LowPass2

LowPass2 smooths a noisy signal with a second-order filter: twice the roll-off of a first-order filter, and a damping setting that decides whether the output overshoots. One cut-off and one damping govern every channel. It publishes the whole derivative stack — value, velocity, acceleration and jerk — so a setpoint path can take all four from one block.

flowchart LR
    i1(["input — signal to smooth"]) --> B["LowPass2"]
    i2(["disable"]) --> B
    i3(["vaLimiterDisable"]) --> B
    B --> o1(["output — smoothed signal"])
    B --> o2(["outputDot — velocity of the output"])
    B --> o3(["outputDDot — acceleration of the output"])
    B --> o4(["outputDDDot — jerk of the output"])
    B --> o5(["isEnabled"])
    B --> o6(["vaLimiterIsEnabled"])

$f_c = \omega/2\pi$ — omega 6.283 rad/s is a 1 Hz cut-off. beta is the damping ratio: overshoot is $e^{-\pi\beta/\sqrt{1-\beta^2}}$, so 37% at beta 0.3, 16% at 0.5, and none at 1.0 or above. Ringing frequency is $\omega\sqrt{1-\beta^2}$ [rad/s]. At the cut-off the gain is $1/(2\beta)$ — above 1 for any beta below 0.5, so a low damping amplifies rather than removes. Phase lag at the cut-off is 90°, twice a first-order filter’s, and that lag is the trade.

Signals

Inputs

Outputs

Parameters

All six parameters are persistent and survive a controller restart. The inputs and outputs do not; output starts from zero. No parameters exist below this block.

Setup

1. Link the source signal: …/actuator/actualPosition → …/positionFilter/input. input follows the source on a trace.

2. Set enable false. output equals input sample for sample and isEnabled reads false.

3. Leave vaLimiterEnable false for the whole of setup. The limiter’s default bounds of 1.0 will throttle any real machine signal.

4. Set omega to 300 and beta to 1.0. Read omega back; a lower value means your task rate capped it, and tells you the highest cut-off this task rate allows.

5. Set enable true. isEnabled reads true and output still tracks input closely, with the noise still visible.

6. Halve omega in steps, watching the noise and the loop consuming it. Stop one step above where that loop feels soft or hunts.

   Step 6 changes what the controller sees. A second-order filter costs twice the phase lag of a first-order one at the same cut-off. Lower the cut-off with the axis at rest before trying it in motion.

7. Trace every element of input and output. An element that reads zero while the machine moves is an unwired channel, not a filtered one.

8. Only if you want the block to shape motion as well as smooth it: set vaLimiterMaxAcc and vaLimiterMaxVel to your machine’s real bounds, then set vaLimiterEnable true and confirm vaLimiterIsEnabled reads true.

Tuning

1. Read the frequency of the ripple you want gone, in Hz, off a trace of input. Set omega to $2\pi$ times that frequency, then lower it until the ripple is gone.
2. Leave beta at 1.0 while you find omega. Damping and cut-off interact, and 1.0 is the setting with no overshoot.
3. Step the source and measure the overshoot on output. If you want a faster response and can accept overshoot, lower beta toward 0.5. Never go below 0.5 unless you intend a resonant peak — below it the filter amplifies at the cut-off instead of cutting.
4. Measure the delay you have bought. Step the source and read the time output takes to reach 90% of the step. Keep it below a tenth of the response time of the loop consuming output.
5. Check the loop in motion, not at rest. Delay costs phase margin only while the axis moves fast enough to need it.
6. 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.
7. If you are using outputDDot or outputDDDot, look at them on a trace before you rely on them. Each derivative multiplies the remaining noise, and jerk is differenced rather than filtered.

Read the overshoot off any curve as its highest point above 1.0.

A conservative starting point for a position signal on a 1 ms task, feeding a loop with a 100 ms response time, with the limiter off:

omega            = 60.0
beta             = 1.0
vaLimiterEnable  = false

This is a starting point, not a final tuning. Work step 1 with a trace of your own signal.

Limits and errors

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

Verified against motorcortex-control3 3.30.0 (bc348fd).