Engine Management

Conclude the discussion about angles.

For operation of an engine, the measurements are all done as angles. Angle of advancement, angle of dwell, and top dead center reference. Switching over a little to engine operation theory... an engine running as a four cycle motor, each cylinder has four points of reference, two are at the upper limit of the stroke, and two at the lower limit of the stroke. The four cycles are the transitions between each of the four states, 1 compression/ignition, 2 power, 3 exhaust, and 4 fueling. The position when the piston is at the upper limit on the compression cycle is called its top dead center. For reference in an engine system, cylinder 1 is the reference, and its top dead center (TDC) is considered zero degrees. Because each cylinder has four cycles, return to TDC occurs every 720 degrees. Also, because each cylinder has four cycles, and operations are tied  to which cycle is in operation, the two rotations is referred to as a cam cycle, because the cam shaft is the device that controls the opening and closing of the valves at the proper time (in mechanical systems).

Each of the pistons is spaced out to provide an ignition at equally spaced locations along the 720 degree cam rotation. This means each cylinder will have a referencing TDC angle. The angle is dependent on the number of cylinders. For a 4 cylinder motor, the TDCs will be at 0 degrees, 180 degrees, 360 degrees, and 540 degrees. Likewise, for a 6 cylinder, the TDCs will be at 0 degrees, 120 degrees, 240 degrees, 360 degrees, 480 degrees, and 600 degrees.  This will be important in just a little bit.

Remembering from before, the angular measurement is 32768 degrees per rotation. so the conversion is angle * 32768 / 360. Many of the angles have direct conversions with no remainder portion (truncated values), but some do. It is important to have update values for the crank teeth. For some tooth configurations, like the common 4x the tooth angle is easily divisible to a whole number, however many advance wheels like 24x or 60-2 do not divide into convenient whole numbers. a quick mechanism for providing angular location. The method used is a carry over from the same one used to draw straight lines on pixel based displays. The method uses an error and correction operation to provide a running update of the angle to maintain a "close as possible" angle. The process works like this...

A value of degrees per tooth is calculated as degrees per rev divided by teeth per crank, which provides a truncated integer division. The error correction value is the remainder after division or mod. The equations then are:

toothAngle = DEG_PER_REV / teeth;

toothError = DEG_PER_REV % teeth;

The values are based on the number of teeth and are constant during runtime. This means, they are calculated in the engine off time, and don't impact the operation timing of engine running. The procedure works in a rather simple way. At each tooth interrupt, a value of cam angle is incremented by the value toothAngle, and at the same time, a cam error is incremented by toothError. When the value of cam error is greater than or equal to the value of teeth, the threshold is reached, and the cam angle is incremented by 1 and the cam error is corrected by subtracting the value of teeth. This provides a running value of the angle of the engine at the most recent tooth interrupt.

The result is having the timer tic value of the most recent tooth interrupt (crkTime), the angle in the cam rotation of the most recent tooth interrupt (camAngle), and the predicted time until the next tooth interrupt event (crkDiff). With this information, it is possible to perform conversions between time and angle, resulting in creating predicted event times for setting timer interrupts. Because the conversions require math (multiplies and divides) also for providing values of proper precision, are performed using 32bit numbers, it is necessary to limit the amount of repetition and unnecessary conversion.

The solution presented here is to use a window of operation. The window will exist based on the most current values of crkTime, crkDiff, and camAngle. Because an operation is needed, the window should be forward of the current position (>camAngle). The system here uses a value of 1/2 the tooth angle. This is the value that is used for "min", or the front edge of the window. The value of "max" will be one tooth angle after "min" with the idea being, from mid tooth to mid tooth. The basis of the operation is to perform an angle based comparison of the event angle to the min and max value. If the event angle falls between the min and max value, then the angle is converted to a time and the timers are updated to generate an event.

In this installment, I will just provide snippets of code to add as correction to existing source. In the next session, I will provide the full file sources.

/* in rtUpdateIgn() in the engine off section */
...
toothAngle = DEG_PER_REV / teeth;
toothError = DEG_PER_REV % teeth;

/* in ISR(INT0_vect) after the if (isInt0Low... */
  camAngle += toothAngle;
  camError += toothError; if (toothError >= teeth) { camAngle++; camError -= teeth; }
...
/* this doesn't provide correction for partial error correction */
  min = camAngle + (toothAngle / 2);
  max = min + toothAngle;
...
/* this is actually a good place to invoke the scheduler, as long as it isn't */
/* called to do too much in its operation. */

The basis of the scheduler does a simple operation based on min and max

/* because min and max are unsigned values making provision for wrap around is done */
/* as duplication of similar operation (just easier than making things complex) */
if (min < max)
     if ((min < eventAngle) && (eventAngle <= max)) { /* convert and update single event timers */ }
} else {
     if ((min < eventAngle) || (eventAngle <= max)) { /* convert and update single event timers */ }
}

Conclude the discussion about angles.

For operation of an engine, the measurements are all done as angles. Angle of advancement, angle of dwell, and top dead center reference. Switching over a little to engine operation theory... an engine running as a four cycle motor, each cylinder has four points of reference, two are at the upper limit of the stroke, and two at the lower limit of the stroke. The four cycles are the transitions between each of the four states, 1 compression/ignition, 2 power, 3 exhaust, and 4 fueling. The position when the piston is at the upper limit on the compression cycle is called its top dead center. For reference in an engine system, cylinder 1 is the reference, and its top dead center (TDC) is considered zero degrees. Because each cylinder has four cycles, return to TDC occurs every 720 degrees. Also, because each cylinder has four cycles, and operations are tied  to which cycle is in operation, the two rotations is referred to as a cam cycle, because the cam shaft is the device that controls the opening and closing of the valves at the proper time (in mechanical systems).

Each of the pistons is spaced out to provide an ignition at equally spaced locations along the 720 degree cam rotation. This means each cylinder will have a referencing TDC angle. The angle is dependent on the number of cylinders. For a 4 cylinder motor, the TDCs will be at 0 degrees, 180 degrees, 360 degrees, and 540 degrees. Likewise, for a 6 cylinder, the TDCs will be at 0 degrees, 120 degrees, 240 degrees, 360 degrees, 480 degrees, and 600 degrees.  This will be important in just a little bit.

Remembering from before, the angular measurement is 32768 degrees per rotation. so the conversion is angle * 32768 / 360. Many of the angles have direct conversions with no remainder portion (truncated values), but some do. It is important to have update values for the crank teeth. For some tooth configurations, like the common 4x the tooth angle is easily divisible to a whole number, however many advance wheels like 24x or 60-2 do not divide into convenient whole numbers. a quick mechanism for providing angular location. The method used is a carry over from the same one used to draw straight lines on pixel based displays. The method uses an error and correction operation to provide a running update of the angle to maintain a "close as possible" angle. The process works like this...

A value of degrees per tooth is calculated as degrees per rev divided by teeth per crank, which provides a truncated integer division. The error correction value is the remainder after division or mod. The equations then are:

toothAngle = DEG_PER_REV / teeth;

toothError = DEG_PER_REV % teeth;

The values are based on the number of teeth and are constant during runtime. This means, they are calculated in the engine off time, and don't impact the operation timing of engine running. The procedure works in a rather simple way. At each tooth interrupt, a value of cam angle is incremented by the value toothAngle, and at the same time, a cam error is incremented by toothError. When the value of cam error is greater than or equal to the value of teeth, the threshold is reached, and the cam angle is incremented by 1 and the cam error is corrected by subtracting the value of teeth. This provides a running value of the angle of the engine at the most recent tooth interrupt.

The result is having the timer tic value of the most recent tooth interrupt (crkTime), the angle in the cam rotation of the most recent tooth interrupt (camAngle), and the predicted time until the next tooth interrupt event (crkDiff). With this information, it is possible to perform conversions between time and angle, resulting in creating predicted event times for setting timer interrupts. Because the conversions require math (multiplies and divides) also for providing values of proper precision, are performed using 32bit numbers, it is necessary to limit the amount of repetition and unnecessary conversion.

The solution presented here is to use a window of operation. The window will exist based on the most current values of crkTime, crkDiff, and camAngle. Because an operation is needed, the window should be forward of the current position (>camAngle). The system here uses a value of 1/2 the tooth angle. This is the value that is used for "min", or the front edge of the window. The value of "max" will be one tooth angle after "min" with the idea being, from mid tooth to mid tooth. The basis of the operation is to perform an angle based comparison of the event angle to the min and max value. If the event angle falls between the min and max value, then the angle is converted to a time and the timers are updated to generate an event.

In this installment, I will just provide snippets of code to add as correction to existing source. In the next session, I will provide the full file sources.

/* in rtUpdateIgn() in the engine off section */
...
toothAngle = DEG_PER_REV / teeth;
toothError = DEG_PER_REV % teeth;

/* in ISR(INT0_vect) after the if (isInt0Low... */
  camAngle += toothAngle;
  camError += toothError; if (toothError >= teeth) { camAngle++; camError -= teeth; }
...
/* this doesn't provide correction for partial error correction */
  min = camAngle + (toothAngle / 2);
  max = min + toothAngle;
...
/* this is actually a good place to invoke the scheduler, as long as it isn't */
/* called to do too much in its operation. */

The basis of the scheduler does a simple operation based on min and max

/* because min and max are unsigned values making provision for wrap around is done */
/* as duplication of similar operation (just easier than making things complex) */
if (min < max)
     if ((min < eventAngle) && (eventAngle <= max)) { /* convert and update single event timers */ }
} else {
     if ((min < eventAngle) || (eventAngle <= max)) { /* convert and update single event timers */ }
}

I did want to add one last item here. In the min / max operation (the scheduler), there is a reference to the "convert and update single event timers", but I did not provide the operation. This is the primary reason for splitting the total degrees of the circle into two component parts (PART1 and PART2). The reason is it is possible to use a calculated value to eliminate much of the operation.  The way it works is to use a base value, where:

base = crkDiff * teeth / PART1;

Then if you are converting from time to angle the operation is:

angle = time * PART2 / base;

...and converting from angle to time is:

time = angle * base / PART2;

The time at the scheduler will be the number of tics from the last tooth. So to set the event timer compare value will be set to (crkTime + time), where time is the converted value.

Jack