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docs: Update Kinematics.md document with "smooth pressure advance"

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Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
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Kevin O'Connor
2019-12-13 16:51:45 -05:00
parent 91bade5824
commit 1d05a34cd7
7 changed files with 169 additions and 410 deletions
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docs/Kinematics.md
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@@ -264,35 +264,36 @@ through the nozzle orifice (as in
key idea is that the relationship between filament, pressure, and flow
rate can be modeled using a linear coefficient:
```
stepper_position = requested_e_position + pressure_advance_coefficient * nominal_extruder_velocity
pa_position = nominal_position + pressure_advance_coefficient * nominal_velocity
```
See the [pressure advance](Pressure_Advance.md) document for
information on how to find this pressure advance coefficient.
Once configured, Klipper will push in an additional amount of filament
during acceleration. The higher the desired filament flow rate, the
more filament must be pushed in during acceleration to account for
pressure. During head deceleration the extra filament is retracted
(the extruder will have a negative velocity).
The basic pressure advance formula can cause the extruder motor to
make sudden velocity changes. Klipper implements "smoothing" of the
extruder movement to avoid this.
![pressure-advance](img/pressure-advance.svg.png)
![pressure-advance](img/pressure-velocity.png)
One may notice that the pressure advance algorithm can cause the
extruder motor to make sudden velocity changes. This is tolerated
based on the idea that the majority of the inertia in the system is in
changing the extruder pressure. As long as the extruder pressure does
not change rapidly the sudden changes in extruder motor velocity are
tolerated.
The above graph shows an example of two extrusion moves with a
non-zero cornering velocity between them. Note that the pressure
advance system causes additional filament to be pushed into the
extruder during acceleration. The higher the desired filament flow
rate, the more filament must be pushed in during acceleration to
account for pressure. During head deceleration the extra filament is
retracted (the extruder will have a negative velocity).
One area where sudden velocity changes become problematic is during
small changes in head speed due to cornering.
The "smoothing" is implemented by averaging the extruder position over
a small time period (as specified by the
`pressure_advance_smooth_time` config parameter). This averaging can
span multiple g-code moves. Note how the extruder motor will start
moving prior to the nominal start of the first extrusion move and will
continue to move after the nominal end of the last extrusion move.
![pressure-cornering](img/pressure-cornering.svg.png)
To prevent this, the Klipper pressure advance code utilizes the move
look-ahead queue to detect intermittent speed changes. During a
deceleration event the code finds the maximum upcoming head speed
within a configurable time window. The pressure is then only adjusted
to this found maximum. This can greatly reduce (or even completely
eliminate) pressure changes during cornering.
Key formula for "smoothed pressure advance":
```
smooth_pa_position(t) =
( definitive_integral(pa_position, from=t-smooth_time/2, to=t+smooth_time/2)
/ smooth_time )
```