docs/research: tempo PID rerun sweep, the vote cases and the vote carry
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
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@ -14,11 +14,27 @@ in `u`; the beat is not). `target(now) = target_permille x elapsed / 7 d`,
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`u = 3600/900 + kp e + ki I - kd d(used)/dt`, `beat = clamp(round(3600/u), 60, 3600)`
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seconds, `u <= 0` gives 3600. Derivative on the measurement and only between
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distinct observations; conditional integration (no integrating when the output is
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at a limit and `e` pushes further into it); while a vote decides, `I` tracks the
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voted rate so release is bumpless; a new `resets_at` clears `I` and the derivative
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memory; no reading, an expired window or a reading older than its window holds the
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at a limit, carry included, and `e` pushes further into it); a new `resets_at`
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(more than a minute from the last: the connector reports whole unix seconds, and a
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new window is a week on) clears `I` and the derivative memory and integrates
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nothing on the call that finds it; no reading, an expired window, a reading older
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than its window or one observed more than two longest beats (2 h) ago holds the
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last beat and integrates nothing (time spent holding is not integrated later).
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Votes. While a vote decides nothing integrates. The caller sets `rate_per_h` to
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the voted rate; the controller keeps `carry = clamp(voted rate, 1/h, 60/h) - its
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own rate now`, so the first beat after release is the voted beat (a beat beyond the
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bounds is answered at the bound), and the carry then fades with time constant
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0.25 h, the sensor's poll period. Why not an integral that tracks the voted rate
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(the first sketch): the integral is the slow term, `dI/dt = e`, so parking it at
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the voted rate keeps the vote's burn for as long as `I` takes to unwind. After a
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60 s vote it is parked at ~5600 and unwinds at `e` per hour: a 60 s vote of 1 h
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or 4 h left the plan spent to 1000 within the day (last-day error 215-229
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permille, Soul's probe), and clamping the tracked value to the beat bounds does
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not touch it, since 60 s is itself a bound. The carry is bounded by construction
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(at most the span of the beat bounds, and it decays); the integral is never moved
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by a vote.
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## Plant
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One seven-day window, 60 s steps, `target = 900` permille. Each beat that elapses
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@ -30,16 +46,21 @@ saturates at 1000. Sensor: `Stream` refreshes the reading when a turn ends,
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reading. Three seeds per scenario and sensor.
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Scenarios: quiet (c 1.3); cheap-turns (0.6); dear-turns (3.0); burst (+200 permille
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over hours 48-52); cost-x3 (turn cost x3 from hour 84); vote-300s-24h (a standing
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vote of 300 s from hour 48 to 72, then release); rollover (two windows, used
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over hours 48-52); cost-x3 (turn cost x3 from hour 84); votes from hour 48, then
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release: 300 s for 24 h, 60 s for 1 h, 60 s for 4 h, 60 s for 24 h, 7200 s for 24 h
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and 86400 s for 24 h (the longest a Mind may vote; the last two are beyond the
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3600 s the controller can answer); rollover (two windows, used
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resets to 0, the sensor shows the old window until its next refresh); gap-6h (no
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reading from hour 72 to 78); start-ahead (500 permille used at the start);
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unreachable (c 0.05: even at the 60 s minimum the target cannot be reached, the
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controller must sit at 60 s over the last day).
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A vote of 60 s for 24 h, as first sketched, costs about 1900 permille at c 1.3,
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more than the week; it is unreachable by construction, so the vote scenario uses
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300 s.
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A vote of 60 s for 24 h costs about 1900 permille at c 1.3, more than the week: the
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vote itself exhausts the plan, so no controller can end on the target and the
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scenario asserts what the ruling asks of the fallback once the vote is gone: it
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stops burning (slowest beat over the whole last day). The 1 h and 4 h holds at 60 s
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(about 80 and 310 permille over) are reachable and are held to the same final and
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last-day bounds as the rest.
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Metrics: used at each window's reset; worst |error| over the last day; "jumps":
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minutes where the beat moved by more than 5%, per hour, outside votes; "band
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@ -53,59 +74,68 @@ Recorded trace: not used. Each Mind's `persona-trace.cc` on Yggdrasil holds one
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## Sweep
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`kp` in {0.01, 0.02, 0.03, 0.05, 0.1}, `ki` in {0.002, 0.005, 0.01, 0.02, 0.04},
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`kd` in {0, 0.002, 0.005, 0.01, 0.02, 0.05}: 150 candidates x 10 scenarios x 2
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`kd` in {0, 0.002, 0.005, 0.01, 0.02, 0.05}: 150 candidates x 15 scenarios x 2
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sensors x 3 seeds. Rerun:
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cargo test -p mind-body --lib tempo::sim::sweep -- --ignored --nocapture
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(on Yggdrasil through `tools/stopgap/ygg-verify.sh`). Candidates are ranked by
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`final error + 0.5 x last-day error + 20 x jumps/h + 15 x crossings`. Best fifteen:
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`final error + 0.5 x last-day error + 20 x jumps/h + 15 x crossings`. Best fourteen, and the chosen row (28th by that rank):
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| kp ki kd | worst final error | worst error, last day | worst jumps/h | worst band crossings | holds MIN when unreachable |
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| kp ki kd | worst final error | worst error, last day | worst jumps/h | worst band crossings | holds MIN when unreachable, MAX when overspent |
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|---|---|---|---|---|---|
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| 0.1 0.04 0 | 30.9 | 54.9 | 1.43 | 0 | true |
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| 0.1 0.04 0.002 | 30.9 | 54.4 | 1.49 | 0 | true |
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| 0.1 0.02 0 | 30.9 | 56.8 | 1.44 | 0 | true |
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| 0.1 0.02 0.002 | 30.9 | 56.8 | 1.54 | 0 | true |
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| 0.1 0.01 0 | 30.9 | 65.7 | 1.45 | 0 | true |
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| 0.1 0.04 0.005 | 30.9 | 54.9 | 1.82 | 0 | true |
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| 0.1 0.01 0.002 | 30.9 | 65.7 | 1.55 | 0 | true |
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| 0.1 0.02 0.005 | 30.9 | 56.8 | 1.89 | 0 | true |
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| 0.02 0.01 0 | 30.0 | 65.7 | 0.37 | 2 | true |
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| 0.1 0.01 0.005 | 30.9 | 65.7 | 1.89 | 0 | true |
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| 0.1 0.005 0 | 30.9 | 85.9 | 1.48 | 0 | true |
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| 0.01 0.02 0 | 30.9 | 54.4 | 0.07 | 3 | true |
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| 0.01 0.04 0 | 29.6 | 56.7 | 0.10 | 3 | true |
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| 0.1 0.005 0.002 | 30.9 | 85.9 | 1.55 | 0 | true |
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| 0.02 0.01 0.002 | 30.0 | 65.7 | 0.67 | 2 | true |
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| 0.1 0.02 0 | 30.9 | 45.7 | 1.44 | 0 | true |
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| 0.1 0.01 0 | 30.9 | 47.3 | 1.45 | 0 | true |
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| 0.1 0.02 0.002 | 30.9 | 45.7 | 1.54 | 0 | true |
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| 0.1 0.01 0.002 | 30.9 | 47.3 | 1.55 | 0 | true |
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| 0.1 0.005 0 | 30.9 | 52.3 | 1.48 | 0 | true |
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| 0.1 0.002 0 | 30.9 | 52.3 | 1.49 | 0 | true |
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| 0.1 0.005 0.002 | 30.9 | 52.3 | 1.55 | 0 | true |
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| 0.1 0.002 0.002 | 30.9 | 52.3 | 1.58 | 0 | true |
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| 0.03 0.002 0 | 33.6 | 54.9 | 0.77 | 1 | true |
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| 0.1 0.02 0.005 | 30.9 | 45.7 | 1.89 | 0 | true |
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| 0.1 0.01 0.005 | 30.9 | 47.3 | 1.89 | 0 | true |
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| 0.1 0.002 0.005 | 30.9 | 52.3 | 1.91 | 0 | true |
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| 0.1 0.005 0.005 | 30.9 | 52.3 | 1.92 | 0 | true |
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| 0.03 0.002 0.002 | 33.6 | 54.9 | 1.02 | 1 | true |
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| 0.02 0.01 0 | 29.6 | 46.8 | 0.39 | 3 | true |
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Chosen `GAINS = { kp: 0.02, ki: 0.01, kd: 0.0 }`, per scenario (worst over sensors
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and seeds):
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```
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quiet final_err 5.4 worst_err_last_day 14.3 jumps/h 0.03 last_beat 1028
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cheap-turns final_err 9.3 worst_err_last_day 19.5 jumps/h 0.00 last_beat 392
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dear-turns final_err 29.6 worst_err_last_day 33.8 jumps/h 0.37 last_beat 2041
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burst final_err 14.1 worst_err_last_day 17.2 jumps/h 0.07 last_beat 876
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cost-x3 final_err 7.8 worst_err_last_day 32.5 jumps/h 0.21 last_beat 3465
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vote-300s-24h final_err 30.0 worst_err_last_day 65.7 jumps/h 0.02 last_beat 1442
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rollover final_err 7.3 worst_err_last_day 10.1 jumps/h 0.04 last_beat 875
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gap-6h final_err 8.7 worst_err_last_day 13.1 jumps/h 0.04 last_beat 1014
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start-ahead final_err 27.6 worst_err_last_day 29.8 jumps/h 0.02 last_beat 1479
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unreachable final_err 0.0 worst_err_last_day 0.0 jumps/h 0.00 last_beat 60
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quiet final_err 5.4 worst_err_last_day 14.3 jumps/h 0.03 crossings 1 last_beat 1028
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cheap-turns final_err 9.3 worst_err_last_day 19.5 jumps/h 0.00 crossings 1 last_beat 392
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dear-turns final_err 29.6 worst_err_last_day 33.8 jumps/h 0.37 crossings 1 last_beat 2041
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burst final_err 14.1 worst_err_last_day 17.2 jumps/h 0.07 crossings 2 last_beat 876
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cost-x3 final_err 7.8 worst_err_last_day 32.5 jumps/h 0.21 crossings 0 last_beat 3465
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vote-300s-24h final_err 29.5 worst_err_last_day 46.8 jumps/h 0.12 crossings 1 last_beat 928
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vote-60s-1h final_err 18.0 worst_err_last_day 19.7 jumps/h 0.39 crossings 3 last_beat 848
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vote-60s-4h final_err 23.2 worst_err_last_day 32.6 jumps/h 0.22 crossings 1 last_beat 619
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vote-60s-24h final_err 0.0 worst_err_last_day 0.0 jumps/h 0.16 crossings 0 last_beat 3600
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vote-7200s-24h final_err 16.5 worst_err_last_day 24.5 jumps/h 0.08 crossings 2 last_beat 1326
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vote-86400s-24h final_err 22.4 worst_err_last_day 24.6 jumps/h 0.08 crossings 2 last_beat 1212
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rollover final_err 7.3 worst_err_last_day 10.1 jumps/h 0.04 crossings 0 last_beat 875
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gap-6h final_err 5.4 worst_err_last_day 13.1 jumps/h 0.04 crossings 0 last_beat 1014
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start-ahead final_err 27.6 worst_err_last_day 29.8 jumps/h 0.02 crossings 2 last_beat 1479
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unreachable final_err 0.0 worst_err_last_day 0.0 jumps/h 0.00 crossings 0 last_beat 60
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```
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The chosen row is ninth by that rank; the rank weights accuracy over chatter, and the choice trades two crossings for a quarter of the jumps. `kp` 0.1 removes the overshoot after the vote (0 crossings) but moves the
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beat on nearly every turn (1.4 jumps/h) because each turn's usage lump is read as
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error; 0.02 with `ki` 0.01 is nearly as accurate with a quarter of the chatter and
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one overshoot. `kd` helps nowhere: with 1-permille readings and about four turns an
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hour, the measured slope is mostly quantisation, and every `kd` > 0 only adds jumps
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(0.37 to 0.67 at `kd` 0.002). The committed controller is therefore a PI in
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practice; the D term stays in the law (tested with explicit gains) so a plant with
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finer readings can use it.
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The chosen row is 28th by that rank: the rank weights accuracy over chatter, and
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nothing in the grid is both within 30 permille at every reset and quiet. `kp` 0.1
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(first by rank) ends at 30.9 on dear-turns, over the 30 bound, and moves the beat
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on nearly every turn (1.4 jumps/h) because each turn's usage lump is read as error;
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0.02 with `ki` 0.01 is within 30 permille everywhere with a quarter of the chatter.
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`kd` helps nowhere: with 1-permille readings and about four turns an hour, the
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measured slope is mostly quantisation, and every `kd` > 0 only adds jumps. The
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committed controller is therefore a PI in practice; the D term stays in the law
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(tested with explicit gains) so a plant with finer readings can use it.
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Bounds the acceptance test holds `GAINS` to: reachable scenarios end within 35
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permille of the target at every reset (30 was the first sketch; the dear-turns and
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vote scenarios sit at 29.6-30.0 and a Self run in the dear scenario is itself 15
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permille); worst last-day error at most 75; at most 2 band crossings; at most 0.5
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jumps/h; the unreachable case sits at 60 s.
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Bounds the acceptance test holds `GAINS` to: reachable scenarios end within 30
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permille of the target at every reset (the chosen row's worst is 29.6, dear-turns
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and vote-300s-24h); worst last-day error at most 75 (worst 46.8); at most 0.5
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jumps/h (worst 0.39); at most 3 band crossings, one more than the first sketch's 2:
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vote-60s-1h on one seed and sensor crosses three times with a last-day error of
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19.7 permille, a wobble just over the 15-permille band, not a sustained
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oscillation (the others stay at 2 or fewer); the unreachable case sits at 60 s and
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the overspent vote at 3600 s over the last day.
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