Injector delivery measurement with leakage correction

1. A method of operating an internal combustion engine having a fuel rail in fluid communication with a fuel pump and a fuel injector, the method comprising:

operating the fuel injector to perform a fuel injection;

sampling a sequence of pressure signals representative of a fuel pressure within the fuel rail during the fuel injection in a crankshaft angular domain;

filtering the sequence of pressure signals to reduce signal noise;

acquiring a first sample of the filtered pressure signals after a top dead center of the fuel pump and before the fuel injection has started in an injection interval;

acquiring a second sample of the filtered pressure signals after the injection and before a next pumping stroke;

calculating a total pressure difference between the first sample and the second sample;

determining a linear pressure slope at least at the second sample and calculating a leakage pressure difference between the first sample and the second sample based on the linear pressure slope;

calculating an injection pressure difference as the difference between total pressure difference and the leakage pressure difference;

calculating a value of a fuel quantity injected by the fuel injection as a function of the calculated value of the injection pressure difference; and

sending a fuel injection command to the fuel injector based on the value of a fuel quantity calculated.

2. The method of claim 1 , further comprising:

acquiring a third sample of the filtered pressure signals after the injection and before a next pumping stroke, wherein the second sample and the third sample are spaced apart from each other;

wherein determining the linear pressure slope includes calculating a pressure difference between the second sample and the third sample and dividing it by the crankshaft angle difference between the second sample and the third sample.

3. The method of claim 2 , wherein the second sample and the third sample are spaced apart about at least 0.05·π of the crankshaft angle.

4. The method of claim 2 , wherein the second sample and the third sample are spaced apart in a range between 0.1·π and 0.2·π of the crankshaft angle.

5. The method of claim 1 , wherein calculating the leakage pressure difference includes multiplying the linear pressure slope at the second sample by the angle difference between the first sample and the second sample.

6. The method of claim 1 , wherein filtering the sequence of pressure signals includes using a SINC filter.

7. The method of claim 6 , wherein the SINC filter is tuned on a rail wave pressure dominant frequency.

8. A fuel injection system comprising:

a fuel pump in fluid communication with a fuel injector through a fuel rail; and

an electronic control unit configured to:

operate the fuel injector to perform a fuel injection;

sample a sequence of pressure signals representative of a fuel pressure within the fuel rail during the fuel injection in a crankshaft angular domain;

filter the sequence of pressure signals so as to reduce signal noise;

acquire a first sample after a top dead center of the fuel pump and before the fuel injection has started in an injection interval;

acquire a second sample after the injection and before a next pumping stroke;

calculate a total pressure difference between the first sample and the second sample;

determine a linear pressure slope at least at the second sample and calculate a leakage pressure difference between the first sample and the second sample based on the linear pressure slope;

calculate an injection pressure difference as the difference between the total pressure difference and the leakage pressure difference;

calculate a value of a fuel quantity injected by the fuel injection as a function of the calculated value of the injection pressure difference; and

send a fuel injection command to the fuel injector based on the value of a fuel quantity calculated.

9. The fuel injection system of claim 8 , further comprising:

choosing a third sample after the injection and before a next pumping stroke, wherein the second sample and the third sample are spaced apart from each other;

wherein determining the linear pressure slope includes calculating a pressure difference between the second sample and the third sample and dividing it by the crankshaft angle difference between the second sample and the third sample.

10. The fuel injection system of claim 9 , wherein the second sample and the third sample are spaced apart about at least 0.05·π of the crankshaft angle.

11. The fuel injection system of claim 10 , wherein the second sample and the third sample are spaced apart in a range between 0.1·π and 0.2·π of the crankshaft angle.

12. The fuel injection system of claim 8 , wherein calculating the leakage pressure difference includes multiplying the linear pressure slope at the second sample by the angle difference between the first sample and the second sample.

13. The fuel injection system of claim 8 , wherein filtering the sequence of pressure signals includes using a SINC filter.

14. The fuel injection system of claim 13 , wherein the SINC filter is tuned on a rail wave pressure dominant frequency.

15. An internal combustion engine comprising:

an engine block having a cylinder with a piston disposed therein and a cylinder head cooperating with the piston to define a combustion chamber;

a fuel pump configured to supply pressurized fuel to a fuel rail;

a fuel injector in fluid communication with the fuel rail and configured to inject fuel into the combustion chamber; and

an electronic control unit configured to:

operate the fuel injector to perform a fuel injection;

sample a sequence of pressure signals representative of a fuel pressure within the fuel rail during the fuel injection in a crankshaft angular domain;

filter the sequence of pressure signals so as to reduce signal noise;

in an injection interval determine a first sample after a top dead center of the fuel pump and before the fuel injection has started;

acquire a second sample after the injection and before a next pumping stroke;

calculate a total pressure difference between the first sample and the second sample;

determine a linear pressure slope at least at the second sample and calculate a leakage pressure difference between the first sample and the second sample based on the linear pressure slope;

calculate an injection pressure difference as the difference between the total pressure difference and the leakage pressure difference;

calculate a value of a fuel quantity injected by the fuel injection as a function of the calculated value of the injection pressure difference; and

send a fuel injection command to the fuel injector based on the value of a fuel quantity calculated.