EP1931868B1 - Method for estimating instantaneous speed produced by each of the cylinders of an internal combustion engine - Google Patents

Description

The present invention relates to a method for estimating in real time the instantaneous speed produced by each cylinder of an internal combustion engine from the instantaneous speed sensor located at the end of the transmission.

The knowledge of the instantaneous regime for each cylinder makes it possible to estimate the average torque produced by each cylinder.

State of the art

Estimating the average torque produced by each cylinder is important for all vehicles, whether they are petrol or diesel engines. In the first case, it conditions a good combustion of the mixture when the richness is close to one, and therefore sensitive to cylinder-to-cylinder difference problems. In the second case, the interest of the knowledge of the couple allows a rebalancing to obtain an optimum operation. In particular, catalysts using a NOx trap lose their effectiveness over time. In order to return to optimum efficiency, the torque of each of the cylinders must be kept identical for a few seconds, then return to normal operation at a lean mixture. The DeNOx catalysis depollution therefore requires precise control of the cylinder-by-cylinder torque.

To do this, an instantaneous speed sensor is placed at the end of the transmission. This measurement is very distorted by the transmission and is noisy.

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 cylinder to cylinder torque is indispensable. The implementation of a digital couplometer under each cylinder is unthinkable on vehicle given their cost.

The method according to the invention proposes to define an estimator operating from the measurement at the end of the transmission chain to estimate the instantaneous speed under each of the cylinders.

The method according to the invention

The invention relates to a method for estimating in real time the instantaneous speed produced by each of the cylinders of an internal combustion engine comprising at least one transmission system connected to the cylinders and a sensor which realizes a measurement ( x ₁ ) in real time. instantaneous regime at the end of said transmission system.

1. a) on construit un modèle physique représentant en temps réel la dynamique dudit système de transmission en fonction : de ladite mesure (x₁ ), de coefficients d'une décomposition en série de Fourier dudit régime instantané produit par chacun des cylindres, et en fonction d'un amortissement et d'une fréquence propre caractérisant ledit système de transmission ;
2. b) on détermine en temps réel les coefficients de ladite décomposition en série de Fourier en couplant ledit modèle avec un estimateur non linéaire de type adaptatif ;
3. c) on réalise une estimation en temps réel du régime instantané produit par chacun des cylindres, à partir desdits coefficients de Fourier.

The method has the following steps:

1. a) constructing a physical model representing in real time the dynamics of said transmission system as a function of: said measurement ( x ₁ ), coefficients of a Fourier series decomposition of said instantaneous regime produced by each of the cylinders, and in function a damping and a natural frequency characterizing said transmission system;
2. b) the coefficients of said Fourier series decomposition are determined in real time by coupling said model with an adaptive type nonlinear estimator;
3. c) real time estimation of the instantaneous regime produced by each of the rolls, from said Fourier coefficients.

We can also estimate in real time the average torque of each of the cylinders from the estimation of these coefficients.

The method according to the invention can be applied to an engine control to adapt the fuel masses injected into each of the cylinders, in order to adjust the average torque produced by each of the cylinders.

Other characteristics and advantages of the method according to the invention will appear on reading the following description of nonlimiting examples of embodiments, with reference to the appended figures and described below.

Brief presentation of the figures

• the figure 1 illustrates the estimation of the instantaneous speed under the cylinders by the method according to the invention, on an operating point of 1250tr / min average load.
• the figure 2 illustrates the estimation of the average cylinder to cylinder torque by the method according to the invention, on an operating point of 1500tr / min.

Detailed description of the method

The method according to the invention makes it possible to estimate the instantaneous speed produced by each of the cylinders of an internal combustion engine comprising at least one transmission system connected to the cylinders. At the end of this transmission system, a sensor realizes a measurement of the instantaneous speed in real time. This signal is noted x ₁ . An instantaneous speed measurement under the cylinders deformed by the transmission shaft is therefore performed. The first step of the invention is therefore to "reverse" the effects of the transmission to obtain the relevant information, that is to say the instantaneous speed produced by each of the cylinders. This relevant information is a periodic signal that we note x ₀ .

• 1- on établit, dans une échelle angulaire (c'est-à-dire en fonction de l'angle vilebrequin et non du temps), un modèle physique représentant en temps réel la dynamique du système de transmission ;
• 2- on caractérise le régime instantané produit par chacun des cylindres, par des paramètres quasi invariants au cours du temps, tels que les coefficients de sa décomposition de Fourier ;
• 3- on couple le modèle physique avec un estimateur non linéaire de type adaptatif ;
• 4- on réalise une estimation en temps réel du régime instantané produit par chacun des cylindres à partir de l'estimateur non linéaire de type adaptatif.

The method consists mainly of the following four steps:

• 1-we establish, in an angular scale (that is to say according to the crank angle and not time), a physical model representing in real time the dynamics of the transmission system;
• 2- the instantaneous regime produced by each of the cylinders is characterized by quasi-invariant parameters over time, such as the coefficients of its Fourier decomposition;
• 3- we couple the physical model with a nonlinear estimator of adaptive type;
• 4-real time estimation of the instantaneous regime produced by each of the cylinders from the adaptive type nonlinear estimator.

1- Physical model of the dynamics of the transmission system

• ω : la fréquence propre de la transmission dans le référentiel tournant
• ζ : l'amortissement de la transmission

To estimate the signal x ₀ , that is to say the instantaneous regime under the cylinders, a physical model of the dynamics of the transmission system is first defined. To do this, we consider that this system behaves like a system of the second order which consists of two parameters:

• ω : the natural frequency of transmission in the rotating repository
• ζ : the damping of the transmission

avec :
x₁ : le régime instantané au bout de la chaîne de transmission : la mesure (y)
x₀ : le régime instantané sous les cylindres : l'inconnu
ω : la fréquence propre du système de transmission dans le référentiel tournant
ζ: l'amortissement du système de transmission
α : l'angle vilebrequin du système de transmissionThus, and placing itself in the angular scale, the dynamics of the transmission shaft is written: $$\{\begin{array}{ccc}\frac{d^2\left(x_1-x_0\right)}{d{\alpha }^2}& =& -\tilde{\xi }\tilde{\omega }\frac{d\left(x_1-x_0\right)}{d\alpha }-{\tilde{\omega }}^2\left(x_1-x_0\right)\\ \mathrm{there}& =& x_1\end{array}$$

with:
x ₁ : the instantaneous regime at the end of the transmission chain: the measure ( y )
x ₀ : the instantaneous regime under the cylinders: the unknown
ω : the natural frequency of the transmission system in the rotating repository
ζ : the damping of the transmission system
α: the crankshaft angle of the transmission system

We can make a change of variable by posing: $$w_0=\frac{d^2{x}_0}{d{\alpha }^2}+\tilde{\xi }\tilde{\omega }+\frac{d{x}_0}{d\alpha }+{\tilde{\omega }}^2{x}_0$$

avec : $$x=\left[\begin{array}{cc}{x}_1& \frac{d{x}_1}{d\alpha }\end{array}\right]$$

$$A=\left[\begin{array}{cc}0& 1\\ -{\bar{\omega }}^2& -\bar{\xi }\bar{\omega }\end{array}\right]$$

$$A_0=\left[\begin{array}{c}0\\ 1\end{array}\right]$$

$$C=\left[\begin{array}{cc}1& 0\end{array}\right]$$

The instantaneous regime under the cylinders x 0 is periodic so w ₀ too. The dynamics can be rewritten in the following form: $$\{\begin{array}{ccc}\frac{\mathrm{dx}}{d\alpha }& =& \mathrm{AT}\mathrm{.}x+{\mathrm{AT}}_0\mathrm{.}{w}_0\\ \mathrm{there}& =& \mathrm{VS}\mathrm{.}x\end{array}$$

with: $$x=\left[\begin{array}{cc}{x}_1& \frac{d{x}_1}{d\alpha }\end{array}\right]$$

$$\mathrm{AT}=\left[\begin{array}{cc}0& 1\\ -{\tilde{\omega }}^2& -\tilde{\xi }\tilde{\omega }\end{array}\right]$$

$${\mathrm{AT}}_0=\left[\begin{array}{c}0\\ 1\end{array}\right]$$

$$\mathrm{VS}=\left[\begin{array}{cc}1& 0\end{array}\right]$$

This equation (2) constitutes the physical model representing in real time the dynamics of the transmission system. An estimate of the signal w ₀ makes it possible to determine an estimate of the signal x ₀ from equation (1).

2- Characterization of the signal x ₀ by quasi invariant parameters over time

We seek to estimate, from this physical model and the measurement y (equal to x ₁ ), the signal x ₀ , that is to say the instantaneous regime produced by each of the cylinders. To make this estimation in real time, the method according to the invention characterizes this signal x ₀ by quasi-invariant parameters over time. In other words, the signal x ₀ is defined using parameters which, at a given moment, are constants. To do this, we exploit the fact that the signal x ₀ is mechanically periodic. Thus, instead of making an estimate of the highly variable signal x ₀ , it is possible to estimate the Fourier coefficients of this signal. It is also possible to use any parameters making it possible to describe the signal x ₀ in relation to its periodic character.

Les d_j représentent les 2n+1 coefficients de Fourier de la décomposition du signal x₀ .The Fourier coefficient decomposition of the signal x ₀ , developed in complex for the clarity of the exposition, is written as follows: $$x_0\left(\alpha \right)={\displaystyle \underset{j=-\mathrm{not}}{\overset{\mathrm{not}}{\Sigma }}}{d}_j{e}^{\left(i\omega \alpha \right)}$$

The _dj represent the 2 n + 1 Fourier coefficients of the decomposition of the signal x ₀ .

A signal is thus defined translating the instantaneous regime x ₀ , as a function of the parameters d _j , invariant over time.

Les c_j représentent les 2n+1 coefficients de Fourier.To estimate the parameters _d, we can again use the change of variable w ₀ and use the physical model described by the system (2). The signal w ₀ is also mechanically periodic, and its decomposition in Fourier coefficients, developed in complex for the clarity of the exposition, is written as follows: $$w_0\left(\alpha \right)={\displaystyle \underset{j=-\mathrm{not}}{\overset{\mathrm{not}}{\Sigma }}}{\mathrm{vs}}_j{e}^{\left(i\omega \alpha \right)}$$

The c _j represent the 2 n + 1 Fourier coefficients.

The estimation of these coefficients c _j thus makes it possible to estimate the Fourier coefficient decomposition of the signal x ₀ and thus also of the signal x ₀ itself.

By using only a finite number of harmonics ([- n ; + n ]), the physical model representing in real time the dynamics of the transmission system is then written: $$\{\begin{array}{ccc}\frac{\mathit{dx}}{d\alpha }& =& \mathrm{AT}\mathrm{.}x+{\mathrm{AT}}_0\mathrm{.}\left({\displaystyle \underset{j=-\mathrm{not}}{\overset{\mathrm{not}}{\Sigma }}}{\mathrm{vs}}_j{e}^{\left(i\omega \alpha \right)}\right)\\ \frac{d{\mathrm{vs}}_j}{d\alpha }& =& 0\\ \mathrm{there}& =& \mathrm{VS}\mathrm{.}x\end{array},\forall j\in \left[-\mathrm{not},\mathrm{not}\right]$$

3- Coupling with a nonlinear estimator of adaptive type

avec :
x̂ : estimateur de x
ĉ_j : estimateur de c_j
L : une matrice à calibrer
L_j : des matrices à calibrer
Un choix de matrices L et L_j assurant la convergence de l'estimateur est : $$L=\left[\begin{array}{c}2\bar{\xi }\bar{\omega }\\ 2{\bar{\omega }}^2\end{array}\right]\mathrm{et}\forall j\in \left[-n,n\right]L_j=\frac{1}{j^2+1}\mathrm{.}$$

From the physical model described by the system (4), a non-linear adaptive-type estimator is defined, on the one hand, a term related to the dynamic and, on the other hand, a correction term: $$\{\begin{array}{lll}\frac{\mathit{dx}}{d\dot{\alpha }}& =& \mathrm{AT}\mathrm{.}\hat{x}+{\mathrm{AT}}_0\mathrm{.}{\displaystyle \underset{j=-\mathrm{not}}{\overset{\mathrm{not}}{\Sigma }}}{\widehat{\mathrm{vs}}}_j{e}^{\left(i\omega \alpha \right)}-\mathrm{The}\mathrm{.}\left(\mathrm{VS}\mathrm{.}\hat{x}-\mathrm{there}\right)\\ \frac{d{\widehat{\mathrm{vs}}}_j}{d\alpha }& =& -e^{\left(-i\omega \alpha \right)}\mathrm{.}{\mathrm{The}}_j\mathrm{.}\left(\mathrm{VS}\mathrm{.}\hat{x}-\mathrm{there}\right);\forall j\in \left[-\mathrm{not},\mathrm{not}\right]\end{array}$$

with:
x: x estimator
ĉ _j : estimator of c _j
L : a matrix to calibrate
L _j : matrices to be calibrated
A choice of matrices L and L _j ensuring the convergence of the estimator is: $$\mathrm{The}=\left[\begin{array}{c}2\tilde{\xi }\tilde{\omega }\\ 2{\tilde{\omega }}^2\end{array}\right]\mathrm{and}\forall j\in \left[-\mathrm{not},\mathrm{not}\right]{\mathrm{The}}_j=\frac{1}{j^2+1}\mathrm{.}$$

The system of equations (5) represents an adaptive-type nonlinear estimator for estimating the coefficients c _j of the Fourier coefficient decomposition of the signal w ₀ .

This estimator (5) was constructed from the variable change w ₀ , but it is obvious that in the same way it is possible to construct an adaptive-type nonlinear estimator directly from x ₀ .

4- Real-time estimation of the instantaneous regime produced by each of the cylinders

It is then estimated from the estimate ĉ _j coefficients c _j the instantaneous regime produced by each cylinder x ₀ .

The estimator (5) makes it possible to reconstruct w ₀ through its Fourier coefficients c _j . The goal is to rebuild x ₀ . Thanks to the expression of w ₀ given by the equation (1), the coefficients d _j are expressed as a function of the coefficients c _j : $$d_j=\frac{{\tilde{\omega }}^2-{\left(j\mathrm{.}\omega \right)}^2-i\mathrm{.}j\mathrm{.}\omega \mathrm{.}\tilde{\xi }\mathrm{.}\tilde{\omega }}{{\left({\tilde{\omega }}^2-{\left(j\mathrm{.}\omega \right)}^2\right)}^2+{\left(i\mathrm{.}j\mathrm{.}\omega \mathrm{.}\tilde{\xi }\mathrm{.}\tilde{\omega }\right)}^2}\mathrm{.}{\mathrm{vs}}_j\forall j\in \left[-\mathrm{not},\mathrm{not}\right]$$

We thus obtain the expression of the instantaneous regime produced by each cylinder, using equations (3) and (6), and the coefficients of its Fourier decomposition by equation (6).

Estimation of the average torque produced by each cylinder

According to the invention, it is possible to provide an estimate of the average torque produced by each cylinder from the estimate of the instantaneous regime produced by each cylinder ( x ₀ ) and more precisely from the estimate of its Fourier decomposition. in coefficients d _j .

The knowledge of the average torque produced by each cylinder is a fundamental and relevant information for the estimation of the combustion; it is the image of the combustion that the engine sees.

The previous estimator (5) allows us to estimate the signal of the regime under the cylinders but also its Fourier decomposition. However, the more torque is important the greater the excitement on the tree. In this sense it is possible to correlate the torque produced by the cylinder and the Fourier coefficients of the decomposition of the instantaneous regime signal ( x ₀ ).

In general, it is therefore possible to identify a function φ, which makes it possible to determine the PMI (Average Indicated Pressure) or, equivalently, the average torque from the coefficients d _j : $$\begin{array}{cc}\phi :& R^{2\mathrm{not}+1}\to R\\ & \left\{d_j\right\}\to \mathit{PMI}\end{array}$$

avec ϕ₀ une constante à calibrer en fonction du régime moteur utilisé à l'aide de corrélations avec les mesures de banc moteur. Ce calibrage peut être réalisé à partir d'une tabulation, issue d'une optimisation linéaire consistant à ajuster la valeur de ϕ₀ pour que les estimations soient le plus proche possible des paramètres du moteur (paramètres permettant le calibrage du moteur et fournis par le constructeur).This function φ can be a polynomial function. It can be determined empirically from test. For example we can choose the following function: $$\phi \left(d_j\right)={\displaystyle \underset{j=-\mathrm{not},j\ne 0}{\overset{\mathrm{not}}{\Sigma }}}\frac{d_j^2}{{\phi }_0}$$

with φ ₀ a constant to be calibrated according to the engine speed used using correlations with the engine bench measurements. This calibration can be done at from a tabulation, resulting from a linear optimization consisting of adjusting the value of φ ₀ so that the estimates are as close as possible to the engine parameters (parameters allowing the calibration of the engine and supplied by the manufacturer).

Results

The figure 1 illustrates the estimate (R _is ) of the instantaneous regime x ₀ under the cylinders from the estimator according to the invention (5) previously described on an operating point at 1250rpm average load. The figure 1 also illustrates the reference instantaneous speed R _ref (calculated from the cylinder pressure measurements on the engine test bench). We observe a very good estimate of the signal.

The figure2 illustrates the estimation ( PMI _est ) of the cylinder-to-cylinder torque on an operating point at 1500tr / min, from the estimator according to the invention (5) and a function φ defined by equation (7) . The figure 2 also illustrates the average reference torque ( PMI _ref ) (calculated from cylinder pressure measurements on the engine test bench). We observe a very good estimate of the signal.

The adaptive filter 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

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

• 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 estimate of the instantaneous speed produced by each cylinder and the estimate of the average cylinder to cylinder torque are numerous:

• reduction of polluting emissions;
• improvement of the driving pleasure (regularization of the delivered torque);
• reduction of fuel consumption;
• diagnosis of the injection system (detection of the drift of an injector or the failure of the injection system).

Claims (3)

1. A method for real-time estimation of the instantaneous condition produced by each of the cylinders of an internal combustion engine comprising at least one transmission system connected to the cylinders and a detector which performs in real time a measurement (x₁) of the instantaneous condition at the end of said transmission system, characterised in that it comprises the following steps:

   a) constructing a physical model representing in real time the dynamics of said system transmission in dependence on: the crankshaft angle, said measurement (x₁), coefficients of a Fourier series analysis of said instantaneous condition produced by each of the cylinders, and in dependence on damping and a natural frequency characterising said transmission system;

   b) determining in real time the coefficients of said Fourier series analysis by coupling said model to a non-linear adaptive type estimator; and

   c) effecting an estimation in real time of the instantaneous condition produced by each of the cylinders from said Fourier coefficients.
2. A method according to claim 1 wherein the mean torque of each of the cylinders is estimated in real time from the estimation of said coefficients.
3. A method according to the preceding claims for adapting by an engine control the masses of fuel injected into each of the cylinders in order to regulate the mean torque produced by each of the cylinders.

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