EP1729001B1 - Estimation method using a non-linear adaptive filter of air-fuel mixture richness in a cylinder of a combustion engine - Google Patents

Description

The present invention relates to a method for estimating the fuel richness of each cylinder of an internal combustion engine injection, from a measurement of the wealth downstream of the collector and an adaptive nonlinear filter.

The knowledge of wealth, characterized by the ratio of the mass of fuel on the air mass, is important for all vehicles, whether they are petrol engines because it conditions a good combustion of the mixture when it is close of 1, or for vehicles with diesel engines for which the interest of the knowledge of the wealth is different since they work with poor mixture (wealth lower than 1). In particular, catalysts using a NOx trap lose their effectiveness over time. In order to return to optimum efficiency, the richness must be kept close to 1 for a few seconds, then return to normal operation at a lean mixture. Depollution by DeNOx catalysis therefore requires precise control of the cylinder-by-cylinder richness.

To do this, a probe, placed at the outlet of the turbine (turbocharged engine) and upstream of the NOx trap, gives a measure of the average richness by the exhaust process. This measurement, being very filtered and noisy, is used for the control of the masses injected into the cylinders during the phases of richness equal to 1, each cylinder then receiving the same mass of fuel.

In order to control in a more precise way, and especially individual, the injection of the masses of fuel in the cylinders, a reconstruction of the wealth in each cylinder is essential. Since the implantation of wealth probes at the outlet of each cylinder is not possible on a vehicle because of their cost price, the implementation of an estimator operating from the measurements of a single probe advantageously makes it possible to know separately the riches of each cylinder.

An engine control can thus, from the reconstructed wealth, adapt the fuel masses injected into each of the cylinders so that the wealth is balanced in all the cylinders.

We know the document FR-2834314 which describes the definition of a model, then its observation and its filtering thanks to a Kalman filter. This model contains no physical description of the mixture in the collector, and does not take into account very pulsating flow phenomena.

The estimation of the richness in the cylinders is only conditioned by the coefficients of a matrix, coefficients which must be identified offline thanks to an optimization algorithm. In addition, at each operating point (speed / load) corresponds a different setting of the matrix, so an identification of its parameters. This estimator therefore requires the establishment of heavy means of testing (with 5 wealth probes) acquisition, and is not robust in the case of a change of engine.

Another method to estimate the richness in the cylinders is described in the document US 5339415 .

The object of the present invention is to model the exhaust process more finely so as, on the one hand, to dispense with the identification step, and on the other hand to bring more robustness to the wealth estimation model. , and this for all operating points of the engine. The invention also makes it possible to perform a measurement every 6 ° of rotation of the crankshaft and thus to have a high frequency information of the measurement of richness, without falling into the measurement noise.

• on établit un modèle physique représentant en temps réel l'éjection des gaz dans chacun desdits cylindres et leur parcours dans ledit circuit d'échappement jusqu'audit capteur;
• on définit une estimation de ladite richesse (λ) mesurée par ledit capteur à partir d'au moins une variable dudit modèle ;
• on couple ledit modèle avec un estimateur non linéaire de type adaptatif dans lequel on prend en compte ladite estimation de la mesure de richesse mesurée ;
• on réalise une estimation en temps réel de la valeur de la richesse dans chacun des cylindres, à partir dudit estimateur non linéaire de type adaptatif.

Thus, the present invention relates to a method for estimating the fuel richness in each of the cylinders of an internal combustion engine comprising a gas exhaust system comprising at least cylinders connected to a cylinder. collector and a wealth measurement sensor (λ) downstream of said collector. The method is characterized in that it comprises the following steps:

• establishing a physical model representing in real time the gas ejection in each of said cylinders and their course in said exhaust circuit to said sensor;
• an estimate of said richness (λ) measured by said sensor is defined from at least one variable of said model;
• said model is coupled with an adaptive-type non-linear estimator in which said estimate of the measure of measured wealth is taken into account;
• a real-time estimate of the value of the richness in each of the cylinders is made from said adaptive-type nonlinear estimator.

It is also possible to evaluate a delay time due to the transit time of the gases and to the response time of the sensor, by performing a test perturbation in a given cylinder and measuring its effect on the sensor.

According to one embodiment, the physical model may comprise at least the following three types of variables: the total mass of gas in the exhaust manifold ( M _T ), the fresh air mass in the exhaust manifold ( M _air ) and the riches in each cylinder (λ _i ). This mode can then comprise at least the two following types of output data: the total mass of gas in the exhaust manifold ( M _T ) and the mass flow rates leaving said cylinders ( d _i ).

The measured richness (λ) can be estimated as a function of the total mass of gas in the exhaust manifold ( M _T ) and the fresh air mass in the exhaust manifold ( M _air ).

The estimation of the value of the richness in each of the cylinders may then comprise a real-time correction of the estimate of the total mass of gas in the exhaust manifold ( M _T ), the estimation of the mass of the fresh air in the exhaust manifold ( M _air ) and estimating the value of the richness in each of the cylinders (λ _i ).

Finally, the method can be applied to an engine control to adapt the fuel masses injected into each of the cylinders to adjust the richness in all the cylinders.

• la figure 1 présente schématiquement les éléments descriptifs du processus d'échappement ;
• les figures 2A et 2B illustrent les richesses de références $\left({\lambda }_i^{\mathit{ref}}\right)$
  
  en fonction du temps (T) et les résultats de l'estimateur selon l'invention (̂λ_i ) en fonction du temps (T), pour chacun des quatre cylindres ;
• la figure 3 illustre la structure de l'estimateur ;
• les figures 4A et 4B illustrent les richesses de références $\left({\lambda }_i^{\mathit{ref}}\right)$
  
  en fonction du temps (T) et les résultats de l'estimateur avec prise en compte du retard selon l'invention (̂λ_i ) en fonction du temps (T), pour chacun des quatre cylindres.

The present invention will be better understood and its advantages will appear more clearly on reading the following description of an embodiment, in no way limiting, illustrated by the appended figures, among which:

• the figure 1 schematically presents the descriptive elements of the escape process;
• the Figures 2A and 2B illustrate the wealth of references $\left({\lambda }_i^{\mathit{ref}}\right)$
  
  versus time (T) and the results of the estimator according to the invention (λ _i) in function of time (T) for each of four cylinders;
• the figure 3 illustrates the structure of the estimator;
• the Figures 4A and 4B illustrate the wealth of references $\left({\lambda }_i^{\mathit{ref}}\right)$
  
  versus time (T) and the results of the estimator taking into account the delay according to the invention (λ _i) in function of time (T) for each of four cylinders.

• gain sur le prix de revient si l'estimation est effectuée à partir d'une seule sonde de richesse en sortie turbine ;
• réduction des émissions polluantes ;
• amélioration de l'agrément de conduite (régularisation du couple délivré) ;
• réduction de la consommation de carburant
• diagnostic du système d'injection (détection de la dérive d'un injecteur ou de la défaillance du système d'injection).

The interest of an estimation of the richness in each of the cylinders individually is numerous compared to an estimate of the average richness of the set of cylinders:

• gain on the cost price if the estimate is made from a single turbine output wealth probe;
• reduction of polluting emissions;
• improvement of the driving pleasure (regularization of the delivered torque);
• reduced fuel consumption
• diagnosis of the injection system (detection of the drift of an injector or the failure of the injection system).

Description of the escape process:

• λ₁ à λ₄ représentent les richesses dans chacun des quatre cylindres ;
• SR représente la sonde de richesse ;
• CE correspond au collecteur d'échappement
• T correspond à la turbine du turbocompresseur ;
• DS1 à DS4 représentent les débits en sorties des cylindres.

The exhaust process includes the path of the gases between the exhaust valve to the free air at the outlet of the muffler. The engine of the present implementation as an example is a 4 cylinders of 2200 cm ³ . It is equipped with a turbocharger with variable geometry. The scheme of the figure 1 presents the descriptive elements of the escape process, in which:

• λ ₁ to λ ₄ represent the wealth in each of the four cylinders;
• SR represents the wealth probe;
• CE is the exhaust manifold
• T corresponds to the turbine of the turbocharger;
• DS1 to DS4 represent the output flows of the cylinders.

• passage à travers la soupape d'échappement. Cette dernière étant commandée par un arbre à came, la loi de levée est en forme de cloche. Les débits passeront d'une valeur élevée, lors de l'ouverture de la soupape, à une valeur plus faible lorsque les pressions cylindre et collecteur s'égaliseront, pour enfin ré-augmenter lorsque le piston commencera à remonter pour éjecter les gaz d'échappement.
• passage dans une courte tubulure reliant le collecteur à la sortie de la culasse.
• phase de mélange dans le collecteur d'échappement (CE) où les débits (DS1 à DS4) des quatre cylindres se rejoignent. C'est ici que se produit le mélange des bouffées, fonction du type de collecteur (symétrique ou asymétrique), de l'AOE (Avance Ouverture Echappement) et du RFE (Retard Fermeture Echappement), qui détermineront la proportion de recouvrements des débits.
• passage à travers la turbine qui fournit le couple nécessaire au compresseur, situé en amont de l'admission. Bien que son action sur les débits soit peu connue, on peut penser qu'elle va mélanger un peu plus encore les bouffées provenant des différents cylindres.
• mesure par la sonde de type UEGO.

The richness probe ( SR ) is located just after the turbine ( T ). The gases, after combustion in the cylinder, undergo the following actions:

• passage through the exhaust valve. The latter being controlled by a camshaft, the law of emergence is bell-shaped. The flow rates will increase from a high value, when opening the valve, to a lower value when the cylinder and manifold pressures equalize, and finally increase when the piston starts to rise to eject the gas exhaust.
• passage in a short pipe connecting the manifold to the output of the cylinder head.
• mixing phase in the exhaust manifold ( CE ) where the flows ( DS1 to DS4) of the four cylinders meet. This is where the mixing of puffs occurs, depending on the type of collector (symmetrical or asymmetric), the AOE (Avance Opening Exhaust) and the RFE (Exhaust Closure Delay), which will determine the proportion of flow recoveries.
• passage through the turbine which provides the torque necessary for the compressor, located upstream of the intake. Although his action on flows is little known, we can think that it will mix a little more puffs from different cylinders.
• measurement by the UEGO type probe.

The composition of the exhaust gas depends on the amount of fuel and air introduced into the combustion chamber, the fuel composition and the development of the combustion.

In practice, the richness probe measures the concentration of O ² inside a diffusion chamber, connected to the exhaust pipe by a diffusion barrier made of porous materials. This configuration may induce differences depending on the location of the chosen probe, in particular because of temperature variations and / or pressures in the vicinity of the richness probe.

This phenomenon of variation of richness depending on the pressure or the temperature has however been neglected, since one is interested in detecting disparities of richness between the cylinders, the average value being normally preserved by the estimator.

In the real-time physical model used by the estimator according to the invention, the measured wealth (λ) is connected to the mass of air (or to the air flow) around the probe and to the total mass ( or at the total rate). The model is based on a three-gas approach: air, fuel and flue gas. Thus, it is considered that at lean mixture, all of the gas remaining after combustion is a mixture of air and flue gas. For a rich mixture, the fuel is in excess, so there is unburned fuel and burnt gases after combustion, while all the air is gone. In reality, the combustion is never 100% complete, but for our estimator, the combustion will be considered complete.

A formulation linking the richness to the masses of the three species mentioned is defined. In the case of a lean mixture: the air is in excess, and there is no fuel remaining after combustion. Before combustion, it is assumed that the following masses are present in the cylinder, with _air , _air mass, M _carb , fuel mass and M _{gas B} , the mass of burnt gases: $$M_{\mathit{air}}=x;M_{\mathit{carb}}=\mathrm{there};M_{\mathit{gazB}}=0$$

Knowing that it takes 14.7 times more air than fuel to be stoichiometric, one can build this table indicating the masses of each species before and after combustion: Air mass Mass of fuel Mass of burnt gases Before combustion x there 0 After combustion x-14,7xy 0 y + 14,7xy

on obtient après calculs la formulation suivante, uniquement valable si le mélange est pauvre : $$\lambda =\frac{M_{\mathit{gaz}B}.\mathit{PCO}}{M_{\mathit{air}}.\left(1+\mathit{PCO}\right)+M_{\mathit{gaz}B}.\mathit{PCO}}$$

où PCO correspond au rapport $\raisebox{1ex}{$M_{\mathrm{air}}$}\!\left/ \!\raisebox{-1ex}{$M_{\mathrm{carb}}$}\right.$

lorsque le mélange est stoechiométrique. PCO est le pouvoir calorifique du carburant.The wealth λ representing the ratio $\raisebox{1ex}{$M_{\mathit{carb}}$}\!\left/ \!\raisebox{-1ex}{$M_{\mathit{air}}$}\right.,$

the following formulation is obtained after calculation, only valid if the mixture is poor: $$\lambda =\frac{M_{\mathit{gas}B}.\mathit{PCO}}{M_{\mathit{air}}.\left(1+\mathit{PCO}\right)+M_{\mathit{gas}B}.\mathit{PCO}}$$

where PCO is the report $\raisebox{1ex}{$M_{\mathrm{air}}$}\!\left/ \!\raisebox{-1ex}{$M_{\mathrm{carb}}$}\right.$

when the mixture is stoichiometric. PCO is the calorific value of the fuel.

For a rich mix, the formula is: $$\lambda =\frac{M_{\mathit{carb}}.\left(1+\mathit{PCO}\right)}{M_{\mathit{gas}B}}+1$$

However, these formulas are valid in the case where the mixture does not contain EGR, since the presence of flue gases on admission modifies the concentrations of the three exhaust gases.

In the present embodiment, only the lean mixture richness formula is used in the estimator, at the level of integration of richness in equation (7), neglecting a very small portion of the air ( <3%). However, the invention is not limited to this mode, in fact, the formula is continuous in the vicinity of a richness equal to 1, and its inversion does not pose a problem for rich mixtures.

In order to gain a better understanding of the way gases mix in the exhaust pipes, a diesel engine model was used under the AMESim software of IMAGINE (France). This model, which can not be reversed, will serve as a reference for validating the model according to the invention.

AMESim is a 0D modeling software, particularly well suited to thermal and hydraulic phenomena. It allows to model volumes, behaviors or restrictions.

• les tubulures d'échappement représentées par un volume et un tube ;
• le collecteur d'échappement avec échanges thermiques ;
• la turbine et la vanne de by-pass ;
• un volume à la confluence des débits turbine et vanne ;
• un tube entre la turbine et la sonde de mesure ;
• un volume et un tube pour la ligne d'échappement.

The exhaust model includes:

• the exhaust pipes represented by a volume and a tube;
• the exhaust manifold with heat exchange;
• the turbine and the bypass valve;
• a volume at the confluence of the turbine and valve flows;
• a tube between the turbine and the measuring probe;
• a volume and a tube for the exhaust line.

The basic tubing, restriction and volume modeling blocks are described in the AMESim "Thermal Pneumatic Library" user manual. Standard equations are used to calculate a flow through a restriction and energy and mass conservations. In addition, the model takes into account gas inertia, which is important for studying the dynamics of gas composition.

Since this model is 0D, the time dimension is not taken into account, and it is not possible to model a delay time with a physical approach. If an input variable is changed, the output is immediately changed. The transport time is neglected. This limitation is important when trying to work on acquisitions in real time.

According to the invention, a unique real-time physical model is defined for modeling the overall system, that is to say the entire path of the exhaust gases, from the cylinders to the downstream exhaust from the turbine, through the collector.

I- Definition of a real-time physical model

In the present embodiment, it is considered that the variation of the temperature is low on a motor cycle, and that its action is limited on the variations of flow rates. It is indeed the pressure variations that are essential in the process, since they are directly related to flow rates. We therefore impose a fixed temperature for each element: cylinders, collector and turbine. Heat exchanges are therefore not modeled either. This simplification hypothesis is not very important.

In a first approach, two gases are considered: fresh air and flue gases. The classical equations describe the evolution of the total mass of gases in volumes, and the mass of fresh air. The flue gas can then be deduced. This approach is valid in the case of a lean mixture operation, but similar equations can be written for the fuel and the flue gases, in the case of rich mixture.

A) Physical model of the exhaust manifold:

The exhaust manifold is modeled according to a volume in which there is conservation of the mass. It is assumed that the temperature is substantially constant, and determined from an abacus function of the load and the engine speed.

avec :

Ne

: Régime moteur

α :

Angle du vilebrequin

M_T

: Masse totale dans le collecteur d'échappement

d_i :

Débit massique sortant du cylindre i

d_T :

Débit total passant par la turbine

According to the invention, it has been chosen to relate the measured richness to the mass of air around the probe and to the total mass. Thus, the conservation of the total mass in the manifold expresses the fact that the mass of exhaust gas in the manifold is equal to the mass of exhaust gas entering the manifold (output flow of the cylinders) minus the mass outgoing collector. It is assumed that the composition of the flow rate in the turbine is the same as at the outlet of the collector. Thus the mass leaving the collector is equal to the flow rate passing through the turbine. We thus have the following formula for the total mass: $$\begin{array}{|c|}\hline {\mathrm{NOT}}_e\frac{{\mathit{dM}}_T}{\mathit{d\alpha }}=\underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)-d_T\left(M_T\right)\\ \hline\end{array}$$

with:

Born

: Engine speed

α :

Angle of the crankshaft

M _T

: Total mass in the exhaust manifold

d _i :

Mass flow coming out of cylinder i

d _T :

Total flow through the turbine

avec

Ne :

Régime moteur

α :

Angle du vilebrequin

M_air :

Masse d'air frais dans le collecteur d'échappement

λ_i :

Richesse dans chacun des cylindres

d_i :

Débit massique sortant du cylindre i

d_air :

Débit d'air passant par la turbine

Similarly for the preservation of the air mass, we have: $$\begin{array}{|c|}\hline {\mathrm{NOT}}_e\frac{d{M}_{\mathit{air}}}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-d_{\mathit{air}}\left(M_{\mathit{air}}\right)\\ \hline\end{array}$$

with

Do not :

Engine speed

α :

Angle of the crankshaft

M _air :

Fresh air mass in the exhaust manifold

λ _i :

Wealth in each of the cylinders

d _i :

Mass flow coming out of cylinder i

_air :

Air flow through the turbine

The physical models for determining cylinder output and flow through the turbine are now described.

Model to determine the output flow of the cylinders: gas ejection

• l'angle du vilebrequin (α);
• le débit aspiré par le cylindre d_asp (variable estimée par le contrôle moteur en amont) ;
• la valeur moyenne de richesse mesurée par la sonde λ̅ sur un cycle.

The output flow rate of the gases at the outlet of the cylinders can be modeled by a physical model describing the output flow of the exhaust valves. For this model, gas ejection by the valves, three variables are used:

• the angle of the crankshaft ( α );
• the flow sucked by the _asp cylinder (variable estimated by the engine control upstream);
• the mean value of richness measured by the probe λ̅ on a cycle.

• l'équilibre de pression cylindre/échappement qui se traduit par un pic de débit en fonction de l'angle du vilebrequin ;
• un débit qui se calque sur la section efficace de la soupape d'échappement qui se traduit par un second pic de débit d'amplitude plus faible.

The average outflow is known from the intake flow and the gasoline flow injected. The instantaneous value of the outgoing flow, for its part, is based on a template dependent on the sucked flow rate. This template is a physical model (a curve) based on an empirical law for estimating a mean flow rate for a cylinder as a function of the crankshaft angle from the engine speed, the crankshaft angle, the flow sucked by the cylinder and the average value of richness measured by the probe on a cycle. This physical law has the only constraint to respect the average outflow (area of the curve) and to provide a curve accounting for the two following phenomena:

• the cylinder / exhaust pressure equilibrium which results in a flow peak as a function of crankshaft angle;
• a flow which is traced on the effective section of the exhaust valve which results in a second peak of lower amplitude flow rate.

avec :

• d_i (α) : le débit de sortie des gaz à la sortie du cylindre i ;
• d̅(α) : le gabarit, c'est-à-dire une estimation du débit en sortie des cylindres ; $$-{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0=d_{\mathit{asp}}.\left(1+\frac{\stackrel{}{\bar{\lambda }}}{\mathit{PCO}}\right)$$
  
• α_i : l'angle de déphasage pour le cylindre i.

This template ( d̅ ) provides an output (curve) of the mass flow rate at the outlet of the exhaust valves d _i , that is to say a common estimate ( d̅ ) of the flow rate for all the cylinders. It is obtained in correlation with engine bench measurements. As a function of the suction flow rate and the average richness measured by the probe λ̅ , the template is then homothed and a phase shift is made for each cylinder as a function of the crankshaft angle, in order to deduce the output flow rate of the gases. at the exit of each cylinder: $$d_i\left(\alpha \right)=\stackrel{}{\tilde{d}}\left({\alpha }_i+\alpha \right).{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0$$

with:

• d _i ( α ): the output flow rate of the gases at the outlet of the cylinder i;
• d̅ ( α ): the template, that is to say an estimate of the output flow of the cylinders; $$-{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0=d_{\mathit{asp}}.\left(1+\frac{\stackrel{}{\tilde{\lambda }}}{\mathit{PCO}}\right)$$
  
• α _i : the phase shift angle for the cylinder i.

We can see schematically the phase shift of the curve of the template on the figure 1 ( DS1 to DS4 ) .

The physical models for determining the flow through the turbine are now described.

Model to determine the flow passing through the turbine: model of the turbine

The turbine is modeled according to a flow passing through a flow restriction. The flow rate in the turbine is generally given by mapping (abacus) as a function of the turbine speed and the upstream / downstream pressure ratio of the turbine.

• La masse totale de gaz d'échappement (M_T ) ;
• La masse d'air (M_air ) ;
• Le régime moteur (N_e ) ;
• Le régime de la turbine (du turbocompresseur).

The flow through the turbine d _T is a function of the total mass ( M _T ) in the exhaust manifold, the temperature in the exhaust manifold, the turbocharger speed and the geometry of the turbocharger. The input data of this model are:

• The total mass of exhaust gas ( M _T );
• The air mass ( M _air );
• The engine speed ( N _e );
• The speed of the turbine (turbocharger).

This flow rate can be estimated from a concave function of the total mass M _T. This function is noted p. The flow rate in the turbine is then written: d _T ( M _T ) = M _T .p ( M _T ).

et du régime de la turbine (du turbocompresseur). La formule utilisée par cette cartographie est : $$p\left(M_T\right)=f\left(\mathit{régime\; turbine}\right).\sqrt{\frac{2.g}{g-1}}.\left({\left(\frac{M_T}{M_0}\right)}^{\frac{-2}{g}}-{\left(\frac{M_T}{M_0}\right)}^{\frac{-\left(g+1\right)}{g}}\right)$$

où :

• f est une fonction polynomiale
• g est une constante

The function p is a function of the root type which is expressed as a function of turbine speed on the one hand and on the other hand as a function of the ratio between the total mass in the exhaust manifold ( M _T ) and the mass in the collector under atmospheric conditions ( M ₀ ). Thus the map gives p ( M _T ) according to the ratio $\frac{{\mathrm{<figure-callout\; id="0"\; label="M\; T\; M"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">M\; </figure-callout>}}_T}{M_{}}$

and turbine (turbocharger) speed. The formula used by this mapping is: $$p\left(M_T\right)=f\left(\mathit{turbine\; scheme}\right).\sqrt{\frac{2.\mathrm{boy\; Wut}}{\mathrm{boy\; Wut}-1}}.\left({\left(\frac{M_T}{M_0}\right)}^{\frac{-2}{\mathrm{boy\; Wut}}}-{\left(\frac{M_T}{M_0}\right)}^{\frac{-\left(\mathrm{boy\; Wut}+1\right)}{\mathrm{boy\; Wut}}}\right)$$

or :

• f is a polynomial function
• g is a constant

The parameters of the function f are optimized by correlation with the mapping of the turbine.

In addition, the air composition is assumed to be the same as in the exhaust manifold. The flow of air passing through the turbine is therefore: $$d_{\mathit{air}}\left(M_{\mathit{air}}\right)=\frac{M_{\mathit{air}}}{M_T}{d}_T\left(M_T\right)=M_{\mathit{air}}.p\left(M_T\right)$$

Thus, using the physical models of gas ejection and the turbine, equations (1) and (2) are written: $$\{\begin{array}{l}{\mathrm{NOT}}_e\frac{d{M}_T}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-M_T.p\left(M_T\right)\\ {\mathrm{NOT}}_e\frac{d{M}_{\mathit{air}}}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-M_{\mathit{air}}.p\left(M_T\right)\end{array}$$

Ne :

Régime moteur

α :

Angle du vilebrequin

d_i :

Débit massique sortant du cylindre i

d_T :

Débit total passant par la turbine

d_air :

Débit d'air passant par la turbine

λ _i :

Richesse dans chacun des cylindres

Et les inconnues du système sont :

M_T :

Masse totale dans le collecteur d'échappement

M_air :

Masse d'air frais dans le collecteur d'échappement

This system of equation (3) constitutes the physical model of the exhaust manifold.
The input data of this model are:

Do not :

Engine speed

α :

Angle of the crankshaft

d _i :

Mass flow coming out of cylinder i

d _T :

Total flow through the turbine

_air :

Air flow through the turbine

λ _i :

Wealth in each of the cylinders

And the unknowns of the system are:

M _T :

Total mass in the exhaust manifold

M _air :

Fresh air mass in the exhaust manifold

The first equation contains an unknown: M _T. The second contains two: M _air and λ _i . This leads to the additional assumptions described below.

B) Hypothesis on the wealth outputs cylinder:

En fait, le calcul s'effectuant en temps réel, l'on estime des constantes λ_i. To complete the real-time physical model (RTM) of the exhaust manifold, it is assumed that the cylindrical outputs are constant on an operating point, so we have: $${\mathrm{NOT}}_e.\frac{d{\lambda }_i}{d\alpha }=0$$

In fact, the computation taking place in real time, one estimates constant λ _i .

C) Expression of the real-time physical model

Les inconnues du modèle physique sont au final M_T, M_air et les λ_i.
Les données de sorties du modèle physique sont M_T et d_i. Finally, the RTM real-time physical model can be in the following matrix form: $$X=\left[\begin{array}{c}{M}_T\\ M_{\mathit{air}}\\ {\lambda }_1\\ {\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_2\\ {\lambda }_3\\ {\mathrm{<figure-callout\; id="4"\; label="\lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_4\end{array}\right]{\mathrm{NOT}}_e.\frac{dX}{d\alpha }=\left[\begin{array}{c}{\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-M_T.p\left(M_T\right)\\ {\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-M_{\mathit{air}}.\mathrm{<figure-callout\; id="0"\; label="p\; M\; T"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">p\; </figure-callout>}\left(M_T\right)\left({}_{}\right)\\ 0\\ 0\\ 0\\ 0\end{array}\right]$$

The unknowns of the physical model are ultimately M _T , M _air and λ _i .
The output data of the physical model is M _T and d _i .

D) Exhaust delay time:

The delay times due to the gas transport in the pipes and the different volumes, as well as the "dead" time of the measuring probe, are not taken into account in the physical model described above (system of equations 5). However, model was built linearly with respect to these delays because we neglect the transport in the pipes. Also, the delays can be compiled in a single delay time for the entire escape process, and the physical model can be reversed as is, the influence of the delay delay can be considered later, as explained below. .

II- Wealth estimator:

The physical model (5) described above that the wealth downstream of the turbine (which is considered identical to the richness in the collector) is expressed as a function of the composition of the gas flow at the inlet of the collector exhaust.

• Richesse mesurée par la sonde: λ

The measured data are:

• Wealth measured by the probe: λ

• Régime moteur : Ne
• Angle du vilebrequin : α
• Régime de la turbine (du turbocompresseur)
• Débit aspiré par le cylindre

The other known data of the system are:

• Engine Speed: Ne
• Angle of the crankshaft: α
• Turbocharger (Turbocharger) Regime
• Flow sucked by the cylinder

• Débit massique sortant du cylindre i : d_i
• Débit total passant par la turbine : d_T
• Débit d'air passant par la turbine : d_air
• Masse totale dans le collecteur d'échappement : M_T

The modeled data of the system are:

• Mass flow rate out of cylinder i : d _i
• Total flow through the turbine: d _T
• Air flow through the turbine: _air
• Total mass in the exhaust manifold: M _T

• Richesses dans chacun des quatre cylindres : λ_i
• Masse d'air frais dans le collecteur d'échappement : M_air

The unknowns are:

• Riches in each of the four cylinders: λ _i
• Fresh air mass in the exhaust manifold: M _air

The physical model (5) is non-linear, and it is impossible to solve such a system in real time. It is therefore necessary to use an estimator, rather than seeking to directly calculate the unknowns of the system. The choice of the estimator according to the invention is based on the fact that the structure of the system is linear as a function of the wealth in the cylinders λ _i (the air mass variation is linear as a function of λ _i ). In this context, a particularly suitable technique is to use an adaptive filter. Thus, to estimate the unknowns from the physical model RTM, the method according to the invention proposes to construct an estimator based on an adaptive filter. This estimator ultimately allows an estimation of the cylinder to cylinder richness from the measurement of wealth by the sensor located behind the turbine.

• le filtrage, c'est-à-dire l'extraction de l'information utile au temps t à partir des données bruitées mesurées jusqu'au temps t inclus ;
• le lissage, qui utilisera aussi les données postérieures au temps t ;
• la prédiction, qui ne se sert que des données jusqu'au temps t-τ pour déduire l'information qui nous intéresse au temps t.

In general, the adaptive filters are systems applied to noisy data in order to obtain useful information at a certain instant t, these systems being implemented in three configurations:

• the filtering, that is to say the extraction of the useful information at time t from the noisy data measured up to the time t included;
• smoothing, which will also use the data after time t;
• prediction, which only uses data up to time t - τ to derive the information of interest at time t.

M_T :

Masse totale dans le collecteur d'échappement

M_air :

Masse d'air frais dans le collecteur d'échappement

λ_i :

Richesse dans chacun des cylindres

Les paramètres d'entrée, mesurés ou modélisés, de l'estimateur sont donc : $$Y=\left[\begin{array}{c}{y}_1\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0002.png"\; state="\{\{state\}\}">y</figure-callout>}}_2\end{array}\right]=\left[\begin{array}{c}{M}_T\\ \lambda \end{array}\right]$$

λ est mesuré par la sonde, et M_T est estimé à partir du modèle RTM (5).In our case, the goal is to reconstruct, from the two elements considered as measures y ₁ = M _T and y ₂ = λ , the following data:

M _T :

Total mass in the exhaust manifold

M _air :

Fresh air mass in the exhaust manifold

λ _i :

Wealth in each of the cylinders

The input parameters, measured or modeled, of the estimator are: $$Y=\left[\begin{array}{c}{\mathrm{there}}_1\\ {\mathrm{there}}_2\end{array}\right]=\left[\begin{array}{c}{M}_T\\ \lambda \end{array}\right]$$

λ is measured by the probe, and M _T is estimated from the RTM model (5).

M̂_T :

Estimateur de la masse totale dans le collecteur d'échappement

M̂_air :

Estimateur de la masse d'air frais dans le collecteur d'échappement

λ̂_i :

Estimateur de la richesse dans chacun des cylindres

l'estimateur s'écrit de la façon suivante : $$\{\begin{array}{l}{N}_e\frac{d{\widehat{M}}_T}{d\alpha }={\displaystyle \sum _{i=1}^{n_{\mathit{cyl}}}{d}_i\left(\alpha \right)}-M_T.p\left(M_T\right)-C_{M_T}\\ N_e\frac{d{\widehat{M}}_{\mathit{air}}}{d\alpha }={\displaystyle \sum _{i=1}^{n_{\mathit{cyl}}}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-M_{\mathit{air}}.p\left(M_T\right)-C_{M_{\mathit{air}}}\\ N_e\frac{d{\widehat{\lambda }}_i}{d\alpha }=-C_{{\lambda }_i}\end{array}$$

En d'autres termes, il s'agît du modèle RTM (5) dans lequel on applique un terme correctif pour chaque paramètre à estimer : C_MT, C_Mair, C_λi. By asking :

M _T :

Estimator of the total mass in the exhaust manifold

M _air :

Estimator of the fresh air mass in the exhaust manifold

λ _i :

Estimator of wealth in each of the cylinders

the estimator is written as follows: $$\{\begin{array}{l}{\mathrm{NOT}}_e\frac{d{\widehat{M}}_T}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-M_T.p\left(M_T\right)-{\mathrm{VS}}_{M_T}\\ {\mathrm{NOT}}_e\frac{d{\widehat{M}}_{\mathit{air}}}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-M_{\mathit{air}}.p\left(M_T\right)-{\mathrm{VS}}_{M_{\mathit{air}}}\\ {\mathrm{NOT}}_e\frac{d{\widehat{\lambda }}_i}{d\alpha }=-{\mathrm{VS}}_{{\lambda }_i}\end{array}$$

In other words, it is the RTM model (5) in which a correction term is applied for each parameter to be estimated: C _MT , C _Mair , C _λi .

En appliquant le même principe pour les corrections de M_T et M_air, on obtient : $$\{\begin{array}{l}{C}_{M_T}=L_1\left({\widehat{M}}_T-M_T\right)\\ C_{M_{\mathit{air}}}=L_2\left({\widehat{M}}_{\mathit{air}}-M_{\mathit{air}}\right)\\ C_{{\lambda }_i}=L_{\lambda }\left(d_i\left(\alpha \right).{\widehat{M}}_{\mathit{air}}-d_i\left(\alpha \right).M_{\mathit{air}}\right)\end{array}$$

où L ₁, L ₂, L_λ sont des paramètres de réglages, permettant de contrôler la vitesse de convergence de la solution aux trois inconnues. Ce sont des paramètres réels strictement positifs. Ces paramètres sont réglés manuellement afin d'obtenir un bon compromis entre la vitesse de convergence et la faible sensibilité au bruit de mesure.
Enfin, en utilisant l'équation de la richesse précédemment décrite, il est possible d'estimer la richesse mesurée à partir de M_T et M_air : $$\lambda =\frac{M_{\mathit{gaz}B}.\mathit{PCO}}{M_{\mathit{air}}.\left(1+\mathit{PCO}\right)+M_{\mathit{gaz}B}.\mathit{PCO}}=1-\frac{M_{\mathit{air}}}{M_T}$$

On en déduit : M_air = (1-λ)M_T
Et en utilisant les notations y ₁ =M_T et y₂ = λ, l'estimateur du modèle physique RTM, basé sur le filtre adaptatif et sur l'estimation de la richesse à partir de M_T et M_air, s'écrit alors : $$\{\begin{array}{l}{N}_e\frac{d{\widehat{M}}_T}{d\alpha }={\displaystyle \sum _{i=1}^{n_{\mathit{cyl}}}{d}_i\left(\alpha \right)}-{\delta }_T{y}_{1}p\left({\delta }_T{y}_1\right)-L_1\left({\widehat{M}}_T-{\delta }_T{y}_1\right)\\ N_e\frac{d{\widehat{M}}_{\mathit{air}}}{d\alpha }={\displaystyle \sum _{i=1}^{n_{\mathit{cyl}}}\left(1-{\lambda }_i\right)d_i\left(\alpha \right)}-\left(1-y_2\right){\delta }_T{y}_{1}p\left({\delta }_T{y}_1\right)-L_2\left({\widehat{M}}_{\mathit{air}}-\left(1-y_2\right){\delta }_T{y}_1\right)\\ N_e\frac{d{\widehat{\lambda }}_i}{d\alpha }=-L_{\lambda }{d}_i\left(\alpha \right)\left({\widehat{M}}_{\mathit{air}}-\left(1-y_2\right){\delta }_T{y}_1\right)\end{array}$$

avec δ _T = 1The principle of the estimator is to converge the physical model (5), and consequently the riches λ _i towards reality. Indeed, the model (5) outputs M _T and M _Air , and we also have input parameters Y. The estimator therefore compares the output values of the RTM model with the input values, then make the appropriate corrections. For example, the wealth λ _i must adapt according to the error on M _T and λ : if the error between the input values, M _T and λ , and the corresponding estimated values, M _T and λ , is negative, then the estimated values must be increased and vice versa. This is why we write: $${\mathrm{NOT}}_e\frac{d{\widehat{\lambda }}_i}{d\alpha }=-{\mathrm{The}}_{\lambda }\left(d_i\left(\alpha \right).{\widehat{M}}_{\mathit{air}}-d_i\left(\alpha \right).M_{\mathit{air}}\right)$$

Applying the same principle for the corrections of M _T and M _air , we obtain: $$\{\begin{array}{l}{\mathrm{VS}}_{M_T}={\mathrm{The}}_1\left({\widehat{M}}_T-M_T\right)\\ {\mathrm{VS}}_{M_{\mathit{air}}}={\mathrm{The}}_2\left({\widehat{M}}_{\mathit{air}}-M_{\mathit{air}}\right)\\ {\mathrm{VS}}_{{\lambda }_i}={\mathrm{The}}_{\lambda }\left(d_i\left(\alpha \right).{\widehat{M}}_{\mathit{air}}-d_i\left(\alpha \right).M_{\mathit{air}}\right)\end{array}$$

where L ₁ , L ₂ , L _λ are adjustment parameters, making it possible to control the speed of convergence of the solution to the three unknowns. These are strictly positive real parameters. These parameters are set manually to obtain a good compromise between the speed of convergence and the low sensitivity to measurement noise.
Finally, using the previously described wealth equation, it is possible to estimate the wealth measured from M _T and M _air : $$\lambda =\frac{M_{\mathit{gas}B}.\mathit{PCO}}{M_{\mathit{air}}.\left(1+\mathit{PCO}\right)+M_{\mathit{gas}B}.\mathit{PCO}}=1-\frac{M_{\mathit{air}}}{M_T}$$

We deduce: M _air = (1 -λ ) M _T
And using the notations y ₁ = M _T and y ₂ = λ , the physical model RTM estimator, based on the adaptive filter and the estimation of the richness from M _T and M _air , is written : $$\{\begin{array}{l}{\mathrm{NOT}}_e\frac{d{\widehat{M}}_T}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-{\delta }_T{\mathrm{there}}_{1}p\left({\delta }_T{\mathrm{there}}_1\right)-{\mathrm{The}}_1\left({\widehat{M}}_T-{\delta }_T{\mathrm{there}}_1\right)\\ {\mathrm{NOT}}_e\frac{d{\widehat{M}}_{\mathit{air}}}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathit{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right)d_i\left(\alpha \right)}-\left(1-{\mathrm{there}}_2\right){\delta }_T{\mathrm{there}}_{1}p\left({\delta }_T{\mathrm{there}}_1\right)-{\mathrm{The}}_2\left({\widehat{M}}_{\mathit{air}}-\left(1-{\mathrm{there}}_2\right){\delta }_T{\mathrm{there}}_1\right)\\ {\mathrm{NOT}}_e\frac{d{\widehat{\lambda }}_i}{d\alpha }=-{\mathrm{The}}_{\lambda }{d}_i\left(\alpha \right)\left({\widehat{M}}_{\mathit{air}}-\left(1-{\mathrm{there}}_2\right){\delta }_T{\mathrm{there}}_1\right)\end{array}$$

with δ _T = 1

The estimator thus constructed makes it possible to correct in real time M _T , M _air and λ , from a first value of M _T provided by the RTM model and from the measurement of richness made by the probe.

The system (8) is numerically solved in real time, the calculator using an explicit Euler discretization, well known to those skilled in the art.

Results in simulation: test of the estimator (8)

From the known individual wealth, one estimates by reference modelization AMESim a richness on the level of the probe ( λ ). This wealth value (λ) is used at the input of the estimator. The dynamics of the probe has not been taken into account. Injection imbalances are applied and the cylinder-to-cylinder estimation of the richness ( λ _i ) is observed from the wealth measurement behind the turbine ( λ ).

données par AmeSim en fonction du temps (T) et en haut les résultats de l'estimateur (̂λ_i ) en fonction du temps (T). Les quatre courbes correspondent à chacun des quatre cylindres. La performance de l'estimateur basé sur le filtre adaptatif est très bonne. On note cependant une légère différence de phase, due à l'inertie du gaz qui n'est pas pris en compte dans le présent modèle. On se propose donc de compléter le modèle et l'estimateur par un estimateur du temps de retard à l'échappement.For the simulation, the 4 cylinders are successively unbalanced by introducing 80 μs of injection into the cylinder, and the cylinder 1 and 4 are unbalanced in the same way. The Figures 2A and 2B show below the wealth of references $\left({\lambda }_i^{\mathit{ref}}\right)$

AMESIM data by a function of time (T) and above the results of the estimator (λ _i) in function of time (T). The four curves correspond to each of the four cylinders. The performance of the estimator based on the adaptive filter is very good. However, there is a slight difference in phase, due to the inertia of the gas which is not taken into account in the present model. It is therefore proposed to complete the model and the estimator by an estimator of the exhaust delay time.

Exhaust delay time estimator:

The estimator implemented as described above, does not allow the estimation method to take into account the delay time between the cylinder exhaust and the signal acquired by the probe. In reality, the delay time comes from several sources: transport time in the pipes and through the volumes, dead time of the measuring probe.

• N_e et α sont les données d'entrées du modèle RTM décrit par les équations (5) ;
• MMBO est le Modèle de Masse Boucle Ouverte (modèle RTM) ;
• D est le retard appliqué aux variables de sorties du modèle RTM (MMBO) ; ce retard est issu de l'équation (9) ;
• SR est la sonde de mesure de la richesse en aval de la turbine utilisée dans l'estimateur via l'équation (7) ;
• ERFA est l'Estimateur de Richesse basé sur un Filtre Adaptatif et décrit par l'équation (8) ;
• λ _i est la richesse du cylindre i estimée par l'ERFA.

By applying a delay time D to the input of the estimator on the variables coming from the model, we can synchronize the estimator with the measures of richness. The structure of the late estimator is illustrated on the figure 3 , in which :

• N _e and α are the input data of the RTM model described by equations (5);
• MMBO is the Open Loop Mass Model (RTM model);
• D is the delay applied to the output variables of the RTM model ( MMBO ); this delay comes from equation (9);
• SR is the measurement of the wealth downstream of the turbine used in the estimator via equation (7);
• ERFA is the Adaptive Filter-based Wealth Estimator and described by Equation (8);
• λ _i is the richness of the cylinder i estimated by the ERFA.

avec :

• ${\mathrm{\Lambda }}_k=\left[\begin{array}{c}{\widehat{\lambda }}_1\\ {\widehat{\lambda }}_2\\ {\widehat{\lambda }}_3\\ {\widehat{\lambda }}_4\end{array}\right]$
  
  : composition au pas k
• ${\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0=\left[\begin{array}{c}{\lambda }_1^{\mathit{<figure-callout\; id="2"\; label="ref\; \lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">ref</figure-callout>}}& \\ {\lambda }_{}^{}{}_2^{\mathit{ref}}\\ {\lambda }_3^{\mathit{<figure-callout\; id="4"\; label="ref\; \lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">ref</figure-callout>}}& \\ {\lambda }_{}^{}{}_4^{\mathit{ref}}\end{array}\right]$
  
  : composition de référence

The delay time depends on the operating conditions: motor speed, load, exhaust manifold pressure, etc. Since the delay is difficult to model, an identification method has been developed to calculate in real time the delay between the estimator and the measurements without any additional instrumentation. The principle consists of applying a small step in the vicinity of the injection point of the cylinder 1, and calculating the estimated variations of richness for each of the cylinders. Then, an identification criterion J _k is constructed so as to penalize the variations of the cylinders 2, 3, and 4. $$\{\begin{array}{l}\beta =\left[0,1,-1,2\right]\\ J_k=\beta *\left({\mathrm{\Lambda }}_k-{\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0\right)\end{array}$$

with:

• ${\mathrm{\Lambda }}_k=\left[\begin{array}{c}{\widehat{\lambda }}_1\\ {\widehat{\lambda }}_2\\ {\widehat{\lambda }}_3\\ {\widehat{\lambda }}_4\end{array}\right]$
  
  : composition in step k
• ${\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0=\left[\begin{array}{c}{\lambda }_1^{\mathit{<figure-callout\; id="2"\; label="ref\; \lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">ref\; </figure-callout>}}& \\ {\lambda }_{}^{}{}_2^{\mathit{ref}}\\ {\lambda }_3^{\mathit{<figure-callout\; id="4"\; label="ref\; \lambda "\; filenames="imgf0002.png"\; state="\{\{state\}\}">ref\; </figure-callout>}}& \\ {\lambda }_{}^{}{}_4^{\mathit{ref}}\end{array}\right]$
  
  : reference composition

The penalty is given by β . If there is a positive variation in the estimated wealth value for cylinder 2, then the delay time between the estimator and the measurements is positive. If there is a variation on cylinder 3, the delay is negative and the penalty is negative. A variation of the cylinder 4 can be considered as a consequence of a positive or negative delay. The delay D applied to the output variables of the RTM model, is an additive delay, it is computed by least squares by minimizing J _k .

The criterion J _k is controlled to zero by a PI (Proportional Integral) controller on the delay of the estimator. When the controller is stabilized, the variation of the estimated richness is maximum on the cylinder 1, and minimum on the cylinder 4. The estimator is then in phase with the measurements.

Results:

en fonction du temps (T) et en bas les résultats de l'estimateur (̂λ_i ) en fonction du temps (T). Les quatre courbes correspondent à chacun des quatre cylindres.The Figures 4A and 4B illustrate the cylinder-to-cylinder richness estimate by the estimator previously described at 1500rpm average load. These figures show up the wealth of references $\left({\lambda }_i^{\mathit{ref}}\right)$

versus time (T) and below the results of the estimator (λ _i) in function of time (T). The four curves correspond to each of the four cylinders.

The present invention relates to an estimation method comprising the construction of an estimator, making it possible, from the measurement of the richness of the probe (λ) and the total mass of gas information inside the collector ( M _T ), to estimate the wealth at the output of the four cylinders (λ _i ). The estimator thus produced is efficient, and above all does not require any additional adjustment in the case of change of the operating point. No identification phase is necessary, only a measurement and model noise adjustment must be made once and only once.

To make the estimation according to the invention more robust, whatever the operating conditions, a delay time controller is put in parallel with the estimator, making it possible to reset the delay time following a step of injection time on a cylinder. This allows optimal calibration of the estimator, for example before a rich phase equal to 1.

The invention also makes it possible to perform a measurement every 6 ° of rotation of the crankshaft and thus to have a high frequency information of the measurement of richness, without falling into the measurement noise. In addition, the high frequency representation makes it possible to take into account the pulsating effect of the system. The modeled system is periodic and makes it possible to obtain an estimator with a better dynamics: one anticipates the pulsation of the escapement.

Moreover, the invention makes it possible to reduce the calculation time by a factor of about 80 compared to the previous methods.

Claims (7)

1. A method for estimating the fuel richness in each of the cylinders of an internal combustion engine comprising a gas exhaust circuit comprising at least cylinders connected to a collector and a sensor for measuring the richness (λ) downstream of said collector, characterised in that it includes the following steps:

   - establishing a physical model in real time of the course of the gases in said exhaust circuit up to said sensor comprising:

   - a physical model of ejection of the gases into each of said cylinders;

   - a physical model of the exhaust collector;

   - a physical model of the flow rate passing through a turbine;

   - a delay time model of the exhaust up to the sensor;

   - defining an estimation of said richness (λ) measured by said sensor from at least one variable of said model;

   - coupling said model to a non-linear adaptive-type estimator wherein said estimation of the measure of the measured richness is taken into consideration;

   - performing an estimation in real time of the value of the richness in each of the cylinders from said non-linear adaptive-type estimator.
2. The method according to Claim 1, wherein a delay time due to the transit time of the gases and the response time of the sensor is evaluated by performing a test disruption in a determined cylinder and measuring its effect at the sensor:
3. The method according to one of the preceding claims, wherein said physical model includes at least the three following types of variables: the total mass of gas in the exhaust collector (M_T ), the mass of fresh air in the exhaust collector (M_air ) and the richness in each of the cylinders (λ _i ).
4. The method according to one of the preceding claims, wherein said physical model includes at least the two following types of output data: the total mass of gas in the exhaust collector (M_T ), and mass flow rates exiting said cylinders (d_i ).
5. The method according to one of the preceding claims, wherein said measured richness (λ) is estimated as a function of the total mass of gas in the exhaust collector (M_T ) and the mass of fresh air in the exhaust collector (M_air ).
6. The method according to one of the preceding claims, wherein said estimation of the value of the richness in each of the cylinders includes a correction in real time of the estimation of the total mass of gas in the exhaust collector (M_T ), of the estimation of the mass of fresh air in the exhaust collector (M_air ) and of the estimation of the value of the richness in each of the cylinders (λ _i ).
7. Application of the method according to one of the preceding claims to a motor control to adapt the masses of fuel injected into each of the cylinders so as to adjust the richness in all of the cylinders.

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