Quadrature Scaling

To have any useful meaning, the counts from the transducer must be scaled to position units. For a quadrature axis, the Position Scale parameter defines the position units as a function of transducer counts. This topic describes how to correctly calculate this parameter for an Quadrature encoder.

Delta recommends using the Scale/Offset Wizard for scaling the position. If you need to manually calculate the scale and offset, read this topic.

If your motion is linear, read this topic. If your motion is purely rotary, see the Rotary Scaling topic.

As described in the Quadrature Fundamentals topic, the resolution of a quadrature encoder is typically given in Pulses per Revolution (PPR), also called Lines per Revolution. The RMC feedback sees each rising or falling edge of the A or B signal as one count. Therefore, each pulse or line of the encoder will result in four counts on the RMC quadrature input. For example, a 1000-line encoder will give the RMC 4000 counts per revolution.

The RMC calculates the quadrature axis Actual Position every control-loop time using the following formula:

Actual Position [pu] = (Change in Counts [cnt] x Position Scale [pu/cnt]) + Last Position

Note:
If the Actual Position filter is applied, the RMC filters the Actual Position after calculating it with the above formula.

The Scale/Offset Wizards provide the easiest method of scaling your axis. If you prefer to do it manually, read this section.

There are two methods of finding the correct Position Scale and Position Offset.

The accuracy of this method depends on how accurately you can measure two positions of the axis.

Physically measure the axis position at two points and record the value of the counts register at each point. Call the first measured position P0, and its corresponding Counts C0. Call the second measured position P1, and its corresponding Counts C1.
Calculate the Position Scale with the following equation:

Position Scale = (P0-P1)/(C0-C1)

Obtain the encoder resolution (usually from the transducer data sheet), for example 4000 counts/turn.
Determine the position units you would like for your Actual Position, for example inches, meter, mm, etc.
Determine how many position units correspond to one count.
For example, consider an encoder with 4000 counts per revolution mounted to a motor that drives a linear axis through a 4:1 gearbox and then a rack and pinion. The rack moves 5 inches for every turn of the pinion. The desired position-units of the linear rack motion are inches.
To find the resolution:
1. Determine the number of counts generated in one revolution of the encoder:
  From the datasheet, this is 4000 counts.
2. Calculate the linear travel (position units) in one revolution of the encoder:
  One revolution of the encoder equals 1/4 revolution of the pinion.
  One revolution of the pinion equals a travel distance of 5 inches.
  Therefore, the linear travel in one turn of the encoder is 5/4 = 1.2 in.
3. To calculate Scale, divide the calculated linear travel (position-units) by the number of counts:
  1.2/4000 = 0.0003 position-units/count
If you wish to reverse the direction of the feedback, make the Scale negative.
Download the Scale to the RMC.

Quadrature Scaling (Linear)