Systems and methods for determining indicated mean effective pressure

An engine control method for a vehicle, comprising:

• determining a target sequence for at least activating and deactivating the next N cylinders in a firing order of an engine based on a torque request,
• wherein N is an integer greater than or equal to two;
• activating and deactivating the next N cylinders in the firing order of the engine according to the target sequence;
• determining a plurality of coefficients and an offset value based on the target sequence, an engine speed, and an engine load;
• and
• determining an IMEP of a first cylinder based on:
• the plurality of coefficients;
• the offset value;
• and
• a plurality of engine speeds at a predetermined crankshaft positions, respectively.

An engine control system of a vehicle, comprising:

• a cylinder control module configured to:
• determine a target sequence for at least activating and deactivating cylinders of an engine based on a torque request;
• and
• activate and deactivate the cylinders of the engine according to the target sequence;
• a values module configured to determine, based on the target sequence a plurality of coefficients and an offset value;
• an indicated mean effective pressure (IMEP) determination module configured to determine an IMEP of a first cylinder based on:
• the plurality of coefficients;
• the offset value;
• and
• a plurality of engine speeds at a predetermined crankshaft positions, respectively;
• and
• a kinetic energy module configured to:
• determine a first kinetic energy for an expansion stroke of the first cylinder based on:
• a first engine speed at a first predetermined crankshaft position during the expansion stroke of the first cylinder;
• and
• a second engine speed at a second predetermined crankshaft position during the expansion stroke of the first cylinder;
• determine a second kinetic energy for a compression stroke of the first cylinder based on:
• a third engine speed at a third predetermined crankshaft position during the compression stroke of the first cylinder;
• and
• a fourth engine speed at a fourth predetermined crankshaft position during the compression stroke of the first cylinder;
• determine a third kinetic energy for an expansion stroke of a second cylinder that is before the first cylinder in a predetermined firing order of the engine based on:
• a fifth engine speed at a fifth predetermined crankshaft position during the expansion stroke of the second cylinder;
• and
• a sixth engine speed at a sixth predetermined crankshaft position during the expansion stroke of the second cylinder;
• determine a fourth kinetic energy for a compression stroke of the second cylinder based on:
• a seventh engine speed at a seventh predetermined crankshaft position during the compression stroke of the second cylinder;
• and
• an eighth engine speed at an eighth predetermined crankshaft position during the compression stroke of the second cylinder;
• determine a fifth kinetic energy for an expansion stroke of a third cylinder that is after the first cylinder in the predetermined firing order based on:
• a ninth engine speed at a ninth predetermined crankshaft position during the expansion stroke of the third cylinder;
• and
• a tenth engine speed at a tenth predetermined crankshaft position during the expansion stroke of the third cylinder;
• and
• determine a sixth kinetic energy for a compression stroke of the third cylinder based on:
• an eleventh engine speed at an eleventh predetermined crankshaft position during the compression stroke of the third cylinder;
• and
• a twelfth engine speed at a twelfth predetermined crankshaft position during the compression stroke of the third cylinder,
• wherein the IMEP module is configured to determine the IMEP of the first cylinder based on:
• the plurality of coefficients;
• the offset value;
• and
• the first, second, third, fourth, fifth, and sixth kinetic energies.