Method to determine the mass of air trapped in each cylinder of an internal combustion engine

A method to determine the mass of air trapped in each cylinder of an internal combustion engine, which comprises determining, based on a model using measured and/or estimated physical quantities, a value for a first group of reference quantities; determining, based on the model, the actual inner volume of each cylinder as a function of the speed of rotation of the internal combustion engine and of the closing delay angle of the intake valve; and calculating the mass of air trapped in each cylinder as a function of the first group of reference quantities and of the actual inner volume of each cylinder.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Patent application claims priority from Italian Patent Application No. 102018000010164 filed on Nov. 8, 2018, the entire disclosure of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method to determine the mass of air trapped in each cylinder of an internal combustion engine.

2. Description of the Related Art

As it is known, an internal combustion engine supercharged using a turbocharger supercharging system comprises a number of injectors injecting fuel into respective cylinders, each connected to an intake manifold by at least one respective intake valve and to an exhaust manifold by at least one respective exhaust valve.

The intake manifold receives a gas mixture comprising both exhaust gases and fresh air, i.e. air coming from the outside through an intake duct, which is provided with an air filter for the fresh air flow and is regulated by a throttle valve. Along the intake duct, preferably downstream of the air filter, there is also provided an air flow meter.

The air flow meter is a sensor connected to an electronic control unit and designed to detect the flow rate of fresh air taken in by the internal combustion engine. The flow rate of fresh air taken in by the internal combustion engine is an extremely important parameter for the engine control, in particular to determine the quantity of fuel to be injected into the cylinders so as to obtain a given air/fuel ratio in an exhaust duct downstream of the exhaust manifold. However, the air flow meter typically is a very expensive and fairly delicate component as oil vapours and dust can dirty it, thus altering the reading of the value of the flow rate of fresh air taken in by the internal combustion engine.

SUMMARY OF THE INVENTION

The object of the invention is to provide a method to determine the mass of air trapped in each cylinder of an internal combustion engine, said method being easy and economic to be implemented.

According to the invention, there is provided a method to determine the mass of air trapped in each cylinder of an internal combustion engine as claimed in the appended claims. Other objects, features and advantages of the present invention will be readily appreciated as the same becomes better understood after reading the subsequent description taken in connection with the accompanying drawings.

DETAILED DESCRIPTION OF THE INVENTION

InFIGS.1and2, number1indicates, as a whole, an internal combustion engine, preferably supercharged using a turbocharger supercharging system.

The internal combustion engine1comprises a number of injectors2, which directly inject fuel into four cylinders3(preferably four cylinders arranged in line), each connected to an intake manifold4by at least one respective intake valve5(shown inFIG.3) and to an exhaust manifold6by at least one respective exhaust valve7(shown inFIG.2). For each cylinder3there is provided a corresponding injector2; according to the embodiment shown inFIG.2, the injection is an indirect injection and, therefore, each injector2is arranged upstream of the cylinder3in an intake duct8connecting the intake manifold4to the cylinder3. According to an alternative embodiment which is not shown herein, the injection is a direct injection and, therefore, each injector2is partially arranged inside the cylinder3through the crown end of the cylinder3.

According toFIG.1, each cylinder3houses a respective piston9, which is mechanically connected, by a connecting rod, to a drive shaft10, so as to transmit to the drive shaft10itself, in a known manner, the force generated by the combustion inside the cylinder3.

The intake manifold4receives a gas mixture comprising both exhaust gases (as described more in detail below) and fresh air, i.e. air coming from the outside through the intake duct8, which is preferably provided with an air filter for the fresh air flow and is regulated by a throttle valve12, which preferably is an electronically controlled valve and is movable between a closing position and a maximum opening position. Furthermore, no air flow meter is provided along the intake duct8.

The intake valves5and/or the exhaust valves7are controlled with a VVT (variable valve timing) device, which hydraulically acts upon the shaft operating the intake valves5and or the exhaust valves7, respectively, changing the inclination thereof relative to a drive shaft.

In particular, the position of each exhaust valve7is directly controlled by a cam shaft13, which receives the motion of the drive shaft10; similarly, the position of each intake valve5is directly controlled by a cam shaft14, which receives the motion of the drive shaft10.

Along the intake pipe8there is preferably arranged an intercooler, which fulfils the function of cooling the air taken in and is preferably built-in in the intake manifold4. The exhaust manifold6is connected to an exhaust duct18, which feeds the exhaust gases produced by the combustion to an exhaust system, which releases the gases produced by the combustion into the atmosphere and normally comprises at least one catalytic converter (if necessary, provided with a diesel particulate filter) and at least one silencer arranged downstream of the catalytic converter.

The supercharging system of the internal combustion engine1comprises a turbocharger provided with a turbine, which is arranged along the exhaust duct18so as to rotate at a high speed due to the action of the exhaust gases expelled from the cylinders3, and a compressor, which is arranged along the intake duct8and is mechanically connected to the turbine so as to be caused to rotate by the turbine itself in order to increase the pressure of the air present in the feeding duct8.

The description above explicitly refers to an internal combustion engine1supercharged by using a turbocharger. Alternatively, the control method described above can find advantageous application in any supercharged internal combustion engine, for example an engine supercharged by using a dynamic or volumetric compressor.

According to one variant, along the exhaust duct18there is provided a bypass duct, which is connected in parallel to the turbine so as to have its ends connected upstream and downstream of the turbine itself.

The internal combustion engine1advantageously comprises, furthermore, a high-pressure exhaust gas recirculation circuit EGRHP, which comprises, in turn, a bypass duct connected in parallel to the assembly consisting of the four cylinders3, the intake manifold4and the exhaust manifold6. Along the bypass duct there is provided an EGR valve, which is designed to adjust the flow rate of the exhaust gases flowing through the bypass duct and is controlled by an electric motor. Along the bypass duct, downstream of the EGR valve, there is provided a heat exchanger, which fulfils the function of cooling the gases flowing out of the exhaust manifold.

Alternatively, along the intake duct8there is provided a bypass duct, which is connected in parallel to the compressor so as to have its ends connected upstream and downstream of the compressor itself; along the bypass duct there is provided a valve Poff, which is designed to adjust the flow rate of the air flowing through the bypass duct and is controlled by an electric actuator.

The internal combustion engine1is controlled by an electronic control unit30, which controls the operation of all the components of the internal combustion engine1. In particular, the electronic control unit30is connected to sensors which measure the temperature Toand the pressure Poalong the intake duct8upstream of the compressor and to sensors which measure the temperature and the pressure along the intake duct8upstream of the throttle valve12as well as to a sensor31which measures the temperature and the pressure of the gas mixture present in the intake manifold4. Furthermore, the electronic control unit30is connected to a sensor which measures the angular position (and, hence, the rotation speed) of the drive shaft10and to a sensor (typically a UHEGO or UEGO linear oxygen sensor—which is known and not described in detail) which measures the air/fuel ratio of the exhaust gases upstream of the catalytic converter and, finally, to a sensor which measures the stroke of the intake and/or exhaust valves.

According to one variant, the internal combustion engine1finally comprises a low-pressure exhaust gas recirculation circuit EGRLP, which comprises, in turn, a bypass duct originating from the exhaust duct18, preferably downstream of the catalytic converter, and leading into the intake duct8, upstream of the compressor; the bypass duct is connected in parallel to the turbocharger. Along the bypass duct there is provided an EGR valve, which is designed to adjust the flow rate of the exhaust gases flowing through the bypass duct. Along the bypass duct, upstream of the EGR valve, there is also provided a heat exchanger, which fulfils the function of cooling the gases flowing out of the exhaust manifold6and into the compressor.

In the electronic control unit30there is stored a calculation model, which is used to determine, among other things, the mass m of air trapped in each cylinder3(for each cycle) and the mass MTOTof air taken in by the internal combustion engine1.

The model includes a plurality of input parameters, among which there are: the number of revolutions (rpm), the pressure value in the intake manifold4and other side conditions (such as, for example, the temperature inside the intake manifold4and the temperature of the coolant fluid used in the supercharged internal combustion engine1).

Since the VVT device varies the timing of the intake valves5and the timing of their crossing with the exhaust valves7(i.e. the phase during which the intake valve5and the exhaust valve7are simultaneously open), the model requires to know the following input parameters for each cylinder3as well; some parameters are illustrated schematically inFIG.5(with respect to the top dead center TDC and the bottom dead center BDC) where:

IVCrefrepresents the reference closing angle of the intake valve5;

IVOrefrepresents the reference opening angle of the intake valve5;

EVCrefrepresents the reference closing angle of the exhaust valve7;

EVOrefrepresents the reference opening angle of the exhaust valve7;

IVC represents the closing advance angle of the intake valve5;

IVO represents the opening advance angle of the intake valve5;

EVC represents the closing advance angle of the exhaust valve7; and

EVO represents the opening advance angle of the exhaust valve7.

Through the input parameters listed above, the following quantities are defined:
VVTI=IVC−IVCref=IVO−IVOref[1]
VVTE=EVO−EVOref=EVC−EVCref[2]

VVTIrepresents the angular extent of the opening or closing difference relative to the reference values concerning the intake valve5; and

VVTErepresents the angular extent of the opening or closing difference relative to the reference values concerning the exhaust valve7.

In order to determine the mass m of air trapped in each cylinder3for each cycle, the model uses the ideal gas law (known from the literature), according to which
m=(P*V)/(R*T)  [3]
where:

P represents the mean of the pressure for the engine cycle inside the intake manifold4;

T represents the temperature of the mixture of fresh air and/or exhaust gases inside the intake manifold4;

R represents the constant of the mixture of fresh air and/or exhaust gases; and

V represents the inner volume of the cylinder3, when the respective intake valve5and the respective exhaust valve7are closed).

The ideal gas law [3] was experimentally adjusted for the model by incorporating the constant R of the mixture of fresh air and/or exhaust gases, so that the mass m of air trapped in each cylinder3for each cycle is expressed as follows:
m=P*V*f1(T,P)*f2(TH2O,P)  [4]
wherein TH2Ois the temperature of the internal combustion engine1(preferably expressed through the temperature of the coolant liquid of the internal combustion engine1).

Parameters P, V, T, on the other hand, have the meaning described above for formula [3].

Finally, the ideal gas law [4] was further experimentally adjusted for the filling model so that the mass m of air trapped in each cylinder3for each cycle takes into account the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3or because they were re-sucked into the cylinder3):
m=(P*V−OFF)*f1(T,P)*f2(TH2O,P)  [5]
wherein OFF is the variable (mass) taking into account the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3or because they were re-sucked into the cylinder3).

Parameters P, V, T, again, have the meaning described above for formula [3].

In reference conditions, in order to calibrate the model, the temperature TH2Oof the internal combustion engine1, namely the temperature of the coolant liquid of the internal combustion engine1, is assumed to be equal to 90° C. and the temperature T is assumed to be equal to 40° C.

Functions f1and f2mentioned above are defined in an experimental phase through (2d) maps as a function, respectively, of the pressure P inside the intake manifold4and of the temperature T inside the intake manifold4for function f1and of the pressure P inside the intake manifold4and of the temperature TH2Oof the internal combustion engine1for function f2. It is evident that, in reference conditions (for example, the reference temperature inside the intake manifold4is equal to 25° C.), functions f1and f2have a unitary value.

The inner volume V of the cylinder is variable3(from a geometrical point of view) as a function of the closing advance angle IVC of the respective intake valve5. Indeed, the actual inner volume V of the cylinder3results from the sum of the dead volume VCCof the combustion chamber of the cylinder3(i.e. the volume that is not scavenged by the respective piston9) and of the volume Vcscavenged by the respective piston9until the closing of the respective intake valve5(i.e. of the angle of rotation of the crank relative to the top dead centre PMS).

Hereinafter you can find the kinematic law (known from the literature and not described in detail) used to calculate the inner volume V of the cylinder3in the area of the crank angle indicated with α:

V represents the inner volume of the cylinder3;

VCCrepresents the dead volume of the combustion chamber of the cylinder3;

α represents the angle of rotation of the crank relative to the top dead centre PMS;

r represents the crank radius;

S represents the surface area of the piston9;

L represents the length of the connecting rod;

d represents the offset between the axis of the cylinder3and the rotation axis of the drive shaft10;

λ represents the r/L ratio; and

According to one variant, generally speaking, the inner volume V of the cylinder3is variable as a function of a geometrical factor represented by the closing advance angle IVC of the respective intake valve5, by a dynamic factor represented by the speed n of rotation of the internal combustion engine1(or number of revolutions rpm) and by the pressure P measured for the engine cycle inside the intake manifold4.

In particular, the law [6] to determine the inner volume V of the cylinder3was experimentally adjusted for the model by introducing the two functions fvand fpand is expressed as follows:
V=fV(IVC,n)*fP(P,n)  [7]

Parameters P, n, IVC have the meaning already discussed above.

Furthermore, it should be taken into account that, at the beginning of the intake stroke of any engine cycle, inside the cylinder3there are also the residual gases of the combustion of the previous engine cycle.

From a geometrical point of view, the volume occupied by the residual gases of the combustion of the previous engine cycle can be expressed through the sum of the dead volume VCCof the combustion chamber of the cylinder3and of a volume VCscavenged by the respective piston9inside the cylinder3.

The volume VCscavenged by the piston9inside the cylinder3is variable as a function of the parameter TVC, which is better described below.

In particular, according to a first variant, the volume VCscavenged by the piston9inside the cylinder3corresponds to the volume scavenged by the piston9until the instant in which the respective exhaust valve7closes, in case the respective intake valve5opens following the closing of the respective exhaust valve7.

According to a second variant, the volume VCscavenged by the piston9inside the cylinder3corresponds to the volume scavenged by the piston9until the instant in which the respective intake valve5opens, in case the respective exhaust valve7closes following the opening of the respective intake valve5.

According to a third variant, the volume VCscavenged by the piston inside the cylinder3corresponds to the volume scavenged by the piston9up to the top dead centre PMS, in case the opening instant of the respective intake valve5is prior to said top dead centre PMS. It is evident that, in this case, the volume VCscavenged by the respective piston inside the cylinder3in zero and the inner volume V of the cylinder3corresponds to the dead volume VCCof the combustion chamber of the cylinder3.

In other words, the parameter TVC can alternatively correspond to the closing advance angle EVC of the exhaust valve7or to the greatest value between zero and the smallest value between the closing advance angle EVC of the exhaust valve7and the opening advance angle IVO of the intake valve5.

Since the VVT system changes the timing of the intake valves5and of their overlap with the exhaust valves7, the model also allows for a determination of the mass flow rate flowing during the overlap phase between each intake valve5and the respective exhaust valve7. In the description below, the term overlap defines the phase (time interval) in which each intake valve5and the respective exhaust valve7are simultaneously open.

According to what is schematically shown inFIG.4, the following geometrical quantities are defined (relative to the top dead centre TDC and to the bottom dead centre BDC):

OVL represents the duration of the overlap phase comprised between the closing advance angle EVC of the exhaust valve7and the opening advance angle IVO of the intake valve5;

G represents the centre of gravity of the overlap phase between each intake valve5and the respective exhaust valve7; and

g represents the difference between the top dead centre PMS and the centre of gravity G.

Hereinafter the law (known from the literature and not described in detail) used to calculate the mass flow rate through a section of a duct (or through an orifice) can be determined. In this case, the law is used to calculate the mass MOVLflowing from the exhaust to the intake through the intake valve5and the exhaust valve7:

A represents the area of the passage section;

P represents the pressure downstream of the passage section;

P0represents the pressure at the inlet of the passage section;

T0represents the temperature at the inlet of the passage section;

R represents the constant of the fluid flowing in the passage section; and

B represents the flow compressibility function expressed by the following equation [8′]:

B=2⁢KK-1*(PP0)2K-(PP0)K+1K[8′]
wherein K represents the ratio between the specific heat Cpat constant pressure and the specific heat Cvat constant volume.

The law [8] is experimentally adjusted for the model by integrating it between the instant t1in which the overlap phase begins and the instant t2in which the overlap phase ends according to the equation [9] below:

If the variable dt is replaced with dθ/ω (wherein θ represents the engine angle and ω represents the speed of rotation of the internal combustion engine1), the following equation [10] is obtained:

Finally, assuming that the speed ω of rotation of the internal combustion engine1is constant during the overlap phase, equation [10] can be simplified in the following equation [11]:

In the preceding equations AISrepresents the isentropic area.

Inside the electronic control unit30, equation [11] is further experimentally adjusted for the model so as to obtain the mass MOVLas follows:

Sidrepresents the ideal section;

n represents the speed of the internal combustion engine (1);

P0_REFrepresents the reference pressure upstream of the passage section;

T0_REFrepresents the reference temperature upstream of the passage section;

T0represents the temperature upstream of the passage section;

P0, P represents the pressure upstream and downstream, respectively, of the passage section; and

B represents the compression ratio.

The ideal section Sidof the passage is obtained from the product of two functions, wherein the first function A is experimentally determined through the (2d) map variable as a function of the speed n of the internal combustion engine1and of the parameter OVL, whereas the second function G is experimentally determined through a (2d) map variable as a function of the speed n of the internal combustion engine1and of the parameter g.

The combustion chamber of the cylinder3is considered to be a passage section (preferably upstream and downstream of the respective valves5,7). In case the intake pressure is greater than the exhaust pressure, the “upstream” pressure and temperature to be taken into account are the pressure and the temperature upstream of the intake valve5(and, hence, measured by the sensor present in the intake manifold4); whereas the “downstream” pressure and temperature to be taken into account are the pressure and the temperature downstream of the exhaust valves7and, hence, the pressure and the temperature of the exhaust gases (typically obtained from a model or, if possible, measured using a dedicated sensor).

If the exhaust pressure is greater than the intake pressure, the reverse logic applies; namely, the “downstream” pressure and temperature to be taken into account are the pressure and the temperature upstream of the intake valve5(and, hence, measured by the sensor present in the intake manifold4); whereas the “upstream” pressure and temperature to be taken into account are the pressure and the temperature downstream of the exhaust valves7and, hence, the pressure and the temperature of the exhaust gases (typically obtained from a model or, if possible, measured using a dedicated sensor).

In both cases, we are dealing with mean values over the engine cycle, namely over the 720° of rotation of the drive shaft10.

In case the pressure in the exhaust manifold6is greater than the pressure in the intake manifold4, a portion of the exhaust gases produced by the combustion flows from the combustion chamber towards the intake manifold4; during the following combustion cycle, the exhaust gas portion will be then reintroduced into the combustion chamber through the intake valve5. This operating mode is indicated as “inner EGR” and formula [12] is adjusted by replacing the downstream pressure P0with the exhaust pressure PEXHand by replacing the downstream temperature T0with the exhaust temperature TEXH. Therefore, in this case, the mass MOVLis expressed as follows:

The mass MEGRIof “inner EGR” can be expressed as follows:
MEGRI=MOVL+PEXH*VCC/(R*TEXH)  [14]

Quantities MOVL, PEXH, VCC, R and TEXHhave the meaning already discussed above.

In case the pressure in the intake manifold4is greater than the pressure in the exhaust manifold6, a portion indicated with MSCAVof fresh air inside the intake manifold4during the overlap phase is directly directed towards the exhaust manifold6through the respective exhaust valve7, also dragging towards the exhaust manifold6a residual flow rate MEXH_SCAVof exhaust gases present inside the combustion chamber. This phenomenon, on the other hand, is indicated as “scavenging” and formula [12] is adjusted by replacing the downstream pressure P0with the pressure P of the incoming air (flowing into the intake manifold4), by replacing the upstream pressure P with the exhaust pressure PEXHand by replacing the downstream pressure T0with the temperature TAIRof the incoming air (flowing into the intake manifold4). Therefore, in this case, the mass MOVLis expressed as follows:

The residual flow rate MEXH_SCAVof exhaust gases present inside the combustion chamber and dragged towards the exhaust manifold6can be expressed as follows:
MEXH_SCAV=fSCAV(MOVL,n)*PEXH*VCC(R*TEXH)  [16]

Quantities MOVL, n, PEXH, VCC, R and TEXHhave the meaning already discussed above. The function fSCAVis experimentally determined through a (2d) map variable as a function of the speed n of the internal combustion engine1and of the mass MOVL.

The portion MSCAVof fresh air inside the intake manifold4directly directed towards the exhaust manifold6through the respective exhaust valve7during the overlap phase can hence be expressed as follows:
MSCAV=MOVL−MEXH_SCAV[17]

In other words, the portion MSCAVof fresh air inside the intake manifold4directly directed towards the exhaust manifold6is equal to the mass MOVLminus the residual flow rate MEXH_SCAVof exhaust gases present inside the combustion chamber and dragged towards the exhaust manifold6.

The model is finally suited to determine the variable OFF, which takes into account the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3or because they were re-sucked into the cylinder3). The calculation of the variable OFF changes as a function of the work conditions, in particular as a function of the ratio between the pressure in the intake manifold4and the pressure in the exhaust manifold6.

In case the pressure in the exhaust manifold6is greater than the pressure in the intake manifold4(“inner EGR” operating mode), the variable OFF corresponds to the total mass MEGRIof “inner EGR” expressed through formula [14].

On the other hand, in case the pressure in the intake manifold4is greater than the pressure in the exhaust manifold6(“washing” operating mode), the variable OFF is expressed through the following formula [16]:
OFF=PEXH*VCC/(R*TEXH)−MEXH_SCAV[18]

In case the pressure in the intake manifold4is greater than the pressure in the exhaust manifold6, indeed, the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3) are at least partially directly directed towards the exhaust manifold6during the overlap phase through the respective exhaust valve7. The value assumed by the variable OFF is substantially positive or equal to zero in case the entire flow rate of the gases produced by the combustion in the previous work cycle and present inside the cylinder3is directly directed towards the exhaust manifold6during the overlap phase; the electronic control unit30is configured to saturate the variable OFF to the zero value.

According to a further variant, in case, due to dynamic and cooling effects of the combustion chamber of the cylinder3, the variable OFF assumes a negative value, the electronic control unit30is configured to saturate the variable OFF to a negative value.

According to a further variant, the ideal gas law [5] can be further generalized in the way expressed by formulas [19] and [20] below in order to estimate the mass m of air trapped in the cylinder3:
m=(P*V−OFF)*Kt*K1(VVTI,VVTE)*K2(VVTE,n)  [19]
m=(P*V(IVC,n)*K(P,n)−OFF)*Kt*K1*K2[20]
where:

Ktrepresents the product of the previously discussed functions f1(T, P) and f2(TH2O, P);

OFF represents the variable (mass) taking into account the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3or because they were re-sucked into the cylinder3);

K1(VVTI, VVTE) is a multiplying coefficient taking into account the angular extent VVTIof the difference relative to the reference values of the intake valve5and the angular extent VVTEof the difference relative to the reference values of the exhaust valve7; and

K2(VVTE, n) is a multiplying coefficient taking into account the angular extent VVTEof the difference relative to the reference values of the exhaust valve7and the speed n of rotation of the internal combustion engine1(or number of revolutions rpm).

The law [19] used to obtain the mass m of air trapped in the cylinder3is used as model to calculate the quantity of fuel to be injected into the cylinder3in order to obtain an objective value of the air/fuel ratio of the exhaust gases. In other words, once the mass m of air trapped in each cylinder3for each cycle has been determined through the model, the electronic control unit30determines the quantity of fuel to be injected into the cylinder3allowing the objective value of the air/fuel ratio of the exhaust gases to be reached.

According to one embodiment, in the electronic control unit30there is also stored a calculation chain which, from the request for torque made by the user by acting upon the accelerator pedal, is capable of providing the mass mobjof combustion air needed by each cylinder3to fulfil the torque request. The calculation chain requires the user to act upon the accelerator pedal, thus determining, through maps stored in the electronic control unit30and knowing the speed n of rotation of the internal combustion engine1(or number of revolutions), the torque Crrequested to the drive shaft10; the torque Crrequested to the drive shaft10is then preferably added to the pumping torques and to the torques of the auxiliary elements so as to obtain the total torque Ctrequested to the drive shaft10; then the torque Ct* requested for each cylinder3is calculated. Once the torque Ct* requested for each cylinder3has been determined, the calculation chain determines the mass mobjof combustion air needed by each cylinder3to obtain said torque value Ct*.

Once the mass mobjof combustion air needed by each cylinder3to obtain said torque value Ct* has been obtained, the electronic control unit30is designed to use law [19] or [20] of the model in a reverse manner relative to what discussed above. In other words, for a given value of the mass mobjof combustion air needed by each cylinder3(which, in this case, corresponds to the mass m of air trapped in each cylinder3for each cycle in formula [19] or [20]), law [19] or [20] is used to calculate the objective pressure value POBJinside the intake manifold4. In particular, by replacing the mass m of air trapped in each cylinder3for each cycle with the mass mobjof combustion air needed by each cylinder3and by replacing the mean P of the pressure for the engine cycle inside the intake manifold4with the objective pressure value POBJinside the intake manifold4in formula [20], the following law [21] is obtained:
POBJ=[mobj/(Kt*K1*K2)+OFF]/(V(IVC,n)*K(P,n))  [21]

The throttle valve12is controlled by the electronic control unit30so as to obtain, inside the intake manifold4, the objective pressure value POBJdetermined through law [21].

The model stored inside the electronic control unit30uses measured and/or estimated physical quantities (such as, for example, the temperature and pressure values) and measured and/or objective physical quantities (such as, for example, the VVT timing of the intake valves5and of their overlap with the exhaust valves7).

In case the internal combustion engine1comprises the low-pressure exhaust gas recirculation circuit EGRLP, the total mass MEGR_TOTrecirculated through the low-pressure circuit EGRLPis calculated through formula [8], which was discussed in the description above.

On the other hand, the mass MEGRrecirculated through the low-pressure circuit EGRLPfor each cylinder3is calculated through the following formula:
MEGR=MEGR_TOT/(n*120*NCYL)  [22]
where:

n represents the speed of rotation of the internal combustion engine1(or number of revolutions rpm);

NCYLrepresents the number of cylinders3; and

MEGR_TOrepresents the total mass recirculated through the low-pressure circuit EGRLPcalculated by the electronic control unit30with a model or, alternatively, measured using a dedicated sensor.

MEGRrepresents the mass recirculated through the low-pressure circuit EGRLPfor each cylinder3.

Hence, laws [19] and [20] can be further generalized as follows in order to also take into account the mass MEGRrecirculated through the low-pressure circuit EGRLP:
m=(P*V−OFF)*Kt*K1*K2−MEGR[23]
m=(P*V(IVC,n)*K(P,n)−OFF)*Kt*K1*K2−MEGR[24]
where:

Ktrepresents the product of the previously discussed functions f1(T, P) and f2(TH2O, P);

OFF represents the variable (mass) taking into account the gases produced by the combustion in the previous work cycle and present inside the cylinder3(because they did not flow out of the cylinder3or because they were re-sucked into the cylinder3);

MEGRrepresents the mass recirculated through the EGR circuit for each cylinder3; and

K1K2are the empirical multiplying coefficients taking into account the angular extent VVTIof the difference relative to the reference values of the intake valve5, the angular extent VVTEof the difference relative to the reference values of the exhaust valve7and the speed n of rotation of the internal combustion engine1(or number of revolutions rpm).

The description above, which deals with the calculation of the mass MEGRrecirculated through the low-pressure circuit EGRLPfor each cylinder3, can also be applied, in an equivalent manner, in case of a high-pressure exhaust gas recirculation circuit EGRHP.

Finally, the total mass MTOTof air taken in by the internal combustion engine1is calculated through the following formula:
MTOT=(m+MSCAV+MEXH_SCAV)*NCYL[23]
where:

MTOTrepresents the total mass of air taken in by the internal combustion engine1;

m represents the mass of air trapped in each cylinder3;

MSCAVrepresents the portion of fresh air inside the intake manifold4directly directed towards the exhaust manifold6for each cylinder3through the respective exhaust valve7during the overlap phase and obtained using formula [17];

MEXH_SCAVrepresents the mass of exhaust gases present in the cylinder3from the previous cycle and expelled, upon exhaust, by the scavenging flow; and

NCYLrepresents the number of cylinders3.

On the other hand, the mass of gases OFF produced by the combustion in the previous work cycle and present inside the cylinder3, in case the pressure of the intake manifold4is greater than the pressure in the exhaust manifold6, is calculated through the following equation:
OFF=PEXH*VCC/(R*TEXH)−MEXH_SCAV
where:

PEXHrepresents the pressure of the gas flow in the exhaust;

TEXHrepresents the temperature of the gas flow in the exhaust;

VCCrepresents the dead volume of the combustion chamber of the cylinder3;

MEXH_SCAVrepresents the residual mass of exhaust gases present inside the combustion chamber of the cylinder3and directly directed towards the exhaust manifold6through the respective exhaust valve7; and

R represents the constant of the mixture of fresh air and/or exhaust gases.

If the internal combustion engine1comprises a low-pressure gas recirculation circuit, the method comprises the further steps of calculating a quantity REGRindicating the incidence of a low-pressure circuit on the gas mixture flowing in the intake duct6:
REGR=MEGR_LP/MTOT
where:

MTOTrepresents the mass of the gas mixture flowing through the intake duct6;

MEGR_LPrepresents the mass of exhaust gases recirculated through the low-pressure circuit which flows in the intake duct6; and calculating the mass of gases OFF produced by the combustion in the previous work cycle and present inside the cylinder3using the following equation:
OFF=PEXH*VCC/(R*TEXH)−MEXH_SCAV*(1−REGR)

The mass of gases OFF produced by the combustion in the previous work cycle and present inside the cylinder3is caused to be equal to zero (is saturated), in case the entire flow rate of gases produced by the combustion in the previous work cycle and present inside the cylinder3is directly directed towards the exhaust manifold6during the overlap phase through the respective exhaust valve7.

On the other hand, the residual mass MEXH_SCAVof exhaust gases is calculated as a function of the mass MOVLflowing from the intake to the exhaust through the intake valve5and the exhaust valve7. The residual mass MEXH_SCAVof exhaust gases is calculated as a function of the speed n of rotation of the internal combustion engine1. The residual mass MEXH_SCAVof exhaust gases is advantageously calculated as a function of the pressure PEXHand of the temperature TEXHof the gas flow in the exhaust and of the dead volume VCCof the combustion chamber of the cylinder3.

The residual mass MEXH_SCAVof exhaust gases is, in particular, calculated using the following equation:
MEXH_SCAV=f(MOVL,n)*PEXH*VCC/(R*TEXH)  [14]
where:

PEXH, TEXHrepresent the pressure and temperature of the gas flow in the exhaust;

VCCrepresents the dead volume of the combustion chamber of the cylinder3;

n represents the speed of rotation of the internal combustion engine1; and

MOVLrepresents the mass flowing from the exhaust to the intake and sucked again into the cylinder3, during the intake stroke, through the intake valve5.

The residual mass MEXH_SCAVof exhaust gases is calculated using the following equation:
MEXH_SCAV=MOVL*f(MOVL,n)*g1(G,n)
where:

n represents the speed of rotation of the internal combustion engine1;

MOVLrepresents the mass flowing from the intake to the exhaust through the intake valve5and the exhaust valve7; and

G represents the centre of gravity of the overlap phase.

Function g1is defined in an experimental phase through a (2d) map as a function of the speed n of rotation of the internal combustion engine1and of the centre G of gravity of the overlap phase, respectively.

The mass MOVLis determined using the following equation:

Sidrepresents the ideal section;

n represents the speed of the internal combustion engine (1);

P0_REFrepresents the reference pressure upstream of the passage section (or overlap);

T0_REFrepresents the reference temperature upstream of the passage section (or overlap);

T0represents the temperature upstream of the passage section (or overlap); and

P0, P represent the pressure upstream and downstream, respectively, of the passage section (or overlap).

The development of function β is shown inFIG.5as a function of the compressibility factor P/P0. Function β is experimentally characterized as a function of the speed n of the internal combustion engine1.

The ideal section S is calculated as the product between a first function A of the speed n of the internal combustion engine1and of the duration OVL of the overlap phase, during which each intake valve5and the respective exhaust valve7are simultaneously open, and a second function G of the speed n of the internal combustion engine1and of the angular difference between the top dead centre PMS and the centre of gravity G of the overlap phase.

The mass (m) of air trapped in each cylinder3is further calculated as a function of a number of (two) multiplying coefficients K1, K2, which take into account the angular extent VVTIof a difference relative to the reference values of the intake valve5, the angular extent VVTEof a difference relative to the reference values of the exhaust valve7and the speed n of rotation of the internal combustion engine1.

In one embodiment, the mass m of air trapped in each cylinder3is calculated as a function of a first multiplying coefficient K1, which takes into account the angular extent VVTIof a difference relative to the reference values of the intake valve5and the angular extent VVTEof a difference relative to the reference values of the exhaust valve7, and of a second multiplying coefficient K2, which takes into account the speed n of rotation of the internal combustion engine1and the angular extent VVTEof a difference relative to the reference values of the exhaust valve7.

In case the internal combustion engine1further comprises the exhaust gas recirculation circuit EGRLP, EGRLP, the method involves determining the mass m of air trapped in each cylinder3also as a function of a mass MEGRrecirculated through the circuit EGRLP, EGRLPfor each cylinder3.

Hence, the mass m of air trapped in each cylinder3is calculated using the following formula:
m=(P*V−OFF)*f1(T,P)*f2(TH2O,P)*−MEGR[22]
where:

f1f2are functions taking into account the temperature T inside the intake manifold4, the intake pressure P and the temperature TH2Oof the coolant fluid of the internal combustion engine1;

OFF represents the mass of gases produced by the combustion in the previous work cycle and present inside the cylinder3; and

MEGRrepresents the mass recirculated through the EGR circuit for each cylinder3.

The dead volume VCCof the combustion chamber of the cylinder3is a function of the speed n of rotation of the internal combustion engine1and of a first parameter TVC, which is alternatively equal to the closing delay angle EVC of the exhaust valve7or to the greatest value between zero and the smallest value between the closing delay angle EVC of the exhaust valve7and the value of the opening advance angle IVO of the intake valve5multiplied by −1. The volume is determined using a map, which is a function of the speed of rotation n of the internal combustion engine1and of the first parameter TVC, and using a map, which is a function of the speed n of rotation of the internal combustion engine1and of the duration OVL of the overlap phase.

The method further comprises determining, based on a calculation model using measured and/or estimated physical quantities, the mass mobjof combustion air needed by each cylinder3in order to fulfil the torque request Ct*; and determining the objective pressure value POBJinside the intake manifold4based on said model as a function of the mass mobjof combustion air needed by each cylinder3in order to fulfil the torque request Ct*, of the actual inner volume V of each cylinder3and of the first group of reference quantities. The method further involves controlling the throttle valve12to obtain the objective pressure value POBJinside the intake manifold4.

Finally, the method comprises detecting a first angular extent VVTIof the opening or closing difference relative to the reference values concerning the intake valve5; acquiring the reference closing angle IVCrefof the intake valve5; and determining the closing delay angle IVC of the intake valve5using the respective reference angle IVCrefand the first angular extent VVTI. Furthermore, the method comprises detecting a second angular extent VVTEof the opening or closing difference relative to the reference values concerning the exhaust valve7; acquiring the reference closing angle EVCrefof the exhaust valve7; and determining the closing delay angle EVC of the exhaust valve7using the respective reference angle EVCrefand the second angular extent VVTE.

The mass MSCAVof fresh air inside the intake manifold4directly directed towards the exhaust manifold6is calculated as the difference between the mass Move, flowing through the overlap and the residual mass MEXH_SCAVof exhaust gases present inside the combustion chamber of the cylinder3and directly directed towards the exhaust manifold6through the respective exhaust valve7.

In case the internal combustion engine1comprises the low-pressure exhaust gas recirculation circuit, the method comprises calculating the quantity REGRand calculating the mass MSCAVof fresh air inside the intake manifold4directly directed towards the exhaust manifold6using the following formula:
MSCAV=(MOVL−MEXH_SCAV)*(1−REGR)

It is then possible to use the masses for each cylinder3and for each engine cycle in order to calculate the flow rates of the internal combustion engine1, taking into account the number of cylinders3and the engine speed n (in particular, multiplying the number of cylinders3by the engine speed n multiplied by ½).

The description above explicitly relates to a supercharged internal combustion engine1, but the strategy described herein can also find advantageous application in an internal combustion engine1which is not provided with a supercharging system.

The advantages of the model described herein are evident from the description above.

In particular, the model described herein represents a method that allows manufacturers to determine the mass m of air trapped in each cylinder3, the total mass MTOTof air taken in by the internal combustion engine1, the scavenging mass MSCAVand the inner EGR mass MEGRIin a manner that is deemed to be efficient (i.e. with an adequate precision), effective (i.e. quickly and without requiring an excessive calculation power for the electronic control unit30) and economic (i.e. without requiring the installation of expensive additional components and/or sensors, such as for example the air flow meter).