UT_FILTER — Smoothing filter

Smooths a noisy value (a level that sloshes, a flow that pulses, a pressure that
jumps) so alarms and controls don't chatter on the noise.

Pins

	Pin	Type	Default	What to wire
in	`In`	REAL	0.0	Noisy value
in	`Tc`	TIME	T#1s	Time constant (low-pass) or window length (averages)
in	`Mode`	UT_FILTER_MODE	UT_FILTER_LOWPASS	`UT_FILTER_LOWPASS` · `UT_FILTER_AVERAGE` · `UT_FILTER_BLOCK_AVG`, see below
in	`Reset`	BOOL	FALSE	Output jumps straight to `In`
out	`Out`	REAL		Smoothed value
out	`BadInput`	BOOL		`In` is NaN or infinite: `Out` is held

Mode	What it does	Use it for
`UT_FILTER_LOWPASS`	First order: after a step, `Out` has moved 63 % of the way after `Tc` and 95 % after 3 × `Tc`	General smoothing, fast to react
`UT_FILTER_AVERAGE`	Moving average of the last `Tc`, updated every scan: the `Tc` window being filled, plus the last whole window's share of the time still to fill. After a step, `Out` starts moving at once and reaches the new value at the end of the next window: `Tc` after the step when the step comes as a window starts, at most 2 × `Tc` after it otherwise (see below)	Levels with waves, flows with pulsation
`UT_FILTER_BLOCK_AVG`	Average of each `Tc` window, updated once at the end of each window	Logging, per-minute averages

The first scan, Reset, and Tc = 0 (or under 1 ms, or negative) pass In straight through.
Changing Mode or Tc carries on from the present Out, without a jump.
Timing uses real elapsed time, so the result is the same at any task
interval, and it keeps working however long the PLC runs.
A NaN or infinite In is ignored: Out holds, BadInput is set, and the time
it lasted does not count. Filtering carries on from the held value when the
input is good again. A NaN on the very first scan leaves Out at 0 until the
first good value, which then passes straight through.
The moving average keeps two sums: the window being filled, and the average of
the last whole window. It takes the last window as even through its length, so it
costs the same small memory at any task interval and any Tc. The windows follow
each other from the first scan (and from a Reset, or a change of Mode or Tc).
After a step part-way through a window, Out moves in a straight line until that
window ends, then on in a second, slower straight line through the next window, and
arrives at its end.

LevelFilt(In := Level, Tc := T#5s, Mode := UT_FILTER_AVERAGE);
LevelSmooth := LevelFilt.Out;