Control of fuel injection in an internal combustion engine based on converged fuel injector slope

A method for controlling operation of an internal combustion engine in a vehicle having a controller and at least one fuel injector, the controller having a processor and tangible, non-transitory memory, the method comprising:

• configuring the controller to selectively command the at least one fuel injector to deliver a primary fuel injection of a first fuel quantity and a secondary fuel injection of a second fuel quantity, the first fuel quantity being above a predefined threshold and the second fuel quantity being at or below the predefined threshold;
• obtaining a respective desired fuel injection mass for the at least one primary fuel injection and the at least one secondary fuel injection, via the controller;
• commanding the at least one fuel injector to deliver a primary pulse width and a secondary pulse width based in part on the respective desired fuel injection mass and respective initialized values of fuel injector slope, via the controller;
• determining a calculated fuel mass based in part on at least one measured engine variable and obtain an estimated fuel mass based in part on the primary pulse width (WP) and the secondary pulse width, via the controller;
• determining a converged primary fuel injector slope and a converged secondary fuel injector slope based in part on a comparison of the calculated fuel mass and the estimated fuel mass, via the controller;
• and
• controlling operation of the at least one fuel injector based in part on the converged primary fuel injector slope and the converged secondary fuel injector slope.

A system for controlling operation of an internal combustion engine in a vehicle having at least one fuel injector, the system comprising:

• a controller configured to selectively command the at least one fuel injector deliver a primary fuel injection of a first fuel quantity and a secondary fuel injection of a second fuel quantity, the first fuel quantity being above a predefined threshold and the second fuel quantity being at or below the predefined threshold;
• wherein the controller includes a processor and tangible, non-transitory memory on which instructions are recorded, execution of the instructions by the processor causing the controller to:
• obtain a respective desired fuel injection mass for the primary fuel injection and the secondary fuel injection;
• command the at least one fuel injector to deliver a primary pulse width and a secondary pulse width, the primary pulse width and the secondary pulse width being based in part on the respective desired fuel injection mass and respective initialized values of fuel injector slope;
• determine a calculated fuel mass based in part on at least one measured engine variable;
• obtain an estimated fuel mass based in part on the primary pulse width and the secondary pulse width;
• determine a converged primary fuel injector slope and a converged secondary fuel injector slope based in part on a comparison of the calculated fuel mass and the estimated fuel mass;
• and
• control operation of the at least one fuel injector based in part on the converged primary fuel injector slope and the converged secondary fuel injector slope;
• and
• wherein obtaining the converged primary fuel injector slope and converged secondary fuel injector slope includes:
• obtaining a primary fuel injector slope and a secondary fuel injector slope over a plurality of time steps, based in part on the primary pulse width and the secondary pulse width;
• and
• updating the primary fuel injector slope and the secondary fuel injector slope at each of the plurality of time steps by minimizing a difference between the estimated fuel mass and the calculated fuel mass.