FR3086000A1 - METHOD FOR REGULATING AN ENGINE SUPERCHARGER ACCORDING TO THE INERTIAL POWER OF THE TURBOCHARGER - Google Patents

Abstract

The invention relates to a method for regulating an air supercharging of an internal combustion engine equipped with a turbocharger comprising a turbine and a compressor, the regulation being made by determining a position setpoint of the turbocharger (Pos comp cons) according to a boost pressure set point (Pr on cons), a compressor power set point (Pu comp cons) being established according to the boost pressure set point (Pr on cons) and used for determining the turbocharger position setpoint (Pos comp cons). An inertial power (Pinertial) of the compressor, at least during transient operating phases of the turbocharger, is taken into account in establishing the compressor power setpoint (Pu comp cons).

Description

The present invention relates to a method for regulating a supercharging pressure of an internal combustion engine by taking into account the inertial power of the turbocharger. during the transitional phase of the ramp-up.

It is known from the state of the art of methods for regulating an air supercharging of an internal combustion engine of a motor vehicle equipped with a turbocharger comprising a turbine and a compressor. Conventionally, the regulation is done by determining a turbocharger position setpoint based on a boost pressure setpoint. More specifically, a compressor power setpoint being established according to the boost pressure setpoint which in turn translated into the position setpoint of the turbocharger.

For example, document FR-A-2 953 253 describes a method for controlling the air supercharging of an internal combustion engine of a motor vehicle equipped with a stepped twin-turbocharger comprising two turbines driven in rotation by the engine exhaust, two boost compressors driven by each of the turbines, and two high pressure and low pressure valve actuators to regulate the boost pressure.

* The method disclosed by this document further comprises regulating the compression ratio of the compressor around a set value of the boost pressure ratio, as well as regulating the expansion rate of the turbine to limit the pressure upstream of the latter, the regulation being implemented as soon as the pressure upstream of the turbine exceeds a threshold value.

In this document, as in many other documents of the state of the art, the law for controlling the supercharging of the engine is designed mainly by neglecting the dynamics of the turbocharger which generates a lack of anticipation and therefore precision in regulation.

In fact, the state of the art is based on the assumption that the power required for the turbine corresponds instantaneously to that required for the compressor, which is only true in steady state and which consequently prevents to reach the maximum potential of the turbocharger in certain circumstances, mainly in load transient situations.

Consequently, the problem underlying the invention is to regulate a supercharging of a turbocharged internal combustion engine which takes into account the power differences between the compressor and the turbine of the turbocharger during load transient phases.

To achieve this objective, there is provided according to the invention a method of regulating an air supercharging of an internal combustion engine equipped with a turbocharger comprising a turbine and a compressor, the regulation being done by a determination of a turbocharger position setpoint as a function of a boost pressure setpoint, a compressor power setpoint being established according to the boost pressure setpoint and used for determining the turbocharger position setpoint, characterized in that an inertial power of the compressor, at least during transient operating phases of the turbocharger, is taken into account in establishing the compressor power setpoint.

The solution proposed by the present invention consists in taking into account the inertial power of the turbocharger in the development of the position setpoint of the turbocharger in the control law of the supercharging of an internal combustion engine. The supercharging control law is advantageously expressed as a function of the boost pressure error and not as a function of the speed of rotation, that is to say of the speed, of the turbocharger which is not measured. The result is a more robust and more easily calibrated regulation compared to those of the state of the art directly exploiting the speed of the turbocharger in compensating for inertial power.

The inertial power of the turbocharger is often overlooked in current control solutions by assuming that the power required from the turbine corresponds instantly to that required from the compressor. This simplification does not make it possible to reach the maximum potential of the turbocharger mainly in transient regime and thus to obtain a sufficiently rapid boost pressure increase. This lack of anticipation must then be managed at the level of the boost pressure regulator, thus adding complexity and non-linearity to the latter.

Thus, the regulation method according to the present invention, taking into account the inertial power of the turbocharger, does not make the regulation explicitly a function of the speed of the turbocharger, speed which is not measured and which is therefore a source of error, in particular when the speed of the turbocharger is derived but makes the latter linearly proportional to the boost pressure error, which was not obtained by the methods proposed by the state of the art.

One of the advantages of the present invention is to transform the compensation for inertial power into a linear proportional regulator. This results in easy calibration, since the calculation of the inertial power involves physical data characterized by tests, in particular during the development and design of the turbocharger.

Advantageously, the compressor power setpoint is obtained by a compressor model based on the corrected boost pressure setpoint, obtained by a first regulation loop (PID 1) proportional integral and derivative, the inertial power being then summed at the compressor power setpoint, a sum resulting from the inertial power and the compressor power setpoint being introduced into an inverse model of the turbocharger as a function of a power of the turbine linearizing said sum, the reverse model delivering a setpoint of position of the turbocharger subjected to a second integral and derived proportional regulation loop for regulating the position of the turbocharger, a boost pressure being measured and subtracted from the boost pressure setpoint before the first regulation loop.

Advantageously, a calculation of the inertial power Pinertieiie is done according to the sum of the torques applied to the turbocharger and its angular speed of rotation ω according to the following equation:

Σάω 1 άω ² Torque - ω. J - - ω. J

J being an inertia of the turbocharger and t being time, either by developing the equation by introducing a temperature upstream from the compressor T1, a speed of the turbocharger N and a reduced speed of the turbocharger Nred, it is obtained:

άω ² 1 /2.π \ ² dN ² 1 /2.π \ ² dN ² _d inertial- ₂ ·) _dt ~ \ 60 J ^J dt ~ 2 '\ 60 J ^{J 1} dt the reduced speed Nred being defined as a function the temperature upstream of compressor T1 and the speed of turbocharger N according to the following equation:

Advantageously, the reduced speed Nred depends directly on the operating point in a field of the compressor according to the following equation, f being a function established during a design of the compressor, n _c being a compression ratio of the compressor and Q _corr a corrected compressor flow:

from where :

hired ~ f ( ^π ο Qcorr) hired f (Fc> Qcorr) Advantageously, since the speed of the reduced turbocharger Nred is not known and therefore cannot be derived, a formulation with derivatives is used partial in the inertial power equation Ρίηθπίθιιθ:

/ df ² drcc df ² dQcorr \ ^ inertial J- _dt ⁺ _dt ) it is then posed:

df ²

Qcorr) T

O7T _C df ² b (lÎ _c , Qcorr) ~ u ^ corr a being a partial derivative of the speed of the turbocharger compared to the rate of compressor and b being a partial derivative of the mode of compression u _c of the turbocharger compared to the corrected flow Qcorr .

Advantageously, the derivative of the compression ratio n _c with respect to the time t dir r · "z —fi is approximated by:

dn _c ^a p _u 1 dP _2s dt dt dt

Pu being a total pressure upstream of the compressor and P _2s a static pressure in the plenum, in other words in the intake air distributor of the internal combustion engine, the corrected flow to the compressor Qcorr, as a function of the temperature in upstream of compressor T1, a reference temperature Tref, a reference pressure of compressor Pref, the total pressure upstream of compressor P11 and the flow of compressor Qcomp, given according to the following equation:

Qcorr Qcomp Advantageously, the flow rate of the compressor Qcomp is obtained from a mass balance at the intake in which Vadm is an intake volume, Qremp a flow rate for filling the engine and P2s a static pressure in the plenum:

dP _2s zx

Vadm ~ (Qcomp ~ Qremp) where, assuming that the temporal variation of the temperature in the plenum is very small implying a derivative of the temperature in the plenum T2s with respect to time substantially zero, r being the constant of the ideal gases and T2s a static temperature in the plenum, we obtain for the flow of the compressor Qcomp:

„- ni Vadm dP _2s

Qcomp - Qremp + the filling rate of the motor Qremp being defined by the static reference pressure P2s in the plenum of the engine and, according to a filling model, a being a slope of the filling model and β a shift of the filling model in as constants dependent on an engine operating point:

Qremp ~ ^ P'2s H β the flow rate of the compressor Qcomp then being defined by the following equation:

nnioi Vadm dP _2s

Qcomp - aP ₂ s + β + _{rT2s dt} hence by introducing this last equation into the equation giving the corrected flow to the compressor Qcorr as a function of the flow from the compressor Qcomp, it is obtained:

Qcorr Qcomp „, n. Vadm dP _2s aP _2s + β + —--— rT _2s dt the derivative of Qcorr with respect to time then written:

dt

Qcorr dt & dP _2s | V _a d _m d P _2s dt rT _2s dt ² Advantageously, in the case of a transient phase, it is approximated that a rise in boost pressure is constant with a derivative of the static pressure in the plenum in function of the time remaining constant and a zero second derivative, from where, by introducing this approximation in the equation of the inertial power Pinertielle, it is obtained:

is :

inertial

dP _2s dt Advantageously, the partial derivative of the speed of the turbocharger with respect to the compression ratio ttc of the compressor a and the partial derivative of the speed of the turbocharger with respect to the corrected flow rate Qcorr b are respectively calculated according to the function f established during d '' a design of the turbocharger which gives respectively, this function being in polynomial form with the coefficients p01, p02, p10, p11, p20:

df ² dn _c = pio + fold. Qcorr + 2. p20. n _c df ²

Ô Qcorr = p01 + ρ11π _ε + 2.p02. Q _CO rr Advantageously, the derivative of the static pressure in the plenum as a function of time is calculated according to a difference between a static reference pressure P2s * in the plenum and the static pressure P2s measured in the plenum according to the equation next :

dP _2s _ P? .s - P? .s dt t (k _mo t)

Where T (/ V _word ) is a time constant as a function of the engine speed Nmot representing a characteristic duration of rise in boost pressure determined during transient tests at constant engine speed by calculating the slope of rise in boost, the partial inertial power being given by the following equation:

Other characteristics, objects and advantages of the present invention will appear on reading the detailed description which follows and with regard to the appended drawings given by way of nonlimiting examples and in which:

FIG. 1 is a representation of an embodiment of a flow diagram of the regulation method according to the present invention,

FIG. 2 shows an implementation diagram of a control law for calculating the inertial power preferably used in the regulation method according to the present invention,

FIG. 3 shows a pressure curve Pr in bars as a function of time t in seconds during a rise in boost pressure at constant engine speed,

- Figure 4 shows power curves Pu in kilowatts of compressor and power setpoints as well as inertial power as a function of time t in seconds during a transient phase.

It should be borne in mind that the figures are given by way of examples and are not limitative of the invention. They constitute schematic representations of principle intended to facilitate the understanding of the invention and are not necessarily at the scale of practical applications.

In what follows, reference is made to all the figures taken in combination. When reference is made to one or more specific figures, these figures are to be taken in combination with the other figures for the recognition of the designated numerical references.

Referring to all the figures and mainly to Figure 1, the present invention relates to a method of regulating an air supercharging of an internal combustion engine in particular but not limited to a motor vehicle equipped with a turbocharger comprising a turbine and a compressor.

The regulation is done by determining a position setpoint of the turbocharger Pos comp cons according to a boost pressure setpoint Pr on cons, a power setpoint of the compressor Pu comp cons being established according to the setpoint of boost pressure Pr on cons and used for determining the compressor position setpoint Pos comp cons. By position reference of the turbocharger Pos comp cons, here is meant the position of the actuator of the turbocharger, which for a turbocharger with fixed geometry actuates the discharge valve of the turbine, commonly known as “wastegate” in English, and which for a variable geometry turbocharger powers the movable blades of the turbine.

In Figure 1, without this being limiting, the control of the boost pressure of an internal combustion engine incorporates two integral proportional and derivative regulation loops PID 1 and PID 2.

The first PID 1 regulating loop regulates the boost pressure by delivering a corrected boost pressure setpoint Pr on cons set which is used for calculating the power of the compressor Pu comp then serving to calculate the power setpoint of the compressor Pu comp cons.

The second PID 2 regulation loop regulates the position of the turbocharger with fixed or variable geometry at the intake of the internal combustion engine Mot.

The flow diagram shown in Figure 1 presupposes a measurement of the boost pressure, which is referenced Pr sural mes as well as the position of the turbocharger.

It is well known to those skilled in the art that the supercharging system is very non-linear. These non-linearities are notably intrinsic to the turbocharger. In order to linearize this system vis-à-vis the regulator, an inverse model M inv of the turbine is integrated into the control law.

We thus calculate, from the corrected boost pressure setpoint Pr on cons cor, a compressor power setpoint Pu comp cons. Then, the compressor power setpoint Pu comp cons is translated into the position setpoint Pos comp cons via the inverse model of the turbine M inv.

The present invention proposes to take into account a inertial Pinertial power of the compressor, at least during transient operating phases of the turbocharger, for a correction of the power setpoint of the compressor Pu comp cons.

In order to take into account the inertial power Pinertielle in the control law, it is advantageous to add this term to the power setpoint of the compressor

Pu comp cons before calculating the position setpoint of the turbocharger Pos comp cons via the reverse turbine model M inv. This is achieved by an additional action compared to a flowchart of the state of the art added to the level of the input of the first regulation loop PID1 regulating the boost pressure pressure setpoint Pr on cons to the power setpoint of the compressor Pu comp cons.

The resulting sum of the Pinertial inertial power and the compressor power setpoint Pu comp cons is then introduced into the inverse model M Inv of the turbocharger as a function of the power of the turbine linearizing said sum.

The reverse model M inv delivers a position setpoint for the pos comp pos turbocharger subjected to a second integral and derivative proportional PID 2 regulation loop for regulating the position setpoint of the comp comp cons compressor.

A boost pressure is measured and subtracted from the boost pressure setpoint Pr on cons before the first PID 1 regulation loop.

There will now be described a preferred method of calculating the inertial power Pinertielle which is not limiting in the context of the present invention. Reference will be made mainly to Figure 2.

The calculation of the Pinertial inertial power is based on the sum of the torques applied to the turbocharger and its angular speed of rotation ω according to the following equation:

Σάω 1 άω ²

Couple - ω. J - - ω. J

J being an inertia of the turbocharger and t being time.

By developing the equation and introducing a temperature upstream from the compressor T1, a speed of the turbocharger N and a reduced speed of the turbocharger Nred, the inertial pressure is obtained:

άω ² 1 /2.π \ ² dN ² 1 /2.π \ ² dN ² .

inertial- _dt ~ \ 60 J ^J dt ~ 2 '\ 60 J ^{J 1} dt The reduced speed Nred is defined as a function of the temperature upstream of the compressor T1 and of the speed of the turbocharger N according to the following equation:

Nred The reduced speed Nred can depend directly on the operating point in a field of the compressor according to the following equation, f being a function established during a design of the compressor, ttc being a compression ratio of the compressor and Qcorr a corrected compressor flow:

Nred ~ f Qcorr where:

Nred f ^ Ac 'Qcorr) Since the speed of the reduced Nred turbocharger is not known and therefore cannot be derived, a formulation with partial derivatives can be used in the inertial power equation Pinertielle:

_ _JT ( ^d f ² dn _c ⁹ f ^{2 d} Qcorr \ ^ inertial ~ J- '1 + g ^ _dt ) It is then posed:

df ^{2 α} ( ^π ο Qcorr) ~ g ^ b (lÎ _c , Qcorr) ~ an u ^ corr a being a partial derivative of the speed of the turbocharger compared to the compression ratio n _c of the compressor and b being a partial derivative of the speed of the turbocharger with respect to the corrected flow Qcorr.

The derivative of the compression ratio ttc with respect to time t can be approximated by:

dn _c ^a p _u 1 dP _2s dt dt dt

P11 being a total pressure upstream of the compressor and P2s a static pressure in the plenum of the internal combustion engine.

This approximation is licit because the variation of the total pressure upstream is slow.

The flow corrected to the compressor Qcorr, as a function of the temperature upstream of the compressor T1, of a reference temperature Tref, of a reference pressure of the compressor Pref, of the total pressure upstream of the compressor P11 and of the compressor flow Qcomp, can be given according to the following equation:

Qcorr Qcomp The flow of the compressor Qcomp can be obtained from an intake mass balance in which Vadm is an intake volume, Qremp an engine filling flow and P2s a static pressure in the plenum :

dP _2s xx

Vadm ~ (Qcomp ~ Qremp) Assuming that the temporal variation of the temperature in the plenum is very small implying a derivative of the temperature in the plenum T2s with respect to time substantially zero, r being the constant of the ideal gases and T2s a static temperature in the plenum, we obtain for the flow of the compressor Qcomp:

„_ _ V _{a (} i _m dP _2s

Qcomp - Qremp + βρ The filling rate of the motor Qremp can be defined by the nominal static pressure P2s in the plenum of the engine and, according to a filling model, a being a slope of the filling model and β an offset of the filling model as constants dependent on an engine operating point:

Qremp Q-V'2.s + β The flow rate of the Qcomp compressor can then be defined by the following equation:

η nioi Vadm dP _2s

Qcomp - aPls + β + _dt hence by introducing this last equation in the equation giving the corrected flow to the compressor Qcorr according to the flow of the compressor Qcomp:

Qcorr Qcomp „,„, V _a d _m dP _2s aP _2s + β + —--— rT _2s dt [0052] What is sought is the derivative of Qcorr with respect to time or which is then written:

Qcorr dt

^ adm ^ 2 _S rT _2s dt ² In the case of a transient phase which is the preferential application of the regulation method according to the present invention, as can be seen in FIG. 3, it can be approximated that 'a rise in supercharging pressure is constant with a derivative of the static pressure in the plenum as a function of time remaining constant and a second derivative zero, hence by introducing this approximation into the equation of inertial power Pinertielle it is obtained :

is :

_ 1

Pinertielle dP _2s

at.--.-;-

Pit dt

This equation is easily implementable in the control law provided that the parameters a, b and the second derivative of the static reference pressure P2s with respect to time t are known.

The partial derivative of the speed of the turbocharger with respect to the compression ratio n _c of the compressor referenced a and the partial derivative of the speed of the turbocharger with respect to the corrected flow rate Qcorr referenced b can be respectively calculated according to the function f established during a turbocharger design.

In order to extract the parameters a and b from the characteristics of the compressor during its design or its development, the function f established during a design of the supplier's turbocharger is interpolated in a polynomial form with the coefficients p01, p02, p10, p11, p20 according to:

f (n _c , Qcorr) ² = poo + pio.rc _c + p01. Q _corr + fold. rc _c .Q _C0rr + p20. + p02. Q _corr ² This polynomial approximation is appropriate because the interpolation error does not exceed 2%.

It is then possible to derive this polynomial function with respect to the compression rate ttc and the corrected flow rate Qcorr to calculate a and b:

df ² o, (tî _c , Q _corr ) - plO + pli. Q _corr + 2. p20. tî _c d7l _c df ² b (n _c , Q _corr ) = —--- = p01 + pll7r _c + 2.p02. Q _corr v ^ ccorr dP The derivative of the static pressure in the plenum as a function of time can be calculated according to a difference between a static reference pressure P2s * in the plenum and the static pressure P2s measured in the plenum according to l following equation:

dfizS- _ P-js - P-js dt

Where r (JV _word ) is a time constant as a function of the engine speed Nmot representing a characteristic duration of rise in boost pressure determined during transient tests at constant engine speed by calculating the slope of rise in boost.

FIG. 3 illustrates a slope of rise in boost pressure at constant engine speed, this during a transient phase. The pressure in bars is referenced Pr and is shown as a function of a time t expressed in seconds. The dotted curve characterizes the climb slope with a change in pressure Pr from 1,050 bar to 1,900 bar in less than two seconds.

Pinertial inertial power can then be given by the following equation:

In order to validate the method of regulating the boost pressure according to the present invention, a simulation of a boost pressure transient was carried out. It was thus possible to calculate the value of the inertial power Pinertial by the calculation proposed according to an optional embodiment of the present invention and to highlight the advantage of the proposed embodiment vis-à-vis the power required at turbine during the transitional phase.

Figure 4 shows various power curves P of the turbocharger expressed in kilowatts kW as a function of time t expressed in seconds. In FIG. 4, also referring to FIG. 1, the curve with triangles represents an estimate of the inertial power Pinertielle. The curve with circles represents the power of the Pu comp compressor.

The curve with rectangles represents the power setpoint of the 5 Pu comp cons compressor added to the estimate of the Pinertial inertial power and the curve without distinctive sign represents the power setpoint of the Pu comp cons compressor.

We therefore see the effect of the method according to the present invention taking into account the inertial power Pinertielle on the power required at the turbine in the sum of the 10 power setpoint of the compressor Pu comp cons and the inertial power

Pinertielle. This power required at the turbine will be increased during a transient phase, which will have the effect of requesting a closure of the relief valve or the blades of the larger turbine, which provides better anticipation.

Claims (8)

1. Method for regulating an air supercharging of an internal combustion engine equipped with a turbocharger comprising a turbine and a compressor, the regulation being made by determining a position reference of the turbocharger (Pos comp cons) according to a boost pressure setpoint (Pr on set), a compressor power setpoint (Pu comp cons) being established according to the boost pressure setpoint (Pr on set) and used for determining the setpoint of position of the turbocharger (Pos comp cons), characterized in that an inertial power (Pinertial) of the compressor, at least during transient operating phases of the turbocharger, is taken into account in establishing the compressor power setpoint ( Pu comp cons). 2. Method according to the preceding claim, in which the compressor power setpoint (Pu comp cons) is obtained by a compressor model as a function of the corrected boost pressure setpoint (Pr on corr cons), obtained by a first loop of proportional integral and derivative regulation (PID 1), the inertial power (Pinertial) then being summed to the compressor power setpoint (Pu comp cons), a resulting sum of the inertial power (Pinertial) and the compressor power setpoint (Pu comp cons) being introduced into an inverse model (M inv) of the turbocharger as a function of a power of the turbine linearizing said sum, the inverse model (M inv) delivering a position reference of the turbocharger (Pos comp cons) subjected to a second integral and derived proportional regulation loop (PID 2) for regulating the position of the turbocharger (Pos comp cons), a pressure boost pressure being measured (Pr sural mes) and subtracted from the boost pressure setpoint (Pr on set) before the first regulation loop (PID 1). ³ 3. Method according to any one of the preceding claims, in which a calculation of the inertial power Pinenieiie is made as a function of the sum of the torques applied to the turbocharger and of its angular speed of rotation ω according to the following equation: Σάω 1 άω ² Torque = ω.] - = J being an inertia of the turbocharger and t being time, either by developing the equation by introducing a temperature upstream from the compressor T1, a speed of the turbocharger N and a reduced speed of the turbocharger Nred it is obtained: 1 dm ² 1/2. τη ² dN ² 1 /2.π \ ² dN ² . Gn _ertÎe u _e - ₂ J _dt ~ - ₂ '\ 60) dt "2'UtV' J ^'11 dt diet reduced Nred being defined as a function of the temperature upstream of the compressor T1 and N turbocharger system according to the following equation: N / T-, Method according to the preceding claim, in which the reduced speed Nred depends directly on the operating point in a field of the compressor according to the following equation, f being a function established during a design of the turbocharger, me being a compression ratio of the compressor and Qcorr a corrected compressor flow: Nred f (j ^l c> Qcorr hence red = f (Xc> Qcorr Method according to the preceding claim, in which, since the speed of the Nred reduced turbocharger is not known and cannot therefore be derived, a formulation with partial derivatives is used in the inertial power equation Pinertielle: _, ^d f ^{2 d} Qcorr i'inerUelle G _dt ⁺ _d Q _corr dt it is then posed: df ² a (u _c , Q _corr ) = b (F _c , Q _CO r _r df ² d Q corr a being a partial derivative of the speed of the turbocharger relative to the compression ratio ttc of the compressor and b being a partial derivative of the speed of the turbocharger with respect to the corrected flow rate Qcorr. 6. Method according to the preceding claim, in which the derivative of the compression ratio n _c with respect to time t is approximated by: _d P _2s dt dt P _lt dt P11 being a total pressure upstream of the compressor and P2s a static pressure in the plenum of the internal combustion engine, the corrected flow at the compressor Qcorr, as a function of the temperature upstream of the compressor T1, of a reference temperature Tref, d '' a reference pressure of the compressor Ready, of the total pressure upstream of the compressor P1t and of the flow of the compressor Qcomp, given according to the following equation: Πξ ”p _ref __ f) ^X ! corr vcomp _τ · _D * ref * it 7. Method according to the preceding claim, in which the flow rate of the compressor Qcomp is obtained from an intake mass balance in which Vadm is an intake volume, Qremp is an engine filling flow rate and P2s is a pressure. static in the plenum, t being time, and assuming that the temporal variation of the temperature in the plenum is very small implying a derivative of the temperature in the plenum T2s with respect to time substantially zero, r being the constant of the ideal gases and T2s a static temperature in the plenum, for the flow rate of the compressor Qcomp: ... —f) j. ^ ^adm ^ 2 s Qcomp Qremp “ÿT the filling flow rate of the motor Qremp being defined by the static reference pressure P2s to in the plenum of the motor and, according to a filling model, a being a slope of the filling model and β an offset of the filling model as constants dependent on an engine operating point: Qremp ⁼ s + β the flow rate of the compressor Qcomp then being defined by the following equation: Qcomp ~ aP _2s + β + ^ adm dP ₂ .s rT _2s dt where by introducing this last equation in the equation giving the corrected flow to the compressor Qcorr according to the flow of the compressor Qcomp it is obtained: Qcorr

aP _2s + β + Vgdm. dP ₂ s ^ j Tj rT _2s dt / ^ Tref Ready Pit the derivative of Qcorr with respect to time, writing: dQcorr {JT Pref dP _2s , V _adm d ² P _2s dt ®ref 'Pit ^a dt' rT _2s dt ² 8. Method according to the preceding claim, in which, in the case of a transient phase, it is approximated that a rise in boost pressure is constant with a derivative of the static pressure in the plenum as a function of the time remaining constant and a zero second derivative, from where by introducing this approximation in the equation of the inertial power Pinertielle, it is obtained: Pinertielle 1 dP _2s y-- · —77 “+ EYE Pl Pref T-ref Pit dP _2s dt either: 1 /2.ît \ ² T, / IL \ dP _2s r inertial ~~ TII -JI ^a fT '* ref · ^α | 77 ' 2 \ ÔU / p-.t \ dref i dt \ y ^r ) 9. Method according to the preceding claim, in which the partial derivative of the speed of the turbocharger with respect to the compression ratio ne of the compressor a and the partial derivative of the speed of the turbocharger with respect to the corrected flow rate Qcorr b are respectively calculated according to the function f established when designing the compressor, this function being in polynomial form with the coefficients p01, p02, p10, p11, p20: ôf ² a (Tt _c , Qcorr) ~ ..... = pio + fold. Qcorr + 2- p20. ff _c Qcorr) df ² ri Qcorr pOl + plln _c + 2.p02. Q _corr 10. Method according to the preceding claim, in which the derivative of the static pressure in the plenum as a function of time is calculated according to a difference between a static reference pressure P2s * in the plenum and the static pressure P2s measured in the plenum according to the following equation: dP _2s P? .s * ~ P? .s dt r (N _word ) Where r (N _word ) is a time constant as a function of the engine speed Nmot representing 0 a characteristic duration of rise in boost pressure determined during transient tests at constant engine speed by calculating the slope of rise in boost, the inertial power Pinertieiie being given by the following equation: 1 /2.π \ ² Ί \ I 71 _? \ P _2s * -P _2s Pinertielle ⁼ Z \ ~ 77T} - / - 77i ^a + b. 77 -Pref- ^to 1 777'7; 7 “ 2 \ 60 / P _u \ T _ref I Htynot)