Method to control a supercharged internal combustion engine provided with a turbocharger by means of an estimation of the average power delivered by the turbine of the turbocharger

1. A method to control a supercharged internal combustion engine ( 1 ) by means of a turbocharger ( 12 ) provided with a turbine ( 13 ) and a compressor ( 14 ) which compresses the air taken in and comprising a number of cylinders ( 3 ); the control method comprises the steps of:

determining the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ); and

calculating the average power ( P T ) delivered by the turbine ( 13 ) by means of the following formula:

P

T

_

w

eng

=

K

*



w

TCj



*

w

TC

[

10

]

K: proportionality constant, calculated by means of the relationship of the inertia (J) of the assembly consisting of the turbine ( 13 ) and the compressor ( 14 ) when subjected to rotation with the product of the organic efficiency (η 0 ) of the turbocharger ( 12 ) and the proportionality coefficient (α) linking the j-th harmonic component (P Tj ) of the average power ( P T ) delivered by the turbine ( 13 ) and the average power ( P T ) delivered by the turbine ( 13 );

P T : average power delivered by the turbine ( 13 );

|w TCj |: absolute value of the j-th harmonic component of the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ); wherein, the j-th harmonic component of the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) is equal to the number of cylinders ( 3 ) for a supercharged internal combustion engine ( 1 ) with equally spaced combustions;

w eng : speed of the supercharged internal combustion engine ( 1 ); and

w TC : instantaneous rotation speed of the turbocharger ( 12 ); and

controlling the supercharged internal combustion engine ( 1 ) as a function of the average power ( P T ) delivered by the turbine ( 13 ).

2. A method according to claim 1 , wherein the step of determining the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) comprises the sub-steps of:

detecting, by means of a sensor ( 25 ), in particular by means of a microphone ( 25 ) or an accelerometer ( 25 ), the intensity of a signal generated by the rotation of the turbocharger ( 12 );

determining a frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the sensor ( 25 );

determining the average rotation speed (w) of the turbocharger ( 12 ) as a function of the frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the sensor ( 25 );

building a band-pass filter as a function of the average rotation speed (w) of the turbocharger ( 12 );

filtering, by means of the band-pass filter, the signal generated by the rotation of the turbocharger ( 12 ) detected by the sensor ( 25 ); and

calculating the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) as a function of the period (Δt[s]) of the signal generated by the rotation of the turbocharger ( 12 ) detected by the sensor ( 25 ) and filtered by means of the band-pass filter.

3. A method according to claim 2 , wherein the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) is calculated as a function of the period (Δt[s]) of the signal generated by the rotation of the turbocharger ( 12 ) detected by the first sensor ( 25 ) and filtered by means of the band-pass filter by means of the following formula:

w TC [rpm]=60/ N *(1/Δ t[s ])  [1]

w TC [rpm]: instantaneous rotation speed of the turbocharger ( 12 );

N: number of blades of the compressor ( 14 );

Δt[s]: period of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter.

4. A method according to claim 2 , wherein the period (Δt[s]) of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter is calculated at the points in which the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter takes a value of zero.

5. A method according to claim 4 , wherein the period (Δt[s]) of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter is calculated at the points in which the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter takes a value of zero in the descending segments of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter.

6. A method according to claim 4 , wherein the period (Δt[s]) of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter is calculated at the points in which the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter takes a value of zero in the ascending segments of the signal generated by the rotation of the turbocharger ( 12 ) and filtered by means of the band-pass filter.

7. A method according to claim 2 , and comprising the further steps of:

identifying the maximum amplitude frequencies in the frequency content of the signal generated by the rotation of the turbocharger ( 12 ); and

determining the average rotation speed (w) of the turbocharger ( 12 ) using the maximum amplitude frequencies in the frequency content of the signal generated by the rotation of the turbocharger ( 12 ).

8. A method according to claim 2 , wherein the step of building a band-pass filter as a function of the average rotation speed (w) of the turbocharger ( 12 ) comprises the sub-step of determining an upper cutoff frequency value (w tH ) and a lower cutoff frequency value (w tL ) of the band-pass filter as a function of the average rotation speed (w) of the turbocharger ( 12 ).

9. A method according to claim 8 , wherein the upper cutoff frequency value (w tH ) and the lower cutoff frequency value (w tL ) define a frequency range centered on the average rotation speed (w) of the turbocharger ( 12 ).

10. A method according to claim 2 , and comprising the further steps of:

detecting, by means of a second sensor ( 25 ), the intensity of a signal generated by the rotation of the turbocharger ( 12 );

determining a frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the second sensor ( 25 ); and

determining the instantaneous rotation speed (w TC _ microphone , w TC _ accelerometer ) of the turbocharger ( 12 ) as a function of the frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the second sensor ( 25 ); and

diagnosing a fault when the difference in absolute value between the instantaneous rotation speed (w TC _ microphone , w TC _ accelerometer ) of the turbocharger ( 12 ) as a function of the frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the first sensor ( 25 ) and the instantaneous rotation speed (w TC _ microphone , w TC _ accelerometer ) of the turbocharger ( 12 ) as a function of the frequency content of the signal generated by the rotation of the turbocharger ( 12 ) detected by the second sensor ( 25 ) exceeds a threshold value.

11. A method according to claim 1 , wherein the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) is calculated by means of a sensor designed to detect the passage of the blades ( 28 ) of the compressor ( 14 ) and to determine the instantaneous rotation speed (w TC ) of the turbocharger ( 12 ) itself as a function of the frequency of passage of the blades ( 28 ) of the compressor ( 14 ).

12. A method according to claim 1 and comprising the further step of determining the temperature (T 3 ) upstream of the turbine ( 13 ) by means of the following formula:

T

3

=

P

T

_

m

.

*

η

T

*

(

1

-

(

p

4

p

3

)

γ

-

1

γ

)

[

12

]

P T : average power delivered by the turbine ( 13 );

{dot over (m)}: gas flow rate flowing through the turbine ( 13 );

η T : internal efficiency of the turbine ( 13 );

p 3 : pressure upstream of the turbine ( 13 );

p 4 : pressure downstream of the turbine ( 13 );

T 3 : temperature upstream of the turbine ( 13 ); and

γ: specific heat of the exhaust gases flowing through the turbine ( 13 ).

13. A method according to claim 1 and comprising the further step of determining the pressure (p 3 ) upstream of the turbine ( 13 ) by means of the following formula:

p

3

=

p

4

1

-

P

T

_

m

.

*

η

T

*

T

3

γ

-

1

γ

[

13

]

P T : average power delivered by the turbine ( 13 );

{dot over (m)}: gas flow rate flowing through the turbine ( 13 );

η T : internal efficiency of the turbine ( 13 );

p 3 : pressure upstream of the turbine ( 13 );

p 4 : pressure downstream of the turbine ( 13 );

T 3 : temperature upstream of the turbine ( 13 ); and

γ: specific heat of the exhaust gases flowing through the turbine ( 13 ).

14. A method according to claim 1 and comprising the further step of determining the temperature (T 4 ) downstream of the turbine ( 13 ) by means of the following formula:

T

4

=

P

T

_

m

.

*

η

T

*

(

(

p

3

p

4

)

γ

-

1

γ

-

1

)

[

15

]

P T : average power delivered by the turbine ( 13 );

{dot over (m)}: gas flow rate flowing through the turbine ( 13 );

η T : internal efficiency of the turbine ( 13 );

p 3 : pressure upstream of the turbine ( 13 );

p 4 : pressure downstream of the turbine ( 13 );

T 3 : temperature upstream of the turbine ( 13 ); and

γ: specific heat of the exhaust gases flowing through the turbine ( 13 ).

15. A method according to claim 1 and comprising the further step of determining the pressure (p 4 ) downstream of the turbine ( 13 ) by means of the following formula:

p

4

=

p

3

1

+

P

T

_

m

.

*

η

T

*

T

4

γ

-

1

γ

[

16

]

P T : average power delivered by the turbine ( 13 );

{dot over (m)}: gas flow rate flowing through the turbine ( 13 );

η T : internal efficiency of the turbine ( 13 );

p 3 : pressure upstream of the turbine ( 13 );

p 4 : pressure downstream of the turbine ( 13 );

T 3 : temperature upstream of the turbine ( 13 ); and

γ: specific heat of the exhaust gases flowing through the turbine ( 13 ).

16. A method according to claim 1 and comprising the further step of determining the gas flow rate ({dot over (m)}) flowing through the turbine ( 13 ) by means of any one of the two following formulas:

m

.

=

P

T

_

T

3

*

η

T

*

(

1

-

(

p

4

p

3

)

γ

-

1

γ

)

[

24

]

m

.

=

P

T

_

T

4

*

η

T

*

(

(

p

3

p

4

)

γ

-

1

γ

-

1

)

[

25

]

P T : average power delivered by the turbine ( 13 );

{dot over (m)}: gas flow rate flowing through the turbine ( 13 );

η T : internal efficiency of the turbine ( 13 );

p 3 : pressure upstream of the turbine ( 13 );

p 4 : pressure downstream of the turbine ( 13 );

T 3 : temperature upstream of the turbine ( 13 );

T 4 : temperature downstream of the turbine ( 13 ); and

γ: specific heat of the exhaust gases flowing through the turbine ( 13 ).

17. A method according to claim 1 and comprising the further step of adjusting the quantity of lubricating fluid for the turbocharger ( 12 ) to be circulated as a function of the average power ( P T ) delivered by the turbine ( 13 ).

18. A method according to claim 1 and comprising the further step of determining the average power ( P C ) delivered by the compressor ( 14 ) by means of the following formula:

P

C

_

=

1

η

C

*

η

0

*

P

T

_

[

17

]

P T : average value of the power delivered by the turbine ( 13 );

P C : average value of the power delivered by the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 ); and

η 0 : organic efficiency of the turbocharger ( 12 ).

19. A method according to claim 18 and comprising the further step of determining the temperature (T 1 ) upstream of the compressor ( 14 ) by means of the following formula:

T

1

=

P

C

_

m

.

*

η

C

*

(

(

p

2

p

1

)

γ

-

1

γ

-

1

)

[

19

]

P C : average value of the power delivered by the compressor ( 14 );

{dot over (m)}: flow rate of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 );

p 1 : pressure upstream of the compressor ( 14 );

p 2 : pressure downstream of the compressor ( 14 );

T 1 : temperature upstream of the compressor ( 14 ); and

γ: specific heat of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 ).

20. A method according to claim 18 and comprising the further step of determining the pressure (p 1 ) upstream of the compressor ( 14 ) by means of the following formula:

p

1

=

p

2

1

+

P

C

_

m

.

*

η

C

*

T

1

γ

-

1

γ

[

20

]

P C : average value of the power delivered by the compressor ( 14 );

{dot over (m)}: flow rate of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 );

p 1 : pressure upstream of the compressor ( 14 );

p 2 : pressure downstream of the compressor ( 14 );

T 1 : temperature upstream of the compressor ( 14 ); and

γ: specific heat of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 ).

21. A method according to claim 18 and comprising the further step of determining the temperature (T 2 ) downstream of the compressor ( 14 ) by means of the following formula:

T

1

=

P

C

_

m

.

*

η

C

*

(

1

-

1

/

(

p

2

p

1

)

γ

-

1

γ

)

[

22

]

P C : average value of the power delivered by the compressor ( 14 );

{dot over (m)}: flow rate of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 );

p 1 : pressure upstream of the compressor ( 14 );

p 2 : pressure downstream of the compressor ( 14 );

T 2 : temperature downstream of the compressor ( 14 ); and

γ: specific heat of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 ).

22. A method according to claim 18 and comprising the further step of determining the pressure value (p 2 ) downstream of the compressor ( 14 ) by means of the following formula:

p

2

=

p

1

1

-

P

C

_

m

.

*

η

C

*

T

2

γ

-

1

γ

[

23

]

P C : average value of the power delivered by the compressor ( 14 );

{dot over (m)}: flow rate of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 );

p 1 : pressure upstream of the compressor ( 14 );

p 2 : pressure downstream of the compressor ( 14 );

T 2 : temperature downstream of the compressor ( 14 ); and

γ: specific heat of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 ).

23. A method according to claim 18 and comprising the further step of determining the flow rate ({dot over (m)}) of the gas mixture flowing through the compressor ( 14 ) by means of any one of the two following formulas:

m

.

=

P

C

_

T

2

*

η

2

*

(

1

-

1

/

(

p

2

p

1

)

γ

-

1

γ

)

[

26

]

m

.

=

P

C

_

T

1

*

η

C

*

(

(

p

2

p

1

)

γ

-

1

γ

-

1

)

[

27

]

P C : average value of the power delivered by the compressor ( 14 );

{dot over (m)}: flow rate of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 );

η C : internal efficiency of the compressor ( 14 );

p 1 : pressure upstream of the compressor ( 14 );

p 2 : pressure downstream of the compressor ( 14 );

T 1 : temperature upstream of the compressor ( 14 );

T 2 : temperature downstream of the compressor ( 14 ); and

γ: specific heat of the gas mixture (air and possible recirculated exhaust gases) flowing through the compressor ( 14 ).