Engine torque estimation and control systems and methods

1. An engine control system, comprising:

a normalization module configured to normalize, to within a predetermined range of values, a spark timing of an engine and at least one other parameter of the engine, thereby producing a normalized spark timing and at least one normalized other parameter, respectively;

a processing module configured to generate a sigmoidal spark timing by applying, to the normalized spark timing, one of (a) a sigmoidal function and a sinusoidal function; and

an estimation module configured to estimate a torque output of the engine based on the normalized spark timing and the at least one normalized other parameter using a mathematical model.

2. The engine control system of claim 1 further comprising an actuator module configured to adjust an engine actuator based on the estimated torque output of the engine.

3. The engine control system of claim 1 wherein the at least one other parameter of the engine includes an engine speed.

4. The engine control system of claim 1 wherein the at least one other parameter of the engine includes a mass of air per cylinder (APC) of the engine.

5. The engine control system of claim 1 wherein the at least one other parameter of the engine includes an intake cam phaser angle.

6. The engine control system of claim 1 wherein the at least one other parameter of the engine includes an exhaust cam phaser angle.

7. The engine control system of claim 1 wherein the at least one other parameter of the engine includes an equivalence ratio (EQR) of the engine.

8. The engine control system of claim 1 wherein the at least one other parameter of the engine includes a maximum braking torque (MBT) spark timing of the engine.

9. The engine control system of claim 1 wherein the at least one other parameter of the engine includes:

an engine speed;

a mass of air per cylinder (APO) of the engine;

an intake cam phaser angle;

an exhaust cam phaser angle;

an equivalence ratio (EQR) of the engine; and

a maximum braking torque (MBT) spark timing of the engine.

10. The engine control system of claim 1 wherein the sigmoid function includes a logistic function.

11. The engine control system of claim 1 wherein the at least one other parameter of the engine includes a timing of a start of fuel injection of the engine.

12. The engine control system of claim 1 wherein the at least one other parameter of the engine includes a timing of an end of fuel injection of the engine.

13. The engine control system of claim 1 wherein the processing module is further configured to generate an exponential engine speed by applying an exponential function to an engine speed, and

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential engine speed using the mathematical model.

14. The engine control system of claim 1 wherein the processing module is further configured to generate an exponential of negative engine speed by applying an exponential function to a negative engine speed, and

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential of negative engine speed using the mathematical model.

15. The engine control system of claim 1 wherein the processing module is further configured to generate an exponential maximum braking torque (MBT) spark timing by applying an exponential function to an MBT spark timing of the engine, and

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential MBT spark timing using the mathematical model.

16. The engine control system of claim 1 wherein the processing module is further configured to generate an exponential of negative maximum braking torque (MBT) spark timing by applying an exponential function to a negative MBT spark timing of the engine, and

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential of negative MBT spark timing using the mathematical model.

17. An engine control system, comprising:

a normalization module configured to normalize, to within a predetermined range of values, a maximum braking torque (MBT) spark timing of an engine and at least one other parameter of the engine, thereby producing a normalized MBT spark timing and at least one normalized other parameter, respectively; and

an estimation module configured to estimate a torque output of the engine based on the normalized MBT spark timing and the at least one normalized other parameter using a mathematical model.

18. The engine control system of claim 17 further comprising a processing module configured to generate an exponential MBT spark timing by applying an exponential function to the MBT spark timing of the engine, and

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential MBT spark timing using the mathematical model.

19. The engine control system of claim 17 further comprising a processing module configured to:

generate an exponential MBT spark timing by applying an exponential function to the MBT spark timing of the engine; and

generate an exponential of negative MBT spark timing by applying an exponential function to the negative MBT spark timing of the engine,

wherein the estimation module configured to estimate the torque output of the engine further based on the exponential MBT spark timing and the exponential of negative MBT spark timing using the mathematical model.

20. The engine control system of claim 17 further comprising an MBT module configured to generate the MBT spark timing based on an air per cylinder, an inverse APC, an engine speed, an intake cam phaser angle, an exhaust cam phaser angle, an equivalence ratio, and an opening of an EGR valve.