not limited to the embodiments of the invention described above but relates to and includes all embodiments within the protective scope of the independent claims attached.