Measurement-based Feedforward Tuning:

Alternative Methods Based on a Single Move

If you make a single move at a decent acceleration and velocity, you will have enough DAC information to calculate the feedforwards. Collect the DAC output and the Commanded Velocity for your move in MoScope measure a few points labeled A, B, and C on the figure below for the DAC output. You will need to know the maximum velocity reached and the acceleration used. Do not use an S-Curve move, it makes the calculations much more involved. A simulated feedforward term using the feedforwards calculated below is plotted on the actual DAC output to show the validity of the feedforward values. For this example, a move of 200,000 encoder counts with 50,000 counts / sec2 acceleration and 100,000 counts / sec max velocity will be used.

In the figure above, I measured:
        DAC_a = 2000 DAC counts
        DAC_b = 4627 DAC counts
        DAC_c = 1800 DAC counts

The motion consisted of:
        Max velocity = 50 encoder counts / sample
        Acceleration = 0.0125 encoder counts / sample²

Examples:

        Kvff = (DAC_b - DAC_a) / max velocity
              = (4627 - 2000) (DAC counts) / 50 (encoder counts / sample)
              = 52.54 (DAC Counts / Encoder Counts * samples)

This compares to the 50.07 value for Kvff we got in the first example.
        Kaff = (DAC_b - DAC_b) / (2 * accel)
              = (4627 - 1800) (DAC counts) / (2 * 0.25) (encoder counts / sample²)
              = 113080 (DAC Counts / Encoder Counts * samples2)

        Kfff = DAC_a - Kaff * Acceleration
              = 2000 (DAC counts) - 113080 (DAC Counts / Encoder Counts * samples²) * 0.0125
                 (encoder counts / sample²)
              = 586.5 DAC counts

This compares to the 583 value for Kfff for the first example.

Let's take a look at the motion, before and after feedforward, using the feedforward values we just calculated.

This is rather conclusive evidence that the position error can be dramatically reduced through the use of feedforwards. But notice that there is not a drastic change in the DAC output. This is because the difference in motion is ~45 encoder counts (peak error with no feedforward) in a 200,000 count move. In precision motion, this improvement in performance is important for two reasons:

To emphasize the fact that the feedforwards we calculated will work with different moves, we will apply the same feedforwards to a different move:

         20,000 counts
         200,000 counts/sec²

Note the reduction in DAC output on acceleration transitions. This is because there is less ringing in the motor position.