.

Shape-based Feedforward Tuning:

Acceleration Pattern — Adjusting Kaff

  General Rule of Kaff:
 
  • If the position error plot and the commanded acceleration plot have a similar shape, add acceleration feedforward (Kaff).

  • If they have a similar, but opposite shape, reduce Kaff.

Notice that in the plot below, the position error plot (white) has a similar shape to the commanded acceleration (yellow), therefore we will add Kaff.

  10,000 count move
Trapezoidal move:
      5e5 accel, decel, vel
Green - Commanded Velocity             
Yellow - Commanded Acceleration                   
White - Position Error
 

Kaff = 0
Kp = 100
Ki = 0
Kd = 2,000
Peak Position Error = 187 counts 

On this stage, adding a Kaff of 1 makes no noticeable difference:

  10,000 count move 
Trapezoidal move:
      5e5 accel, decel, vel
Green - Commanded Velocity             
Yellow - Commanded Acceleration                   
White - Position Error
 

Kaff = 1
Kp = 100
Ki = 0
Kd = 2,000

After doubling Kaff each move, we eventually get the following plot when Kaff = 50,000.

  10,000 count move
Trapezoidal move:
      5e5 accel, decel, vel
Green - Commanded Velocity             
Yellow - Commanded Acceleration                   
White - Position Error
 

Kaff = 50,000
Kp = 100
Ki = 0
Kd = 2000

It looks like the position error was roughly reduced by half when we changed Kaff = 50,000. That means that if change the Kaff = 100,000, the position error should be fairly close to zero.

  10,000 count move
Trapezoidal move:
      5e5 accel, decel, vel
Green - Commanded Velocity             
Yellow - Commanded Acceleration                   
White - Position Error
 

Kaff = 100,0000
Kp = 100
Ki = 0
Kd = 2,000
Peak Position Error = 28 counts 

The resulting plot shows a position error that is very close to zero and only has a peak position error of 28 counts—an impressive 85% reduction.

NOTE: This reduction comes with no reduction in stability.

As you can see, adding Kaff (acceleration feedforward) can dramatically reduce position error. The stage is actually more stable because P, I, and D need to deal with smaller disturbances, while Kaff is doing most of the work.

Obviously, for the example above, we found a good value for Kaff rather quickly. To see some additional plots with different Kaff values (for the same commanded move) to show that the shape pattern of Kaff is fairly simple and consistent, click here.

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