EP1729000A1 - Method for estimating the air/fuel ratio in a cylinder of an internal combustion engine using an extended Kalman filter - Google Patents

Abstract

The method for estimating the richness of the fuel mixture in the cylinders of an i.c. engine with a sensor (SR) located after its exhaust manifold (CE) consists of defining an estimate of the richness measured by the sensor, modelling the transfer function of the sensor, and establishing a physical model in real time of the gases ejected from the cylinders. The model is connected to an extended Kalman-type non-linear estimator, which is used to estimate a real-time value for the fuel mixture richness in each of the cylinders.

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 richness downstream of the collector and an extended Kalman 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 indispensable. 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.

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 définit une estimation de ladite richesse (λ) mesurée par ledit capteur à partir d'au moins une variable dudit modèle ;
• on réalise une modélisation de la fonction de transfert dudit capteur dans lequel on prend en compte ladite estimation de la mesure de richesse mesurée ;
• 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 dans lequel on prend en compte ladite modélisation de ladite fonction de transfert ;
• on couple ledit modèle avec un estimateur non linéaire de type Kalman étendu ;
• 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 Kalman étendu.

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 circuit comprising at least cylinders connected to a collector and a sensor for measuring the wealth. (λ) downstream of said manifold. The method is characterized in that it comprises the following steps:

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

Depending on the method, one can model the transfer function from a first-order filter.

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 can comprise at least the following four variables: the total mass of gas in the exhaust manifold ( M _T ), the fresh air mass in the exhaust manifold (M _air ) the wealth measured by said sensor (λ) and the wealth in each of the cylinders ( λ _i ). This mode can then comprise at least the two following output data: the total mass of gas in the exhaust manifold ( M _T ) and mass flow rates out of said cylinders (d;).

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 ;
• la figure 2 illustre les richesses de références $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  en fonction du temps (T) et les résultats de l'estimateur selon l'invention (λ̂ _i ) en fonction du temps (T), pour chacun des quatre cylindres ;
• la figure 3 illustre la structure de l'estimateur ;
• les figures 4A à 4C illustrent les richesses de références $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  en fonction du temps (T) et les résultats de l'estimateur avec prise en compte du retard selon l'invention (λ _i ) sur un premier point de fonctionnement 2000tr/min forte charge (9 bar), en fonction du temps (T) et pour chacun des quatre cylindres.
• les figures 4D à 4F illustrent les richesses de références $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  en fonction du temps (T) et les résultats de l'estimateur avec prise en compte du retard selon l'invention (λ _i ) sur un second point de fonctionnement 2500tr/min faible charge (3 bar), en fonction du temps (T) et 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:

• Figure 1 schematically shows the descriptive elements of the exhaust process;
• Figure 2 illustrates the wealth of references $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  as a function of time (T) and the results of the estimator according to the invention (λ _i ) as a function of time (T), for each of the four cylinders;
• Figure 3 illustrates the structure of the estimator;
• FIGS. 4A to 4C illustrate the wealth of references $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  as a function of time (T) and the results of the estimator taking into account the delay according to the invention (λ _i ) on a first operating point 2000tr / min high load (9 bar), as a function of time (T ) and for each of the four cylinders.
• FIGS. 4D to 4F illustrate the wealth of references $\left({\lambda }_i^{\mathrm{ref}}\right)$
  
  as a function of time (T) and the results of the estimator taking into account the delay according to the invention (λ _i ) on a second operating point 2500tr / min low load (3 bar), as a function of time (T ) and for each of the 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:

• λ ₁ à λ ₄ 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 diagram in Figure 1 presents the descriptive elements of the exhaust 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 réaugmenter 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. 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 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 its action on the 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, the totality of the gas remaining after combustion is a mixture of air and gas burned. 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 M _air, the air mass M _carb, the fuel mass M and _gazB, the mass of burnt gases: $$M_{\mathrm{air}}=x;M_{\mathrm{carb}}=\mathrm{there};M_{\mathrm{gas}B}=0$$

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

où PCO correspond au rapport M _air /M _carb lorsque le mélange est stoechiométrique. PCO est le pouvoir calorifique du carburant.The richness λ representing the ratio M _carb / M _air , we obtain after calculations the following formulation, only valid if the mixture is poor: $$\lambda =\frac{M_{\mathrm{gas}B}.\mathrm{PCO}}{M_{\mathrm{air}}.\left(1+\mathrm{PCO}\right)+M_{\mathrm{gas}B}.\mathrm{PCO}}$$

where PCO corresponds to the ratio M _air / M _carb when the mixture is stoichiometric. PCO is the calorific value of the fuel.

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

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 :

N _e

: 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: $$\begin{array}{||}\hline {\mathrm{NOT}}_e\frac{d{M}_T}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathrm{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-d_T\left(M_T\right)\\ \hline\end{array}$$

with:

N _e

: Engine speed

α

: Angle of the crankshaft

M _T

: Total mass in the exhaust manifold

d _i

: Mass flow coming out of the cylinder i

d _T

: Total flow through the turbine

avec

N _e

: 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: $$\begin{array}{||}\hline {\mathrm{NOT}}_e\frac{d{M}_{\mathrm{air}}}{d\alpha }={\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathrm{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-d_{\mathrm{air}}\left(M_{\mathrm{air}}\right)\\ \hline\end{array}$$

with

N _e

: 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

of _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.

Le débit sortant moyen est connu à partir du débit aspiré et du débit d'essence injectée. La valeur instantanée du débit sortant, quant à elle, est basée sur un gabarit dépendant du débit aspiré. Ce gabarit est un modèle physique (une courbe) reposant sur une loi empirique permettant d'estimer un débit moyen pour un cylindre en fonction de l'angle de vilebrequin à partir du régime moteur, de l'angle du vilebrequin, du débit aspiré par le cylindre et de la valeur moyenne de richesse mesurée par la sonde sur un cycle. Cette loi physique a pour seule contrainte de respecter le débit sortant moyen (aire de la courbe) et de fournir une courbe rendant compte des deux phénomènes suivants :

• 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. Ce gabarit (d̅) fournit en sortie une allure (courbe) du débit massique en sortie des soupapes d'échappement d _i , c'est-à-dire une estimation commune (d̅) du débit pour tous les cylindres. Il est obtenu en corrélation avec les mesures de banc moteur. En fonction du débit aspiré et de la richesse moyenne mesurée par la sonde λ̅, on effectue ensuite une homothétie du gabarit et l'on effectue un déphasage pour chaque cylindre en fonction de l'angle de vilebrequin, pour déduire le débit de sortie des gaz à la sortie de chaque cylindre : $$d_i\left(\alpha \right)=\bar{d}\left({\alpha }_i+\alpha \right).{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0$$
  
  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 ;
  • ${\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0=d_{\mathrm{asp}}.\left(1+\frac{\bar{\lambda }}{\mathrm{PCO}}\right)$
    
  • α _i : l'angle de déphasage pour le cylindre i.

On peut observer schématiquement le déphasage de la courbe du gabarit sur la figure 1 (DS1 à DS4). 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 rate sucked by the cylinder _asp (variable estimated by the engine control upstream);
• the mean value of richness measured by the probe λ̅ on a cycle.

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. 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: $$d_i\left(\alpha \right)=\tilde{d}\left({\alpha }_i+\alpha \right).{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0$$
  
  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;
  • ${\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0=d_{\mathrm{asp}}.\left(1+\frac{\tilde{\lambda }}{\mathrm{PCO}}\right)$
    
  • α _i : the phase shift angle for the cylinder i.

It is possible to observe schematically the phase shift of the curve of the template in FIG. 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 rate passing 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 _MT. 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 : $$p\left(M_T\right)=f\left(\mathrm{régime\; turbine}\right).\sqrt{\frac{2.g}{g-1}}.\left({\left(\frac{M_T}{M_0}\right)}^{\frac{-2}{g}}-{\left(\frac{M_T}{M_0}\right)}^{\frac{-\left(g+1\right)}{g}}\right)$$

où :

• f est une fonction polynomiale
• g est une constante

Les paramètres de la fonction f sont optimisés par corrélation avec la cartographie de la turbine.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 $\frac{{\mathrm{<figure-callout\; id="0"\; label="M\; T\; M"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">M\; </figure-callout>}}_T}{M_{}}$

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

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: $$d_{\mathrm{air}}\left(M_{\mathrm{air}}\right)=\frac{M_{\mathrm{air}}}{M_T}{d}_T\left(M_T\right)=M_{\mathrm{air}}.p\left(M_T\right)$$

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

N _e :

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

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

N _e :

Engine speed

α:

Angle of the crankshaft

d _i :

Mass flow coming out of cylinder i

d _T :

Total flow through the turbine

of _air

: Air flow through the turbine

λ _i :

Wealth in each of the cylinders

M _T

: Masse totale dans le collecteur d'échappement

M _air :

Masse d'air frais dans le collecteur d'échappement

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 one 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:

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) Hypothesis on the dynamics of the sensor

In the previous equations, the measured richness at the sensor is calculated from the richness in the cylinders, the air flow at the cylinder output and the total gas flow rate. This structure is hardly used in a Kalman filter, because it is necessary to estimate the entries of the model. The model is therefore completed by the addition of entries, M _T and λ (Mohinder S. Grewal: "Kalman Filtering Theory and Practice" Prentice Hall 1993).

To do this, the response dynamics of the richness sensor are taken into account, and the transfer function of the measurement probe (of the "UEGO" probe type) is modeled according to a first-order filter. The richness (λ) given by the model downstream of the turbine is equal to the richness in the collector, and by using the equation of wealth previously described, it is possible to estimate the wealth measured from M _T and M _air : $$\lambda =\frac{M_{\mathrm{gas}B}.\mathrm{PCO}}{M_{\mathrm{air}}.\left(1+\mathrm{PCO}\right)+M_{\mathrm{gas}B}.\mathrm{PCO}}=1-\frac{M_{\mathrm{air}}}{M_T}$$

avec :

τ :

Constante de temps du capteur de richesse considéré comme un premier ordre.

Thus, we can model the response of the probe by the following relation: $${\mathrm{NOT}}_e.\frac{d\lambda }{d\alpha }=\frac{1}{\tau }\left(\frac{M_T-M_{\mathrm{air}}}{M_T}-\lambda \right)$$

with:

τ:

Time constant of the wealth sensor considered as a first order.

D) Expression of the real-time physical model

Les inconnues du modèle physique sont au final M _T , M _air , λ et les λ _i .
Les données de sorties du modèle physique sont M _T et d _i . Finally, the real-time physical model RTM can be put in the following matrix form from equations (3), (5) and (6): $$X=\left[\begin{array}{c}{M}_T\\ M_{\mathrm{<figure-callout\; id="1"\; label="air\; \lambda \; \lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">air\; </figure-callout>}}& \\ \lambda \\ {\lambda }_{}{}_1\\ {\lambda }_{\mathrm{two}}\\ {\mathrm{<figure-callout\; id="3"\; label="\lambda "\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_3\\ {\mathrm{<figure-callout\; id="4"\; label="\lambda "\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_4\end{array}\right]{\mathrm{NOT}}_e.\frac{dX}{d\alpha }=\left[\begin{array}{l}{\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathrm{cyl}}}{\Sigma }}{d}_i\left(\alpha \right)}-M_T.p\left(M_T\right)\hfill \\ {\displaystyle \underset{i=1}{\overset{{\mathrm{not}}_{\mathrm{cyl}}}{\Sigma }}\left(1-{\lambda }_i\right).d_i\left(\alpha \right)}-M_{\mathrm{air}}.\mathrm{<figure-callout\; id="1"\; label="p\; M\; T"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">p\; </figure-callout>}\left(M_T\right)\left({}_{}\right)\hfill \\ \frac{1}{\tau }\left(\frac{M_T-M_{\mathrm{air}}}{M_T}-\mathrm{<figure-callout\; id="0"\; label="\lambda "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\lambda </figure-callout>}\right)\hfill \\ 0\hfill \\ 0\hfill \\ 0\hfill \\ 0\hfill \end{array}\right]$$

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

E) 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 7). However, the model has been built linearly with respect to these delays because the transport in the pipes is neglected. 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 (7) 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 : N _e
• 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: N _e
• 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 passing through the turbine flow rate: of _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

• Greg Welch and Gary Bishop : « An Introduction to the Kalman Filter ».
• University of North Carolina - Chapel Hill TR95-041. May 23, 2003).

On rappelle ci-après la structure d'un filtre de Kalman étendu. Le filtre de Kalman étendu, aussi appelé EKF (Extented Kalman Filter) permet d'estimer le vecteur d'état d'un processus dans le cas où celui-ci, ou le procédé de mesure, est non linéaire.The physical model (7) 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 this model has a structure that can be used in an extended Kalman 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 extended Kalman filter. Such a filter is well known to those skilled in the art and is described in the following document:

• Greg Welch and Gary Bishop: An Introduction to the Kalman Filter .
• University of North Carolina - Chapel Hill TR95-041. May 23, 2003).

The following is a reminder of the structure of an extended Kalman filter. The extended Kalman filter, also called EKF (Extented Kalman Filter) makes it possible to estimate the state vector of a process in the case where the latter, or the measurement method, is nonlinear.

It is assumed that a process (x) is governed by a nonlinear stochastic equation ( f ). At the time step k, we can write: $$x_k=f\left(x_{k-1},w_{k-1}\right)\mathrm{with}:x_k=\left[\begin{array}{c}{M}_{T\left(k\right)}\\ M_{\mathrm{air}\left(k\right)}\\ {\lambda }_{\left(k\right)}\\ {\lambda }_{1\left(k\right)}\\ {\lambda }_{\mathrm{two}\left(k\right)}\\ {\lambda }_{3\left(k\right)}\\ {\lambda }_{4\left(k\right)}\end{array}\right]$$

où les variables aléatoires w _k et v _k représentent respectivement les bruits de modèle et les bruits de mesure.A measure ( y ) is given by a nonlinear observation equation h . At the time step k, we can write: $${\mathrm{there}}_k=h\left(x_k,v_k\right)$$

where the random variables w _k and v _k respectively represent the model noises and the measurement noises.

• On note :
  • x̂ _k̅ la prédiction de x au pas de temps k.
  • x̂ _k l'estimation de x au pas de temps k.

The estimation method includes an estimator based on a prediction / correction technique. That is, a prediction of the variable is made and then a correction is applied at each time step. These steps of the following prediction / correction are described below in the general framework of an extended Kalman filter:

• We notice :
  • x _k̅ the prediction of x at time step k.
  • x _k the estimate of x at the time step k.

Prediction stage: $$\begin{array}{||}\hline \begin{array}{l}{\widehat{x}}_k^{-}=f\left({\widehat{x}}_{k-1},0\right)\\ P_k^{-}={\mathrm{AT}}_k{P}_{k-1}{\mathrm{AT}}_k^T+W_k{Q}_{k-1}{W}_k^T\end{array}\\ \hline\end{array}$$

• P _k est la matrice symétrique définie positive de dispersion de l'erreur
• Q _k est la matrice symétrique définie positive de dispersion du bruit blanc gaussien w _k
• R _k est la matrice symétrique définie positive de dispersion du bruit blanc gaussien v _k
• $P_k^{-}$
  
  est la matrice symétrique définie positive de propagation de l'erreur

In the previous equations, we use the following variables:

• P _k is the symmetric positive definite matrix of dispersion of the error
• Q _k is the positive definite symmetric matrix of Gaussian white noise dispersion w _k
• R _k is the positive definite symmetric matrix of dispersion of Gaussian white noise v _k
• $P_k^{-}$
  
  is the definite positive symmetric matrix of propagation of the error

The different elements are initialized thanks to the values obtained in simulation with AmeSim.

• L'estimation de x au pas de temps k, x _k , est obtenue par correction de la prédiction ${\widehat{x}}_k^{-}$
  
  de la façon suivante : $$\begin{array}{||}\hline \begin{array}{l}{K}_k=P_k^{-}{H}_k^T{\left(H_k{P}_k^{-}{H}_k^T+V_k{R}_k{V}_k^T\right)}^{-1}\\ {\widehat{x}}_k={\widehat{x}}_k^{-}+K_k\left(y_k-h\left({\widehat{x}}_k^{-},0\right)\right)\\ P_k=\left(I-K_k{H}_k\right)P_k^{-}\end{array}\\ \hline\end{array}$$
  
  
  où :
  • A est la matrice Jacobienne des dérivées partielles de f par rapport à x : $$A_{\left[i,j\right]}=\frac{\partial f_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k,0\right)$$
    
  • W est la matrice Jacobienne des dérivées partielles de f par rapport à w : $$W_{\left[i,j\right]}=\frac{\partial f_{\left[i\right]}}{\partial w_{\left[j\right]}}\left({\widehat{x}}_k,0\right)$$
    
  • H est la matrice Jacobienne des dérivées partielles de h par rapport à x : $$H_{\left[i,j\right]}=\frac{\partial h_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k^{-},0\right)$$
    
  • V est la matrice Jacobienne des dérivées partielles de h par rapport à v : $$V_{\left[i,j\right]}=\frac{\partial h_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k^{-},0\right)$$
    

Correction step:

• The estimate of x at the time step k, x _k , is obtained by correcting the prediction ${\widehat{x}}_k^{-}$
  
  as follows : $$\begin{array}{||}\hline \begin{array}{l}{K}_k=P_k^{-}{H}_k^T{\left(H_k{P}_k^{-}{H}_k^T+V_k{R}_k{V}_k^T\right)}^{-1}\\ {\widehat{x}}_k={\widehat{x}}_k^{-}+K_k\left({\mathrm{there}}_k-h\left({\widehat{x}}_k^{-},0\right)\right)\\ P_k=\left(I-K_k{H}_k\right)P_k^{-}\end{array}\\ \hline\end{array}$$
  
  
  or :
  • A is the Jacobian matrix of the partial derivatives of f with respect to x: $${\mathrm{AT}}_{\left[i,j\right]}=\frac{\partial f_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k,0\right)$$
    
  • W is the Jacobian matrix of the partial derivatives of f with respect to w: $$W_{\left[i,j\right]}=\frac{\partial f_{\left[i\right]}}{\partial w_{\left[j\right]}}\left({\widehat{x}}_k,0\right)$$
    
  • H is the Jacobian matrix of the partial derivatives of h with respect to x: $$H_{\left[i,j\right]}=\frac{\partial h_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k^{-},0\right)$$
    
  • V is the Jacobian matrix of the partial derivatives of h with respect to v: $$V_{\left[i,j\right]}=\frac{\partial h_{\left[i\right]}}{\partial x_{\left[j\right]}}\left({\widehat{x}}_k^{-},0\right)$$
    

It should be noted that, in order to lighten the notations, the index of the time step k has not been indicated, even if these matrices are actually different at each step.

At the input of the Kalman filter, the wealth λ downstream of the turbine and the total mass of gas in the manifold ( M _T ), are necessary. The input parameters, measured or modeled, of the estimator are: $$Y=\left[\begin{array}{c}{M}_T\\ \lambda \end{array}\right]$$

The richness is measured, the total gas mass is the result of the calculation of the model (7) in parallel with the Kalman filter.

This estimator based on a Kalman filter allows, ultimately, an estimation of the cylinder to cylinder richness from the measurement of wealth by the sensor located behind the turbine.

The estimator thus constructed, makes it possible to correct in real time M _T , M _air , λ _i and λ, from a first value of M _T provided by the RTM model (7) and from the measurement of wealth performed. by the probe.

The Kalman filter is solved numerically in real time, the calculator using explicit Euler discretization, which is well known to those skilled in the art.

Results in simulation: test of the estimator (9)

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 (λ̂ _i ) en fonction du temps (T). Les quatre courbes correspondent à chacun des quatre cylindres. La performance de l'estimateur basé sur le filtre de Kalman 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. Figures 2A and 2B show below the wealth of references $\left({\lambda }_i^{\mathrm{ref}}\right)$

given by AmeSim as a function of time (T) and at the top the results of the estimator (λ _i ) as a function of time (T). The four curves correspond to each of the four cylinders. The performance of the estimator based on the Kalman 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 (7) ;
• 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 (10) ;
• SR est la sonde de mesure de la richesse en aval de la turbine utilisée ;
• ERFK est l'Estimateur de Richesse basé sur un Filtre de Kalman et décrit par l'équation (9) ;
• λ _i est la richesse du cylindre i estimée par l'ERFK.

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 delay estimator is illustrated in Figure 3, in which:

• N _e and α are the input data of the RTM model described by equations (7);
• 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 (10);
• SR is the measurement of the wealth downstream of the turbine used;
• ERFK is the Kalman Filter-based Richness Estimator and described by Equation (9);
• λ _i is the richness of the cylinder i estimated by the ERFK.

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
• ${\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="\lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_1^{\mathrm{<figure-callout\; id="2"\; label="ref\; \lambda "\; filenames="imgf0002.png,imgf0006.png"\; state="\{\{state\}\}">ref</figure-callout>}}& \\ {\lambda }_{}^{}{}_2^{\mathrm{<figure-callout\; id="3"\; label="ref\; \lambda "\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">ref</figure-callout>}}& \\ {\lambda }_{}^{}{}_3^{\mathrm{<figure-callout\; id="4"\; label="ref\; \lambda "\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">ref</figure-callout>}}& \\ {\lambda }_{}^{}{}_4^{\mathrm{ref}}\end{array}\right]:$
  
  : 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. $$\{\begin{array}{l}\beta =\left[0,1,-1,\mathrm{two}\right]\\ J_k=\beta *\left({\mathrm{\Lambda }}_k-{\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0\right)\end{array}$$

with:

• ${\mathrm{\Lambda }}_k=\left[\begin{array}{c}{\widehat{\lambda }}_1\\ {\widehat{\lambda }}_{\mathrm{two}}\\ {\widehat{\lambda }}_3\\ {\widehat{\lambda }}_4\end{array}\right]:$
  
  composition in step k
• ${\mathrm{<figure-callout\; id="0"\; label="\Lambda "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\Lambda </figure-callout>}}_0=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="\lambda "\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}_1^{\mathrm{ref}}\\ {\lambda }_{\mathrm{two}}^{\mathrm{<figure-callout\; id="3"\; label="ref\; \lambda "\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">ref\; </figure-callout>}}& \\ {\lambda }_{}^{}{}_3^{\mathrm{<figure-callout\; id="4"\; label="ref\; \lambda "\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">ref\; </figure-callout>}}& \\ {\lambda }_{}^{}{}_4^{\mathrm{ref}}\end{array}\right]:$
  
  : 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 (λ̂ _i ) en fonction du temps (T). Les quatre courbes correspondent à chacun des quatre cylindres.FIGS. 4A to 4F illustrate the estimation of cylinder to cylinder richness by the estimator previously described on two operating points 2000tr / min high load, 9 bar, (FIGS. 4A to 4C) and 2500 rpm low load, 3 bar, (Figures 4D to 4F). These figures show up the wealth of references $\left({\lambda }_i^{\mathrm{ref}}\right)$

as a function of time (T) and at the bottom the results of the estimator (λ _i ) as a 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 carried out, 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 (8)

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 wealth measurement sensor (λ) downstream of said collector , characterized in that it comprises the following steps: an estimate of said richness (λ) measured by said sensor is defined from at least one variable of said model; a modeling is carried out of the transfer function of said sensor in which said estimate of the measurement of measured wealth is taken into account; a physical model is established in real time of the path of the gases in said exhaust circuit to said sensor, in which the modeling of the transfer function is taken into account, and comprising: a physical model for ejecting gases into each of said cylinders; a physical model of said exhaust manifold; - a physical model of the flow passing through a turbine; - a model of delay time from the exhaust to the sensor; said model is coupled with a nonlinear estimator of the extended Kalman type; a real-time estimation of the value of the richness in each of the cylinders is made from said nonlinear estimator of the extended Kalman type. The method of claim 1, wherein said modeling of the transfer function is performed from a first order filter. Method according to one of the preceding claims, 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 perturbation in a given cylinder and measuring its effect on the sensor. Method according to one of the preceding claims, wherein said physical model comprises at least the following four types of variables: the total mass of gas in the exhaust manifold ( M _T ), the fresh air mass in the exhaust manifold ( M _air ), the wealth measured by said sensor (λ) and the wealth in each of the cylinders ( λ _i ) Method according to one of the preceding claims, wherein said physical model comprises at least the following two types of output data: the total mass of gas in the exhaust manifold ( M _T ) and mass flow rates exiting said cylinders ( d _i ). 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 manifold ( M _T ) and the fresh air mass in the exhaust manifold ( M _air ). Method according to one of the preceding claims, wherein said estimation of the value of the richness in each of the rolls comprises a real time correction of the estimate of the total mass of gas in the exhaust manifold ( M _T ), estimating the fresh air mass in the exhaust manifold ( M _air ) and estimating the value of the richness in each of the cylinders (λ _i ). Application of the method according to one of the preceding claims to an engine control to adapt the fuel masses injected into each of the cylinders to adjust the richness in all the cylinders.

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