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Title:
ESTIMATION OF A DEVIATION FOR AT LEAST ONE MODEL VARIABLE OF A CATALYST MODEL
Document Type and Number:
WIPO Patent Application WO/2011/093771
Kind Code:
A1
Abstract:
The present invention comprises a method and a system for estimation of a deviation for at least one model variable of a catalyst model, which estimation is based on the catalyst model and on at least one measured sensor signal from at least one sensor which is so situated that it comes into contact with exhaust gases downstream from a catalyst. According to the present invention, an actual signal is compared with an estimated signal, such that said actual signal depends on said measured sensor signal and that said estimated signal depends on at least one estimation function and represents the catalyst model's match with said actual signal, said catalyst model being spatially resolved. This comparison is thereafter used to determine at least one deviation parameter for the respective one or more estimation functions, such that each of these at least one deviation parameters describes a relation between a value for a model variable of a catalyst model and a corresponding actual value.

Inventors:
WESTERBERG, Björn (Myntstigen 15, 5 tr, Södertälje, S-151 48, SE)
Application Number:
SE2011/050069
Publication Date:
August 04, 2011
Filing Date:
January 25, 2011
Export Citation:
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Assignee:
Scania CV AB (S- Södertälje, 151 87, SE)
WESTERBERG, Björn (Myntstigen 15, 5 tr, Södertälje, S-151 48, SE)
International Classes:
F01N3/20; F01N9/00
Foreign References:
EP2025388A12009-02-18
US20040098974A12004-05-27
EP1992398A12008-11-19
Attorney, Agent or Firm:
GARDEMARK, Niklas (Scania CV AB, Södertälje, S-151 87, SE)
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Claims:
Claims

1. A method for estimation of a deviation for at least one model variable of a catalyst model, which estimation is based on said catalyst model and on at least one measured sensor signal from at least one sensor (131) which is so situated that it comes into contact with exhaust gases downstream from a catalyst (1 10),

characterised

- by comparing an actual signal with an estimated signal, such that said actual signal depends on said measured sensor signal and that said estimated signal depends on at least one estimation function and represents the catalyst model's match with said actual signal, said catalyst model being spatially resolved, and

- by using said comparison to determine at least one deviation parameter for the respective said at least one estimation function, such that each of said at least one deviation parameter describes a relation between a value for a model variable and a corresponding actual value. 2. The method according to claim 1 , whereby said model variable corresponds to an input signal which pertains to a concentration of nitrogen oxides NOx upstream from said catalyst (1 10), and

- one of said at least one deviation parameter is a deviation parameter cNO for concentration of nitrogen oxides NOx upstream from said catalyst (110).

3. The method according to claim 2, whereby said model variable corresponds to two separate input signals which pertain respectively to a concentration of nitrogen monoxide NO upstream from said catalyst (110) and a concentration of nitrogen dioxide N02

upstream from said catalyst (1 10).

4. The method according to claim 1, whereby said model variable corresponds to at least one condition which pertains to a temperature in said catalyst, and

- one of said at least deviation parameter is a deviation parameter cT for the condition for temperature in said catalyst (110).

5. The method according to claim 1 , whereby said model variable corresponds to a characteristic which pertains to an activity in said catalyst, or an input signal which pertains to a flow in said catalyst, and - one of said at least one deviation parameter is a deviation parameter ckT for the characteristic for activity in said catalyst or for the input signal for flow in said catalyst (110).

6. A method according to any one of claims 2-5, whereby:

- said actual signal takes the form of said measured sensor signal which corresponds to a concentration of nitrogen oxides NO downstream from said catalyst (1 10),

- said estimated signal takes the form of a modelled concentration of nitrogen oxides NOx downstream of said catalyst (1 10), and

- one of said at least one estimation function is an estimation function for nitrogen oxides fm, which relates said modelled concentration of nitrogen oxides NOx to said measured sensor signal.

7. The method according to claim 6, whereby said comparison of said measured sensor signal with said estimated signal uses the relationship in which

- yNO is said measured sensor signal,

- fNO (c, ,...,ck ) is said estimated signal,

- c ,...,ck is at least one deviation parameter which describes how well the model corresponds to reality, where k > 1 , and

- ε is a residual.

8. A method according to either of claims 4 and 5, whereby:

- said actual signal takes the form of said measured sensor signal which corresponds to a concentration of ammonia NH3 downstream from said catalyst (1 10), and

- said estimated signal takes the form of a modelled concentration of ammonia NH3 downstream of said catalyst (1 10), and

- one of said at least one estimation function is an estimation function for ammonia fm which relates said modelled ammonia NH3 of ammonia fNH to said measured sensor signal.

9. The method according to claim 8, whereby said comparison of said measured sensor signal with said estimated signal uses the relationship

yNH, = NH, (Cl ' " - > Cjt ) + ε

in which

- ym is said measured sensor signal,

- fNH (c, ,...,ct) is said estimated signal,

- cx,...,ck is at least one deviation parameter which describes how well the model corresponds to reality, where k > 1 , and

- ε is a residual.

10. A method according to any one of claims 2-5, whereby:

- said actual signal takes the form of said measured sensor signal which corresponds to an aggregate of a concentration of nitrogen oxides NOx and a concentration of ammonia NH} , - said estimated signal takes the form of an aggregate of a modelled concentration of nitrogen oxides NOx downstream of said catalyst (1 10) and a modelled concentration of ammonia

NH} downstream of said catalyst (1 10),

- one of said at least one estimation function is an estimation function for nitrogen oxides fNO which relates said modelled concentration of nitrogen oxides fm to said measured sensor signal, and

- one of said at least one estimation function is an estimation function for ammonia fNH which relates said modelled concentration of ammonia NH3 of ammonia fNH to said measured sensor signal 1 1. The method according to claim 10, whereby said comparison of said measured sensor signal with said estimated signal uses the relationship

y sensor ~ ΝΟΧ (Cl '·"' k ) + /NH, (C\ Ck ) + £

in which

- ysem()r is said measured sensor signal,

- fm, (ci '-' ck ) + fm, (ci ck ) is said estimated signal, - cx,...,ck is at least one deviation parameter which describes how well the model corresponds to reality, where k≥ 1 , and

- ε is a residual. 12. The method according to claim 1 , whereby said model variable corresponds to an input signal which pertains to a flow of dosed urea, and

- one of said at least one deviation parameter is a deviation parameter cUrea for the flow of dosed urea. 13. A method according to claim 12, whereby

- said actual signal corresponds to an actual flow of dosed urea which is determined on the basis of a measured concentration of nitrogen oxides NOx upstream from said catalyst, and on the basis of said at least one measured sensor signal from said at least one sensor (131) which is so situated that it comes into contact with exhaust gases downstream from the catalyst (110), such that said at least one measured sensor signal comprises a measured concentration of nitrogen oxides NOx and a measured concentration of ammonia NH3 ,

- said estimated signal takes the form of a modelled flow of dosed urea, and

- one of said at least one estimation function is an estimation function for urea fUrea which relates said modelled flow of dosed urea to said actual flow of dosed urea.

14. The method according to claim 13, whereby said comparison of said actual flow of dosed urea with said estimated signal uses the relationship in which

- FUrea is said actual flow of dosed urea,

- furea {Furea , c1 , ... , ck ) is estimated flow of dosed urea,

- cx,...,ck is at least one deviation parameter which describes how well the model corresponds to reality, and

- ε is a residual.

15. The method according to claim any one of claims 7, 9, 11 or 14, whereby a calculation method from among the following is used for estimation of said at least one deviation parameter cl,c2...,ck which minimises said residual ε :

- a calculation method using a Kalman filter,

- a calculation method using an extended Kalman filter,

- a calculation method using an unscented Kalman filter, and

- a recursive least-squares method.

16. A method for correcting at least one input signal in a catalyst model, characterised in that said correction is effected by use of estimation of said deviation for at least one model variable of said catalyst model according to any of claims 1-15, such that each of said at least one input signal relates to at least one of said at least one model variable.

17. A method for correcting at least a characteristic for a catalyst model, characterised in that said correction is effected by use of estimation of said deviation for at least one model variable of said catalyst model according to any of claims 1-15, such that each of said at least one characteristic relates to at least one of said at least one model variable.

18. A computer programme which comprises programme code and which, when said programme code is executed in a computer, causes said computer to apply the method according to claims 1-17.

19. A computer programme product comprising a computer-readable medium and a computer programme according to claim 18, which programme is contained in said computer- readable medium which is from among ROM (read-only memory), PROM (programmable

ROM), EPROM (erasable PROM), flash memory, EEPROM (electrically erasable PROM) and hard disc unit.

20. A system (100) for estimation of a deviation for at least one model variable of a catalyst model, which system is arranged to base said estimation on said catalyst model and on at least one measured sensor signal from at least one sensor (131) which is so situated that it comes into contact with exhaust gases downstream from a catalyst (110),

characterised - by a means adapted to comparing an actual signal with an estimated signal, such that said actual signal depends on said measured sensor signal and that said estimated signal depends on at least one estimation function and represents the catalyst model's match with said actual signal, said catalyst model being spatially resolved, and

- by a means adapted to using said comparison to determine at least one deviation parameter for the respective said at least one estimation function, such that each of said at least one deviation parameter describes a relation between a value for a model variable and a corresponding actual value.

Description:
Estimation of a deviation for at least one model variable of a catalyst model

Technical field

The present invention relates to a method for estimation of a deviation for at least one model variable of a catalyst model, according to the preamble of claim 1.

The present invention relates also to a computer programme and a computer programme product which implement the invention.

The present invention relates also to a system for estimation of a deviation for at least one model variable of a catalyst model, according to the preamble of claim 20.

Background

In substantially all of today's motor vehicles, e.g. cars, trucks, buses and other vehicles, a catalyst is used to clean exhaust gases from an engine of the vehicle. The use of catalysts is important for keeping below the emission limit values laid down by authorities and laws in different countries or regions. Figure 1 depicts schematically a catalyst system 100 which is implementable in substantially all types of motor vehicles. In the catalyst system 100, a catalyst 1 10 is so arranged that exhaust gases 120 upstream from the catalyst, which come from an engine, pass through the catalyst 1 10. Exhaust gases 130 which have passed the catalyst then proceed towards an exhaust pipe of the vehicle. The catalyst 1 10 may take the form of an SCR (selective catalytic reduction) catalyst. If the catalyst is an SCR catalyst, a reducing agent, usually in the form of urea, is dosed before the catalyst 1 10. The reducing agent is thus supplied to the exhaust gases 120 which have not yet passed through the catalyst 110. This dosing is effected in the catalyst system 100 by means of a dosing nozzle 121 which is supplied with the reducing agent from a tank 150. In the system exemplified below the reducing agent supplied is urea and the tank 150 takes the form of a urea tank 150.

The urea is usually in the form of an aqueous solution which is vaporised and decomposes to form ammonia. The ammonia then constitutes the active reducing agent in the catalyst 1 10 and reacts with nitrogen oxides NO x in the exhaust gases to form nitrogen gas and water. Nitrogen oxides NO x comprises here and throughout this specification both nitrogen monoxide NO and nitrogen dioxide NO 2. For the desired reaction in the catalyst 110 a stoichiometric relationship prevails between the ammonia formed and the nitrogen oxides NOr in the exhaust gases which are to be cleaned. One ammonia molecule is needed for each molecule of nitrogen oxides NO x . For the catalyst process to be effective, the concentration of ammonia, and hence also the amount of urea dosed, has therefore to correspond to and track the concentration of nitrogen oxides NO x in the exhaust gases which it is desired to clean. The concentration of nitrogen oxides NO x in the exhaust gases 120 before the catalyst, and also the operating conditions, e.g. the temperature, vary over time. These variations may depend for example on how the vehicle is run and on the surrounding temperature. For example, the ability of the catalyst to accumulate ammonia varies with temperature, so its ability to accumulate ammonia is greater at low temperatures than at high temperatures. The dosage of urea has to be balanced with these variations to achieve desired cleaning of the exhaust gases. For example, higher dosage of urea is required if the temperature goes down and lower dosage if the temperature goes up. The urea dosage has therefore to be adjusted to achieve an effective stoichiometric catalyst process and counteract the presence of nitrogen oxides NO x and/or ammonia in the exhaust gases 130 which flow from the exhaust pipe after the catalyst.

To be able to calculate the flows of dosed urea needed, their regulation is adapted to the concentration of nitrogen oxides NO x in exhaust gases 120 upstream from the catalyst 1 10, i.e. the exhaust gases which the system 100 receives from the engine, and a model of the catalyst 1 10 may be used for necessary amounts of accumulated ammonia. The catalyst model comprises conditions for the catalyst, e.g. temperatures, and amounts of ammonia accumulated in the catalyst. A description of such a catalyst model appears below.

The concentration of nitrogen oxides NO x upstream from the catalyst 110 may be determined by using an NO x detecting sensor 122 so situated that it comes into contact with the exhaust gases 120 before they pass the catalyst 110. The concentration of nitrogen oxides NO x in the exhaust gases 120 from the engine may also be determined by using a model which describes the concentration of nitrogen oxides NO x at each operating point.

The calculation of urea flows needed may also take into account the exhaust flow from the engine. The exhaust flow can be measured but may also be calculated on the basis of operating parameters such as engine speed, charging pressure, intake temperature and amounts of fuel injected.

Figure 1 depicts schematically a sensor 122 which may comprise a temperature sensor and an NO x sensor and which is so situated that it comes into contact with the exhaust gases from the engine 120. The schematically illustrated sensor 122 may here detect concentrations of nitrogen oxides NO x and/or temperatures and/or the flow for the exhaust gases 120. In Figure 1 the sensor 122 is schematically depicted as being situated upstream from the dosing nozzle 121. However, the temperature sensor comprised in the sensor 122 may be situated either upstream or downstream from the dosing nozzle 121. The NO x sensor comprised in sensor 122 should nevertheless be situated upstream from the dosing nozzle to avoid being affected by the dosing. The sensor 122 supplies to a control unit 160 one or more signals representing concentrations of nitrogen oxides NO x and/or temperatures and/or the flow for the exhaust gases 120. The sensor 122 may be situated both before and after the dosing nozzle 121. The control unit 160 is also adapted to receiving a signal 132 from an NO x sensor 131 which is so situated that it comes into contact with exhaust gases 130 downstream from the catalyst 1 10, i.e. with exhaust gases which have passed the catalyst 110, and is intended to detect nitrogen oxides NO x , i.e. both nitrogen monoxide NO and nitrogen dioxide NO 2 , and also ammonia N¾ in these exhaust gases 130.

The control unit 160 controls an operating means (actuator) 140 which is in communication with a urea tank 150 and with the dosing nozzle. The operating means 140 regulates the flow of urea from the urea tank 150 to the dosing nozzle 121 according to the control signals supplied to the operating means 140 by the control unit 160. The control unit 160 uses the catalyst model to decide how the operating means is to be controlled. Model-based regulation of the urea dosage for an SCR catalyst generally allows effective use of the catalyst's capacity for NO x reduction, but the model's accuracy is a crucial factor in urea dosage control (regulation) performance. The model's accuracy depends on the accuracy of one or more model variables of the model which correspond to input signals to the model and then in particular to input signals for concentrations of NO x in the exhaust gases 120 from the engine and for flows of dosed urea, conditions in the catalyst, and characteristics used for the catalyst.

However, the accuracy of the model variables is not always satisfactory. There is relatively often a deviation of one or more model variables of the catalyst model, resulting in the catalyst model not corresponding to reality. These deviations may vary over time and may also vary in magnitude depending on the magnitude of the model variable. For example, a deviation of the input signals for both NO x before catalyst and the flow of dosed urea results in an error, which varies over time, in respective modelled concentrations of nitrogen oxides NO x and ammonia NH 3 after catalyst.

Brief description of the invention

An object of the present invention is to propose, for estimation of a deviation of at least one model variable of a catalyst model, a method and a system which wholly or partly solve the problem mentioned above.

This object is achieved by a method for estimation of a deviation for at least one model variable of a catalyst model according to the characterising part of claim 1. The object is also achieved by a system for estimation of a deviation for at least one model variable of a catalyst model according to the characterising part of claim 20.

The object is also achieved by a computer programme and a computer programme product which implement the method according to the invention.

The model variables for which deviations are estimated correspond to one or more from among input signals to the catalyst, conditions in the catalyst and characteristics for the catalyst. The invention derives one or more deviation parameters which each describe a relation between an actual value for any from among these input signals to the catalyst, conditions in the catalyst and characteristics for the catalyst and a value for a corresponding model variable. These one or more deviation parameters may then be used to correct errors in input signals to, or characteristics for, the catalyst model. The present invention makes it possible for these deviation parameters to be calculated in a computationally very effective way.

The catalyst model is formulated as a spatially resolved model which can describe variations both in the catalyst's longitudinal direction and in the porous catalyst material from the surface and in towards the centre of the duct wall. The catalyst model according to the invention is a tank series model whereby variations in model variables, e.g. in one or more conditions or characteristics of the catalyst, can be modelled from the catalyst's inlet, along the catalyst, and to the catalyst's outlet. Dividing the active material into layers caters also for variations from the surface and in towards the centre of the duct wall. This spatially resolved catalyst model results in a very good match between the catalyst model and reality.

Specifically, this match is improved in brief and passing operating situations, called transient operating sitatuions, which cause successive changes in the catalyst, from its inlet to its outlet, and through the duct wall. The spatial resolution of the model results in a need for calculation capacity which depends on the number of tanks and layers used in the catalyst model.

Choosing the number of tanks and layers therefore involves striking a balance between the need for accuracy and the need for access to calculation capacity.

The NO x sensor 131 after the catalyst is used here to estimate deviations related to model variables, i.e. to estimate deviation parameters, thereby making it possible to correct these related input signals to, and characteristics for, the catalyst model, so that better accuracy for the model is achieved. The present invention can be used for continuous estimation of deviations, i.e. for continuous comparison between estimated and actual signals, which makes it possible for systematic deviations for the model variables of the catalyst model to be determined and corrected. A complete catalyst model which corresponds very well to reality is thus achievable, and hence also better urea dosage regulation performance.

The estimated deviation for a model variable can thus be determined, e.g. for a condition, whereas the correction is applied to an input signal or a characteristic which causes the deviation in the condition. An example of this is the case of estimation of deviation for the condition catalyst temperature, which is then used to correct the input signal for exhaust gas temperature before the catalyst. Here the input signal which relates to the estimated deviation for the condition is therefore corrected.

The present invention can be used to continuously adjust the catalyst model's input signals so that they correspond well to reality. This means that the regulation of urea can be made very exact, i.e. making it possible to reduce urea consumption while at the same time the emission requirements are effectively met.

As exhaust gas cleaning becomes very effective when the present invention is applied, the emission requirements can be achieved with a smaller catalyst. A smaller catalyst also causes the engine less backpressure, with consequently less fuel consumption. The present invention may also be used in model-based regulation of urea dosage for an SCR catalyst. The present invention is also usable for other types of catalysts. It may for example be used for applications in which a model is used to determine how much nitrogen monoxide NO is oxidised to nitrogen dioxide NO 2 across an oxidation catalyst. For this application, the method is used to estimate deviations in the concentration of nitrogen oxides NO x upstream from the oxidation catalyst and to estimate deviations for the activity in the oxidation catalyst.

An embodiment of the present invention determines the value for the deviation parameter c NO which describes the deviation of the input signal for concentration of nitrogen oxides

NO x upstream from the catalyst.

An embodiment of the present invention determines the value for the deviation parameter c T which describes the deviation for the condition temperature in the catalyst. This deviation is related to a deviation of the input signal for temperature upstream from the catalyst. An embodiment of the present invention determines the value for the deviation parameter c kT which describes the deviation for a characteristic which pertains to activity in the catalyst, or the deviation for the input signal which relates to flow in the catalyst. An embodiment of the present invention determines the value for the deviation parameter c e which describes deviation for a condition which pertains to degree of coverage of ammonia.

An embodiment of the present invention determines the value for the deviation parameter c Urea which describes the deviation of the input signal for flow of dosed urea.

These embodiments of the invention are thus used to arrive at values for deviation parameters which can then be used to correct the respective input signals to, or characteristics for, the catalyst model. In other words, the deviation parameters are used to correct the input signals to, and characteristics for, the catalyst to which they relate. Deriving these deviation parameters thus makes it possible for urea dosage regulation to be done effectively and exactly.

The deviation parameters may also be used for diagnosing faults of the system. For example, a fault in a sensor upstream from the catalyst can be diagnosed if major errors are detected in the input signal for concentration of nitrogen oxides NO x upstream from the catalyst.

Brief list of drawings

The invention is explained in more detail below with reference to the attached drawings, in which:

Figure 1 is a schematic drawing of a catalyst system,

Figure 2 is a flowchart for the method according to the present invention,

Figure 3 depicts schematically a control unit, and

Figure 4 depicts a tank series model of the catalyst.

Description of preferred embodiments

The method according to the present invention comprises estimation of errors in model variables of the catalyst model, e.g. in input signals to the model, conditions in the model and characteristics for the model. The estimation is based inter alia on the sensor signal provided by the NO x sensor 131. The NO x sensor 131 may provide either respective separate signals for nitrogen oxides )?ΝΟ Χ and ammonia y NH or a composite signal y semor for them (i.e. the NO x sensor 131 is a cross-sensitive NO x sensor). The cross-sensitive NO x sensor 131 has approximately the same sensitivity for nitrogen monoxide NO (standardised sensitivity with the value 1) as for ammonia NH 3 (standardised sensitivity with the value 1) but a somewhat lower sensitivity for nitrogen dioxide NO 2

(standardised sensitivity with the value 0.7). However, what normally remains in the exhaust gases after an effective catalyst process is mostly carbon monoxide NO. An estimation method does however make it possible to obtain from the sensor signal y sensor a separate signal y NOx for the concentration of nitrogen oxides and a separate signal y NH for the concentration of ammonia.

There follows a description of a catalyst model. As specialists will appreciate, catalyst models can be defined in many different ways, the model described here being an example. A list of variables and indices used in the description of the catalyst model and in the equations set out below appears at the end of the description.

The catalyst model is formulated as a tank series model in which active material is divided into layers. Such a tank series model 400 is depicted schematically in Figure 4. The tank series model 400 is here divided into a number of tanks 401 from inlet to outlet. The duct wall is also divided into a number of layers 402 of active material.

The catalyst model is therefore a spatially resolved model which caters for how model variables for the catalyst vary from the catalyst's inlet, along the catalyst, to the catalyst's outlet, and through the active material from the surface and in towards the centre of the duct wall. This spatial resolution of the model makes it possible to achieve a very good match between the catalyst model and reality, since variations for conditions and concentrations along the catalyst and through the duct wall can be modelled. For example, information about temperature and/or accumulated ammonia 3 in the various parts of the catalyst is obtainable from this spatially resolved model of the catalyst.

The catalyst model covers the following reactions:

Urea + H 2 0→ 2NH 3 + C0 2 (eq. 1)

S + NH 3 →S - NH 3 (eq. 2) S - NH 3 →S + NH 3 (eq. 3)

4S - NH 3 + 4NO + 0 2 →4S + 6H 2 0 + 4N 2 (eq. 4) 4S - NH 3 + 50 2 →4S + 6H 2 0 + 4NO (eq. 5) The model also covers urea decomposition (the first reaction) from the dosing nozzle 121 to the catalyst 110. The model applies the simplification that the isocyanic acid (HNCO) formed by urea decomposition is treated as match with ammonia.

The urea decomposition is treated as a homogeneous reaction with the reaction rate

r .u,k = k u ,k " c tot,k " Yurea,k,0 ( e 1-6)

Other reactions are catalytic. The reaction rate for adsorption in tank k and layer n is expressed as

rc,a,k,n = ^a,k ' tot,k Ύ ' ^ ~ &k,n ) ( e ¾-

The reaction rate for desorption in tank k and layer n is expressed as

rcd , k , n = kd f d k n (eq. 8)

The reaction rate for NO X reduction in tank k and layer n is expressed as

rc.r,k,n = k r , ' c tot,k ,η " k,n ( et l- 9)

The reaction rate for ammonia oxidation in tank k and layer n is expressed as

rc,o,k,n = k 0 , ' c tot,k ' @k,n ( e< T 10) The rate constant for both homogeneous and catalytic reactions is determined from the Arrhenius equation as k iM = k o r e * r " (eq. 1 1)

The total gas concentration is determined from the general gas law as

c toU = -^ - (eq. 12)

K ' 1 s,k The total pressure P may be added to the pressure after the catalyst 110 which is equal to atmospheric pressure if the catalyst is situated last in the exhaust system. For a more accurate value, the pressure drop from the respective tank to the end of the catalyst is calculated from formulae for laminar flow in a duct and is added to the pressure after the catalyst. If the catalyst is not last in the system, the pressure may be measured or calculated from pressure drops across the unit or units situated after the catalyst.

For the catalyst the following material balance of the gas flow may be set up for substance i:

F - yi,k,o )- Ti,k,o - {Υι ο - / ,*.* - r hj,k V k = 0 (eq. 13)

The following material balance of the gas phase in layer n may be set up for substance i (ignoring homogeneous reactions):

i,k.n-1 · ( / ,ϋ-ί - Υί ,η )- T i,k,n ' (Vi.k.n ~ //,*.„+* ) +∑ v i,j ' r c.j.k.n · W k , n = 0 (eq. 14)

For the innermost layer the second term drops out as follows:

ri.k.N-i {yi.k.N-1 - //,*,¾)+∑ v r c j k N w k N = 0 (eq. 15) j

The material balances for the gas flow and for the gas phase in the active layers form an equation system from which mole fractions are determined for the various substances in the gas flow and in the gas phase in the active layers. The mass transfer coefficient for transfer between the gas flow and the first layer is determined as

kc.i.k D, eff.i.k

The mass transfer coefficient for transfer between layers is determined as

The film transfer coefficient is determined as k c k =—^ (eq. 18) For the Sherwood number Sh, asymptotic values for the respective duct geometry may be used. The ordinary diffusivity is determined as

-.us

' s,k

0 .* = Dref (eq. 19)

' ref

The Knudsen diffusivity is determined as

D _ d ϋ

K,i,k - 1/ .. (eq. 20)

3 π Mi

The effective diffusivity is determined as

f,

D, eff.i.k (eq. 21)

1 1

D i D K i

The time-dependent material balance for adsorbed ammonia gives the time derivative for degree of coverage as

-NH 3 .j ' 'c,j,k,n ' w ,n (eq. 22)

The degree of coverage at each point in time is then integrated on the basis of the time derivative. The temperature in the gas flow through the catalyst 1 10 is determined by solving a heat balance which takes into account the heat transferred to the solid material and the reaction heat for homogeneous reactions. The effect from the reaction heat for homogeneous reactions is determined as

h, k =∑r h _ k V k (- AHj ) (eq. 23)

The heat balance for the gas flow is then solved by

T _ F ' c p,g ' Tg,k-1 + ' A C h, k T s k + Q h k

P,9 H ch,k in which the heat transfer coefficient is determined as

Nu - A a

h k = - (eq. 25) k d For the Nusselt number Nu , asymptotic values for the respective duct geometry may be used. The effect from the reaction heat for catalytic reactions is determined as

<¼.* =∑∑ r c,j.k , n w (-AHj ) (eq. 26) n j The time-dependent heat balance for the solid material in the catalyst gives the time derivative for temperature as ) + <¼,* ) (e - 27)

The temperature at each point in time is then integrated on the basis of the time derivative.

If the catalyst model, including its input signals, fully matches reality, the regulation of the flow of dosed urea becomes relatively exact and effective cleaning is achieved.

However, the catalyst model's accuracy depends on the accuracy of its input signals. The two input signals of greatest significance for the catalyst model's accuracy are the input signal for NO x from the engine, i.e. for the concentration of NO x upstream from the catalyst 1 10, and the input signal for the flow of dosed urea. When the model is used for regulation of urea dosage, errors in the input signals will affect the emissions of nitrogen oxides NO x and ammonia NH 3 downstream from the catalyst 1 10. If for example the input signal for the concentration of NO x upstream from the catalyst 1 10 is too high, the regulation will dose more urea relative to NO x , resulting in a higher concentration of ammonia NH 3 after the catalyst 110, i.e. downstream from the catalyst 1 10. A similar deviation resulting in a similar consequence will occur if the actual flow of dosed urea is greater than the ordered flow.

The catalyst model's accuracy also depends on the accuracy of its characteristics used, e.g. catalyst ageing may result in a deviation of the characteristic activity such that the activity is impaired over time.

The present invention utilises the principle that deviations for one or more model variables of the catalyst model can be estimated by comparing actual concentrations of nitrogen oxides NO x and ammonia NH 3 downstream from the catalyst 1 10 with respective modelled concentrations. The NO x sensor 131 after the catalyst is therefore used here to estimate deviations related to model variables, i.e. to estimate deviation parameters. These one or more deviation parameters describe systematic deviations for the model variables, i.e.

systematic deviations for one or more from among at least one input signal, at least one variable and at least one condition for the catalyst model. The estimation of deviation parameters may according to the present invention be done continuously, allowing continuous correction of input signals to, and characteristics for, the catalyst model so that good correspondence between catalyst model and reality is achieved. The concept is that the model calculates output signals in the form of, for example, concentrations after the catalyst. How well these output signals correspond to reality depends on the accuracy for a number of model variables which correspond to input signals to the catalyst, conditions in the catalyst or characteristics for the catalyst. It is also possible to derive relationships which represent how these model variables differ from reality, i.e.

deviation parameters. The fact that relationships can be set up between these deviations and the input signals to respective characteristics for the catalyst model also makes it possible to estimate respective errors in the input signals and in the characteristics, and to correct them, so that better accuracy for the model is achieved. For example, to correct input signals based on the estimation, it is possible to determine how the input signals used (input signals used by the model which have errors/deviations) behave relative to the actual input signals (the input signals without errors/deviations). Errors in the modelled concentrations of nitrogen oxides NO x and ammonia NH 3 downstream from the catalyst then relate to the errors/deviations in the input signals for, for example, NO x from the engine, the flow of dosed urea and for temperatures and flows. It is thus also possible to correct the deviations in these input signals.

Figure 2 is a flowchart for a method according to the present invention. Its first step 201 compares an actual signal with an estimated signal. The actual signal depends here on the sensor signal measured by the NO x sensor 131. The estimated signal depends on at least one estimation function and represents the catalyst model's match with the actual signal. A second step 202 of the method uses the comparison to determine at least one deviation parameter for the respective at least one estimation function. Each of these one or more deviation parameters describes a relation between an actual value and a value for a corresponding model variable.

The value for the model variable is therefore matched by the actual value, so deviation parameter relates the actual value to the value for the model variable. The one or more deviation parameters therefore describe how well the model corresponds to reality. The value for the model variable may for example be based on a measurement or on a separate model which may be a different model from the catalyst model used according to the present invention.

The invention thus identifies a difference between what the model indicates that a model variable should be like and what reality indicates that the corresponding actual value is like, and relates this difference to input signals to, and characteristics for, the catalyst.

The fact that these one or more deviation parameters can be determined in this way means that errors in the input signals to, and the characteristics for, the catalyst which relate to these deviation parameters can be determined and corrected. Correcting these errors results in greater accuracy respectively for the input signals to and for the characteristics for the catalyst and hence in more effective regulation of the urea dosage. The method according to the present invention therefore achieves a more effective cleaning process for the catalyst, thereby reducing urea consumption. Fuel consumption may also be reduced in that a smaller catalyst, with less backpressure for the engine, may be used to reach the emission requirements.

Different embodiments of the present invention use different estimation functions to determine the deviation parameters. These estimation functions are described below, one of them for nitrogen oxides f NO and one for ammonia f m . The estimation function for nitrogen oxides f N0 depends on a material balance for a modelled reaction in the catalyst model and relates a modelled concentration of nitrogen oxides NO x downstream from the catalyst 1 10 to the sensor signal JKM ? measured by the NO x sensor 131. As described above, a separate signal y NOx for the concentration of nitrogen oxides NO x and a separate signal y NH for the concentration of ammonia may be obtained by simultaneous estimation from the sensor signal y semor

The relation between the modelled concentration of nitrogen oxides NO x downsteam of the catalyst 1 10 and the measured sensor signal y ΝΟχ is described by one or more of the deviation parameters c N0 , c T and c kT . The deviation parameter c N0 describes the deviation for concentration of nitrogen oxides NO x upstream from the catalyst 1 10. The deviation parameter c T describes the deviation for the condition temperature in the catalyst 110. The deviation parameter c kT describes the deviation for the characteristic activity in the catalyst or for the input signal flow in the catalyst.

The estimation function for nitrogen oxides may be derived from the material balance for a first-order reaction in a tank series. The estimation function then becomes a product arrived at by multiplying the deviation parameter c N0 for nitrogen oxides NO x upstream from the catalyst 110 by the mole fraction for NO x upstream from the catalyst 1 10 and by a factor for each tank which describes how much of the NO input remains after the respective tank: in which the conversion represents a first-order rate constant multiplied by the dwell time and is determined from nitrogen oxides NO x input and output from the respective tank as

The deviation parameter for conversion gives the respective influences of deviation in activity/flow, degree of coverage of ammonia and temperature as h = c kT .e NH - c <> - e R T ^ * (eq. 30) in which

- c kT is the deviation parameter for the characteristic activity or the input signal flow,

- Cg is the deviation parameter for the condition degree of coverage of ammonia,

- c T is the deviation parameter for the condition temperature in the catalyst, and

- E A is the activation energy for reduction of NO x .

A common feature of the deviation parameters is that the value one (1) means absence of deviation. For all of the deviation parameters other than degree of coverage of ammonia, the value for the deviation parameter indicates the factor by which the value used needs to be multiplied for it to correspond to the actual value. For degree of coverage of ammonia, the value two (2) minus the deviation parameter indicates the value by which the degree of coverage has to be raised for it to correspond to actual value. According to an embodiment of the present invention, the estimation function for nitrogen oxides f NO comprises a first relation between a modelled concentration of carbon monoxide

NO downstream from the catalyst 110 and the sensor signal y sensor measured by the NO x sensor 131, and a second relation between a modelled concentration of nitrogen dioxide NO 2 downstream from the catalyst 110 and the sensor signal y semor measured by the NO x sensor 131.

Moreover, according to an embodiment of the present invention, the estimation function for ammonia f NH relates a modelled concentration of ammonia N¾ downstream of the catalyst to the sensor signal y NH measured by the NO x sensor 131 and depends on an equilibrium between modelled adsorbed ammonia and modelled ammonia in gaseous form at an outlet end of the catalyst 110. The outlet end of the catalyst normally takes the form of the last tank in the catalyst 1 10.

The deviation function for ammonia f m may be derived from the equilibrium between adsorbed ammonia and ammonia in gaseous form in the last tank of the catalyst. The deviation parameters relate the catalyst model's value for ammonia NH 3 after the catalyst to actual value by deviation in temperature and degree of coverage of ammonia NH 3 as follows:

in which

- c e is the deviation parameter for the condition degree of coverage of ammonia,

- C j is the deviation parameter for the condition temperature in catalyst, and

- AH is adsorption enthalpy for adsorption of ammonia NH } .

According to an embodiment of the present invention, the estimation function for ammonia f m therefore relates a modelled concentration of ammonia NH 3 downstream from the catalyst 110 to the sensor signal f m measured by the NO x sensor 131. This is therefore done by using at least one deviation parameter c T for the condition temperature in the catalyst, and a deviation parameter c e for the condition degree of coverage of ammonia.

Moreover, the respective estimation functions for nitrogen oxides f NO and ammonia f m are used to estimate deviations of one or more model variables of the catalyst model. The model variables may take the form of input signals to the catalyst, conditions for the catalyst or characteristics for the catalyst, as described below.

An embodiment of the present invention uses the estimation function for nitrogen oxides f NO to estimate errors in an input signal corresponding to a concentration of nitrogen oxides NO x upstream from the catalyst 1 10. This is done by estimating the deviation parameter c NO for concentration of nitrogen oxides NO x upstream from said catalyst.

An embodiment of the present invention uses the estimation function for nitrogen oxides f NO , which comprises a first relation between a modelled concentration of nitrogen monoxide NO downstream from the catalyst 110 and the sensor signal y ΝΟχ measured by the NO x sensor 131, and a second relation between a modelled concentration of nitrogen dioxide NO 2 downstream from the catalyst 1 10 and the sensor signal y ΝΟχ measured by the NO x sensor 131.

This estimation function f NO comprising these first and second relations may be used in conjunction with two separate deviation parameters for nitrogen monoxide c NO and for nitrogen dioxide c NO to make an estimate of a deviation for model variables which relate respectively to concentration of nitrogen monoxide NO upstream from the catalyst and concentration of nitrogen dioxide NO 2 upstream from the catalyst. Thereafter it is possible to determine errors in two separate input signals which respectively represent a concentration of nitrogen monoxide NO upstream from the catalyst 1 10 and a concentration of nitrogen dioxide ¾ upstream from the catalyst 110, when they are related to the model variables.

An embodiment of the present invention uses the estimation function for nitrogen oxides f m to estimate errors in an input signal which relates to a temperature in the catalyst 110. This is done by determining a deviation parameter c T for the model variable for the condition which relates to temperature in the catalyst 1 10. This deviation parameter c T is related to an input signal which influences the temperature in the catalyst, making it possible to determine the error in this input signal, since it is a deviation for this input signal which results in the deviation in the condition for temperature in the catalyst.

For example, errors in the input signal from the sensor 122 for exhaust gas temperature upstream from the catalyst may cause a deviation in the condition for temperature in the catalyst 110. Determining this deviation of the condition for temperature in the catalyst also makes it possible to determine and correct the error in this input signal.

An embodiment of the present invention uses the estimation function for nitrogen oxides f NO to estimate deviation of a characteristic which pertains to an activity in the catalyst 1 10, or to estimate deviation of an input signal corresponding to flow in the catalyst 1 10. This is done by determining a deviation parameter c kT for the characteristic activity or the input signal flow in said catalyst 1 10. An embodiment of the present invention esimates any from among the deviation parameters c NO which describes the deviation of the input signal for concentration of nitrogen oxides

NO x upstream from the catalyst, c T which describes the deviation of the condition temperature in the catalyst 1 10, and c kT which describes the deviation of the characteristic activity or the input signal flow in the catalyst, by doing a comparison between the sensor signal y^o, measured by the NO x sensor 131, corresponding to a concentration of nitrogen oxides NO x , and the estimated corresponding signal.

This comparison utilises the relationship

y m = f m {c ...,c k ) + s (eq. 32) in which

- y NO is the separate value for nitrogen oxides from the measured sensor signal,

- f NOx (c 1 t ..., c k ) is the estimated signal,

- c t ,...,c k is at least one deviation parameter out of c m , c T and c kT , and

- ε is a residual.

An embodiment of the present invention uses the estimation function for ammonia f NH to estimate either of the deviation parameters c T , which describes the deviation of the condition temperature in the catalyst 1 10, and c kT , which describes the deviation of the characteristic activity or the input signal flow in the catalyst, by doing a comparison between the sensor signal y NH measured by the NO x sensor 131, corresponding to a concentration of ammonia, and the estimated corresponding signal.

This comparison utilises the relationship

J N H, = / NH} {c x ,...,c k )+ s (eq. 33) in which

- y NH is the separate value for ammonia from the measured sensor signal,

- f NH3 {c 1 ,...,c k ) is the estimated signal,

- c ...,c k is at least one deviation parameter out of c T and c kT , and - ε is a residual.

An embodiment of the present invention uses both the estimation function for nitrogen oxides f N0 and the estimation function for ammonia f NH to estimate any of the deviation parameters c NO which describes the deviation of the input signal for concentration of nitrogen oxides NO x upstream from the catalyst, c T which describes the deviation of the condition temperature in the catalyst 1 10, and c kr which describes the deviation of the characteristic activity or the input signal flow in the catalyst, by doing a comparison between the sensor signal y senmr measured by the NO x sensor 131 and the estimated corresponding signal.

According to this embodiment, the measured sensor signal y semnr corresponds to the aggregate of a concentration of nitrogen oxides NO x and a concentration of ammonia NH 3 , which aggregate is normally provided as an output signal by the cross-sensitive NO x sensor 131. The estimated signal here represents the model's match with the aggregate of the concentration of nitrogen oxides NO x downstream from the catalyst 110 and the

concentration of ammonia NH 3 downstream from the catalyst 1 10.

The estimation is done by comparing the measured sensor signal with the estimated signal as follows:

y sensor = f NO x ( C l >···, C k ) + f N H 3 ( C l »-» C k ) + £ ( ε ¾· 34 )

in which

- y ~ smsor is said measured sensor signal representing the aggregate of a concentration of nitrogen oxides NO x and a concentration of ammonia NH 3 ,

- f WOx (c i ,..., c^ ) + f WH3 (c i ,..., c^ ) is the estimated signal,

- c ] ,...,c k is at least one deviation parameter out of c NO c T and c kT , and

- ε is a residual.

This embodiment can be used to estimate deviations in model variables directly on the basis of the input signal from the cross-sensitive NO x sensor 131. An embodiment of the present invention makes an estimate of deviation for a model variable which is an input signal corresponding to the flow of dosed urea, whereby a deviation parameter c l!rea for the flow of dosed urea is estimated and used. A problem in estimating deviations in the flow of dosed urea is that there is a dynamic between dosage of urea and reduction of nitrogen oxides and ammonia NH 3 after the catalyst. The dynamic effect arises because the flow of dosed urea initially gives rise to ammonia NH 3 which is subsequently adsorbed in the catalyst. This adsorbed ammonia NH 3 thereafter reduces NO x or, when there are temperature transients, gives rise to ammonia NH 3 after the catalyst when ammonia desorbs.

To deal with this problem, this embodiment uses instead another equivalent measure of the flow of dosed urea, based on the fact that the urea dosed causes reduction of either nitrogen oxides NO x or ammonia NH 3 after the catalyst. The aggregate of reduced nitrogen oxides

NO x and ammonia NH 3 after catalyst is therefore an equivalent measure of the flow of dosed urea. An equivalent flow of dosed urea according to the catalyst model (modelled flow of dosed urea) is also derived and is used in conjunction with an estimation function for urea furea which relates said modelled flow of dosed urea to said actual flow of dosed urea to arrive at a measure of modelled flow of dosed urea. This equivalent measure of the flow of dosed urea is then used in a comparison to determine an error in input signals for the flow of dosed urea.

According to the embodiment, the actual signal therefore corresponds to an equivalent actual flow of dosed urea F Urea , which is determined on the basis of current exhaust flow, a measured concentration of nitrogen oxides NO x upstream from the catalyst, and on the basis of the sensor signal measured by the NO x sensor 131 , which signal comprises a measured concentration of nitrogen oxides NO x and a measured concentration of ammonia NH 3 downstream from said catalyst 1 10, as follows:

Furea = F (/wo x ,o - YNO X + Y NH 3 ) (eq. 35) in which

- F Urea is equivalent actual flow of dosed urea, - F is the exhaust flow,

- y N0 0 is measured concentration of nitrogen oxides NO x upstream from the catalyst,

- y NO is the separate value for nitrogen oxides from the measured sensor signal,

- y NH is the separate value for ammonia from the measured sensor signal.

The sensor signal measured by the NO x sensor may here comprise actual separate values for nitrogen oxides NO x and ammonia NH 3 . These separate values may be determined by separate sensors, i.e. sensor 131 comprising separate sensors for nitrogen oxides NO x and ammonia NH 3 . These separate values for nitrogen oxides NO x and ammonia NH 3 may also be determined by simultaneous estimation from a NO x sensor which measures the aggregate of NO x and NH 3 , i.e. from a cross-sensitive sensor 131.

The equivalent flow of dosed urea according to model F Urea may be expressed as

Furea = F - Y NO X ,K + YNH 3 ,K ) (eq- 36) in which

- F Ureo is an equivalent actual flow of dosed urea according to model,

- F is the exhaust flow,

- y NO 0 is measured concentration of nitrogen oxides NO x upstream from the catalyst,

- y m K is a modelled value for nitrogen oxides downstream from the catalyst, and

- y m K is a modelled value for ammonia downstream from the catalyst.

The estimation of deviation parameters for urea uses the relationship

Furea ~ ^urea {Furea . Ci , - : C k ) + e (eq. 37) in which

- F Urea is the equivalent actual flow of dosed urea,

- f U rea {Furea ' c i ' - - c k ) ls estimated flow of dosed urea,

- c x ,..., c k are deviation parameters for urea, and

- ε is a residual. In the simplest version the estimation function is linear as follows: furea {^urea · c 1 > ■■■ < c k ) = c Urea ' ^urea ( e< ¾- 38) in which

- f urea {F ureg , c c fc ) is estimated flow of dosed urea,

- c Urea is a deviation parameter for the flow of dosed urea, and

- F Urea is an equivalent flow of dosed urea according to model.

Alternatively it is for example possible to use a polynomial function, in which case the deviation is described by several deviation parameters. Estimating the error in the flow of dosed urea thus involves using a representative value for actual flow of dosed urea, i.e. the equivalent value for the actual flow of dosed urea F Urea . A representative value for actual flow of dosed urea F Urea may be determined from actual nitrogen oxides NO ^ converted (the difference between nitrogen oxides NO x before and after catalyst) plus actual ammonia NH 3 after catalyst. This value is a correct measure of the flow of dosed urea, since most of the flow of dosed urea either reduces NO,, or gives rise to ammonia NH 3 after the catalyst.

The error in the flow of dosed urea may then be estimated by comparing the representative (equivalent) value for actual flow of actual dosed urea F Urea with corresponding equivalent modelled values F Urea from the catalyst model. The comparison is therefore done between actual aggregate and modelled aggregate of nitrogen oxides NO x converted across catalyst plus ammonia NH 3 after catalyst. This minimises the influence of the problematic dynamic effect for the flow of dosed urea, which depends on adsorption and desorption of ammonia in the catalyst.

If a linear estimation function is used (according to equation 38), the estimation produces a value for the deviation parameter c Urea which indicates the value by which the input signal corresponding to the flow of dosed urea has to be multiplied for it to correspond to actual value. The value one (1) therefore means absence of deviation. An embodiment of the present invention determines the at least one deviation parameter c, ,...,c k by analysing which value of the at least one deviation parameter c, ,...,c k minimises the residual ε in equations 32, 33, 34, 37 and 38. The value of the at least one deviation parameter c x ,...,c k which minimises the residual ε is adopted. This way of determining the value of the at least one deviation parameter c, ,...,c k may be applied effectively and with use of little calculation capacity, since effective estimation algorithms can be used.

These effective estimation algorithms involve using, according to an embodiment of the invention, a Kalman filter if equations 32, 33, 34, 37 and 38 are linear. If the equations are non-linear, an extended Kalman filter or an unscented Kalmen filter may be used. The extended Kalman filter is preferably used where there are small non-linearities for the equations and the unscented Kalman filter is used if the non-linearities are large. An embodiment of the invention uses a recursive least-squares method. This recursive least- squares method may be used if the equations are linear or moderately non-linear.

An embodiment of the present invention uses derived deviation parameters c, ,...,c k to correct at least one input signal in, or at least one characteristic for, the catalyst model, where the at least one input signal or the characteristic has caused the deviation determined of the model variable. The one or more input signals or characteristics to be corrected therefore have a relation to one or more respective model variables. When the deviations, i.e. the deviation parameters, for these one or more model variables have been determined, they can be used to correct the respective input signals or characteristics.

Derived values for any of the deviation parameters c m , c T , c kT , c e , c Urea are thus used here to correct corresponding input signals or characteristics. c NO describes the deviation of the input signal for concentration of nitrogen oxides NO x upstream from the catalyst. c T describes the deviation for the condition temperature in the catalyst, which is related to the input signal for temperature upstream from the catalyst 1 10. c kT describes the deviation for a characteristic which pertains to activity in the catalyst, or deviation for the input signal for activity which pertains to flow in the catalyst. c e describes deviation for a condition which pertains to degree of coverage of ammonia. c Urea describes the deviation of the input signal for the flow of dosed urea. This embodiment of the invention is thus used to arrive at values for deviation parameters which can then be used to correct the respective input signals and characteristics to which they relate.

For all deviation parameters other than degree of coverage of ammonia c e , the value determined for the respective deviation parameter value indicates the factor by which the input signal needs to be multiplied for it to correspond to the actual value. For degree of coverage of ammonia, 2 minus the value of the deviation parameter c e indicates the value by which the input signal for the degree of coverage has to be raised for it to correspond to actual value.

Degree of coverage of ammonia depends on a number of model variables and is influenced by a number of deviations for the model. If the invention is used to correct all of the input signals in, and characteristics for, the catalyst model so that it corresponds to reality, the degree of coverage of ammonia for the catalyst model will also correspond to reality.

Where the deviation parameters describe a linear deviation, the correction according to this embodiment of the invention will result in the input signal affected by errors being multiplied by the value for the respective deviation parameter to arrive at a corrected value

corresponding to the actual value which, after the multiplication, is not affected by errors.

The corrected value for the concentration of nitrogen oxides NO x is thus arrived at by multiplying the input signal for concentration of nitrogen oxides NO x by the deviation parameter c NO . In a similar way, the corrected value for temperature in the catalyst is arrived at by multiplying the input signal for the temperature by the deviation parameter c T , and the corrected value for the flow of dosed urea by multiplying the input signal for the flow of dosed urea is arrived at by the deviation parameter c Urea . The corrected value for degree of coverage of ammonia is arrived at by raising the input signal for degree of coverage of ammonia by two (2) minus the value of the deviation parameter c e . The value one (1 ) for these deviation parameters therefore means absence of deviation. According to an embodiment of the present invention, the deviation parameters may also be used for error diagnosis of parts of the system 100. If for example a sensor 100 upstream from the catalyst malfunctions, it may happen that it provides output signals with large errors. The present invention makes it easy to diagnose this by detecting large errors in input signals for concentration of nitrogen oxides NO x upstream from the catalyst. A similar example is that malfunctions in the urea dosage regulating system can be detected if large errors are detected in the input signal for the flow of dosed urea. Specialists will appreciate that other deviation parameters described above may also be used similarly for diagnosis of other malfunctions.

The present invention comprises also a system 100 for estimation of a deviation for at least one model variable of a catalyst model. The system 100 is adapted to basing the estimation on the catalyst model described above and on at least one measured sensor signal from at least one sensor 131 which is so situated that it comes into contact with exhaust gases downstream from a catalyst 110.

According to the present invention, the system 100 comprises a means adapted to comparing an actual signal with an estimated signal, such that the actual signal depends on the measured sensor signal and that the estimated signal depends on at least one estimation function and represents the catalyst model's match with the actual signal.

The system 100 further comprises a means adapted to using this comparison to determine at least one deviation parameter for the respective at least one estimation function, such that each of the one or more deviation parameters describes a relation between a value for a model variable and a corresponding actual value.

Specialists will appreciate that a method for estimation of deviation of at least one model variable of a catalyst model according to the present invention may also be implemented in a computer programme which, when executed in a computer, causes the computer to apply the method. The computer programme is contained in a computer-readable medium of a computer programme product, which medium takes the form of a suitable memory, e.g. ROM (read-only memory), PROM (programmable read-only memory), EPROM (erasable PROM), flash memory, EEPROM (electrically erasable PROM), a hard disc unit, etc. Figure 3 depicts schematically a control unit 160. The control unit 160 comprises a calculation unit 161 which may take the form of substantially any suitable type of processor or microcomputer, e.g. a circuit for digital signal processing (digital signal processor, DSP) or a circuit with a predetermined specific function (application specific integrated circuit, ASIC). The calculation unit 161 is connected to a memory unit 162 which is incorporated in the control unit 160 and which provides the calculation unit 161 with the regulating algorithm used, the catalyst model and, for example, the stored programme code and/or the stored data which the calculation unit 161 needs for it to be able to perform calculations. The calculation unit 161 is also adapted to storing partial or final results of calculations in the memory unit 162.

The control unit 160 is further provided with respective devices 163, 164, 165 for receiving input signals and sending output signals. These input and output signals may comprise waveforms, pulses or other attributes which the signal receiving devices 164, 165 can detect as information and which can be converted to signals processable by the calculation unit 161. The calculation unit 161 is then provided with these signals. The signal sending device 163 is adapted to converting signals received from the calculation unit 161 in order, e.g by modulating them, to create output signals which can be transmitted to other parts of the system.

Each of the connections to the respective devices for receiving input signals and sending output signals may take the form of one or more from among a cable, a data bus, e.g. a CAN (controller area network) bus, an MOST (media orientated systems transport) bus or some other bus configuration, or a wireless connection. The connections between the sensors 122,

131 and the control unit 160 and between the operating means 140 and the control unit 160 depicted in Figure 1 may also take the form of one or more of these cables, buses or wireless connections. Specialists will appreciate that the aforesaid computer may take the form of the calculation unit 161 and that the aforesaid memory may take the form of the memory unit 162.

Specialists will also appreciate that the above system can be modified according to the various embodiments of the method according to the invention. The present invention is not limited to its embodiments described above, but relates to and comprises all embodiments of the invention within the scope of protection of the attached independent claims.

Description of variables in the catalyst model

Variable List

Geometric area, tank k

Deff.i.k Effective diffusivity, substance i, tank k

D i Ordinary diffusivity, substance i, tank k

D K,i,k Knudsen diffusivity, substance i, tank k

Drefj Reference diffusivity, substance i

l≡A,j Activation energy, reaction j

F Molar flow, exhaust gases

M, Molar mass, substance i

N c Number of active seats

Nu Nusselt number

Pk Total pressure, tank k

Qck Power output, reaction heat of catalytic reations

Q h ,k Power output, reaction heat of homogeneous reations

R General gas constant

S Active seat

Sh Sherwood number

Reference temperature

~Tg,k Gas temperature, tank k

T s ,k Catalyst temperature, tank k

v k Gas volume in catalyst duct, tank k

cp.g Specific heat, gas

cp,s Specific heat, catalyst

ctot,k Total gas concentration, tank k

d Duct size

Pore diameter

f D Coefficient for porosity and pore convolution

k Boundary layer heat transfer coefficient, tank k

^c,i,k Boundary layer mass transfer coefficient, substance i , tank k kj,k Rate constant, reaction j, tank k

^OJ Pre-exponential factor of reaction j

ms,k Catalyst weight, tank k

^c,j,k,n Reaction rate, catalytic reaction j, tank k, layer n

rh,j,k Reaction rate, homogeneous reaction j, tank k

t Time

Yi .n Mole fraction, substance i, tank k, layer n

Wk,n Active material weight, tank k, layer n

^i. .n Mass transfer coefficient, substance i, tank k, layer n

AHj Reaction enthalpy, reaction j

Ax n Thickness, layer n

λ 9 Thermal conductivity of gas

List of indices in the catalyst model