HighPass2

  8 minute read  

HighPass2 is the second-order washout filter. Feed it an acceleration and it removes the sustained part — the part a platform cannot reproduce without running out of travel — and returns the transient part, plus the velocity and position that follow from it. The three outputs are three different filters, not three views of one: output keeps the fast content, outputInt keeps only content near the cut-off, and outputIInt keeps the slow content.

flowchart LR
    i1(["input — acceleration to wash out"]) --> B["HighPass2"]
    i2(["disable"]) --> B
    B --> o1(["outputIInt — position, slow content only"])
    B --> o2(["outputInt — velocity, cut-off content only"])
    B --> o3(["output — acceleration, fast content only"])
    B --> o4(["isEnabled"])

$f_c = \omega/2\pi$ — omega 6.283 rad/s is a 1 Hz cut-off. beta is the damping ratio: 1.0 gives one small undershoot, below 1.0 the outputs ring at $\omega\sqrt{1-\beta^2}$ [rad/s]. output settles to zero for any constant input. outputInt peaks at the cut-off with gain $1/(2\beta\omega)$. outputIInt settles to $1/\omega^2$ times a constant input — a factor of 0.025 at the default, so do not expect it to match the input’s magnitude.

Leave this block enabled. Disabling it does not idle it: output drops to zero rather than passing the input through, and outputIInt drifts. It also has no reset input — see Limits and errors.

Signals

Inputs

Path	Unit	Range	Description
input	m/s² for a washout, or any signal unit	unbounded	The signal to wash out, normally an acceleration. One element per channel; the channel count is fixed by the machine configuration.
disable	-	-	True forces output to zero and leaves the other two outputs coasting. It is not a bypass and does not pass input through. Use enable for the configured intent, and read the note above before using either.

Outputs

Path	Unit	Description
outputIInt	m for a washout, or input unit × s²	Position. Keeps the slow content of input and settles to $1/\omega^2$ times a constant input. The smoothest of the three. Starts from zero after every controller start, and is never cleared once running.
outputInt	m/s for a washout, or input unit × s	Velocity. Keeps only content near the cut-off, and settles to zero for both a constant input and a very fast one. Starts from zero after every controller start.
output	m/s² for a washout, or the input unit	Acceleration. Keeps the fast content and settles to zero for a constant input. It is not smoothed — noise on input reaches it at full size and undelayed. Zero while disable is true or enable is false.
isEnabled	-	True when enable is true and disable is false. A single value for the whole block, not one per channel.

Parameters

Path	Unit	Default	Range	Effect
omega	rad/s	6.283 (1 Hz)	0.1 – 0.628/task period [s]	Cut-off, shared by all channels. Lower keeps more of the sustained content and washes it out more slowly, so the platform travels further. Higher washes out sooner and the motion feels thinner. Out-of-range values are corrected silently — see Limits and errors.
beta	-	1.0	0.1 – 2	Damping ratio, shared by all channels. 1.0 gives one small undershoot and no ringing. Below 1.0 the outputs ring, badly below 0.5. Above 1.0 the washout is slower and gentler. Out-of-range values are corrected silently.
enable	-	true	-	False forces output to zero. It does not bypass the block. See the note under the diagram.

All three parameters are persistent and survive a controller restart. The inputs and outputs do not; all three outputs start from zero. No parameters exist below this block.

Setup

1. Link the source signal: …/model/commandedAcceleration → …/washout/input. input follows the source on a trace.

2. Leave enable true for the whole of setup. There is no useful idle state, and the outputs are already zero before any input arrives.

3. Set omega to 6.283 and beta to 1.0. Read omega back; a lower value means your task rate capped it.

4. Decide which output your consumer needs, and wire only that one. A platform position command takes outputIInt; a velocity feedforward takes outputInt; an accelerometer-matching path takes output.

5. Apply a sustained acceleration on input and hold it. output must return to zero, and outputIInt must settle to a constant, not keep climbing.

   Step 5 is the check that the washout works. If outputIInt keeps climbing while input is held constant, stop and fix that before you connect a platform — it will run to its travel limit.

6. Read the settled value of outputIInt and divide it by the input you applied. It should be close to $1/\omega^2$. This confirms the scaling you have to compensate downstream.

7. Trace every element of input and each output you use. An element that reads zero while the machine moves is an unwired channel.

Tuning

1. Measure your consumer’s travel budget first, in metres. That budget, not the feel of the motion, sets the lowest omega you can use.
2. Apply the largest sustained acceleration your application produces and read the peak of outputIInt. Raise omega until that peak fits the budget with margin.
3. Leave beta at 1.0 while you find omega. Damping and cut-off interact, and 1.0 is the setting with almost no undershoot.
4. Step the input and watch output return through zero. The undershoot is the platform being pulled back to centre; it is unavoidable in a washout.
5. If that return is too abrupt, raise beta toward 2.0. If the motion feels dead, lower beta toward 0.7 — but never below 0.5 unless you intend ringing.
6. Re-check the travel budget after every beta change. Damping changes the peak excursion as well as its shape.
7. Re-check omega after any task-rate change. The upper bound scales with the task period, so a slower task can clamp a cut-off that used to be accepted.
8. Look at output on a trace before relying on it. It is unsmoothed, so it carries whatever noise input carries.

Read the pull-back off any curve as its lowest point below zero.

Symptom	Cause	Action
outputIInt is far smaller than the input	Expected: its steady gain is $1/\omega^2$, which is 0.025 at the default cut-off	Scale it downstream; there is no gain parameter in this block
outputIInt keeps climbing while input is held constant	The block is not running the washout — check isEnabled reads true	Set enable true and disable false; a disabled block coasts instead of washing out
outputIInt reached the platform’s travel limit	Cut-off too low for the accelerations you are feeding it	Raise omega and re-check step 2 of Tuning
output is noisy	Expected: output is not smoothed, unlike the two integrals	Filter input upstream, or take outputInt instead
output sits at zero while input clearly has a value	Expected for a constant input, since a constant has no fast content. Otherwise enable is false	Read isEnabled; if it is true, this is normal washout behaviour
All three outputs ring after a step	beta below 1	Raise beta toward 1.0; ringing stops almost entirely at 1.0
The motion pulls back too hard after a step	Damping too low for the feel you want	Raise beta toward 2.0, then re-check the travel budget
The motion feels dead and thin	Cut-off too high — the sustained content is being removed too soon	Lower omega, within the travel budget
omega or beta reads back different from what you wrote	Outside the accepted band	Read the value back and work within it; the task rate sets omega’s upper bound
omega used to be accepted and now clamps	The task period grew, so the upper bound fell	Raise the task rate back, or lower omega
outputIInt sits at a large offset and will not return, even with input at zero	The block’s state is off-centre and it has no reset	Restart the controller. Nothing in the parameter tree can clear it
outputIInt drifted while the block was disabled	Expected: a disabled block holds its velocity and keeps integrating it	Leave the block enabled; restart the controller to clear the drift
Some channels wash out faster than others	Not possible — all channels share one omega and one beta	Use a separate washout per channel group
An output went to a non-numeric value and stays there	A non-numeric value reached input, omega or beta	Fix the source, then restart the controller. Disabling the block does not clear it

A conservative starting point for a motion-platform washout on a 1 ms task, with a generous travel budget:

omega  = 6.283
beta   = 1.0
enable = true

This is a starting point, not a final tuning. Work steps 1 and 2 with your own travel budget.

Limits and errors

Limit	Set by	What happens	Reported
omega ≥ 0.1 rad/s	Fixed	A slower value is replaced by 0.1 rad/s	Silently; read omega back
omega ≤ 0.628 / task period [s]	Task rate — 628 rad/s on a 1 ms task, 62.8 rad/s on a 10 ms task	A faster value is replaced by the edge. This is what keeps the filter stable at any setting	Silently; read omega back
beta within 0.1 – 2	Fixed	A value outside the band is replaced by the nearest edge. Note the upper bound is 2, lower than the second-order low-pass filter’s	Silently; read beta back
outputIInt, outputInt, output	Nothing	Unbounded. outputIInt in particular has no travel limit of its own — bound it downstream before it reaches a platform	Not reported
Block state	Nothing	There is no reset input and no way to clear the outputs in service. Once outputIInt is off-centre, only a controller restart returns it to zero	Not reported
Channel count	Machine configuration	Fixed once the controller starts; it cannot be changed at runtime	Not reported

The block raises no errors or warnings and logs nothing. Every failure above shows as a value on a trace, not as a message.

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Verified against motorcortex-control3 3.30.0 (bc348fd).