FA-93531 / Solar tracker geometry / Open access
Tracker actuator step command: step truncation direction · case 01
Eastward moves overshoot the slew limit by one motor step.
ROOT CAUSE
Floor division rounds negative moves away from zero.
VERIFIED REPAIR
Truncate the step count toward zero.
Unsuccessful approach: Rounding to nearest can exceed the slew limit in both directions.
Case contract
Angles in millidegrees. The target is clamped to [lo, hi]. If |target - current| < deadband no move is made. Otherwise the move is limited to +-max_step, converted to whole motor steps of dps millidegrees truncated toward zero. Return [new position, signed steps].
Why this case matters
Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(err) < deadband:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = move // dps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [87, 3902, 250, 500, 90, -52000, 55000], [3452, -5]],
['regression: step truncation direction (partial repair)',
[1899, -3811, 250, 5000, 300, -60000, 60000], [989, 16]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-54271, -9833, 0, 2000, 90, -52000, 52000],
[-11813, -22]],
['regression: step truncation direction (partial repair)',
[-47305, -34773, 1000, 5000, 300, -60000, 55000], [-39573, -16]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [25571, 48224, 500, 2000, 90, -52000, 55000],
[46244, -22]],
['regression: step truncation direction (partial repair)',
[-24432, -36322, 1000, 5000, 300, -60000, 52000], [-31522, 16]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-50922, -33896, 1000, 2000, 7, -52000, 60000],
[-35891, -285]],
['regression: step truncation direction (partial repair)',
[56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [3491, 18980, 250, 2000, 7, -55000, 60000],
[16985, -285]],
['regression: step truncation direction (partial repair)',
[60232, -13012, 500, 500, 300, -60000, 55000], [-12712, 1]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [59994, 142] | [59994, 142] | Passed |
| normal: negative move truncation | [-2100, -7] | [-1800, -6] | Failed |
| regression: step truncation direction | [3362, -6] | [3452, -5] | Failed |
| regression: step truncation direction (partial repair) | [989, 16] | [989, 16] | Passed |
| control 1 | [-54317, 6] | [-54317, 6] | Passed |
| control 2 | [-34789, -17] | [-34489, -16] | Failed |
SHA-256 / cdcabf9aef4070ec237f260c443ccaa1736061a6ba047c8d03f1c6483ac1adf3
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(err) < deadband:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = round(abs(move) / dps)
if move < 0:
steps = -steps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [87, 3902, 250, 500, 90, -52000, 55000], [3452, -5]],
['regression: step truncation direction (partial repair)',
[1899, -3811, 250, 5000, 300, -60000, 60000], [989, 16]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-54271, -9833, 0, 2000, 90, -52000, 52000],
[-11813, -22]],
['regression: step truncation direction (partial repair)',
[-47305, -34773, 1000, 5000, 300, -60000, 55000], [-39573, -16]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [25571, 48224, 500, 2000, 90, -52000, 55000],
[46244, -22]],
['regression: step truncation direction (partial repair)',
[-24432, -36322, 1000, 5000, 300, -60000, 52000], [-31522, 16]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-50922, -33896, 1000, 2000, 7, -52000, 60000],
[-35891, -285]],
['regression: step truncation direction (partial repair)',
[56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [3491, 18980, 250, 2000, 7, -55000, 60000],
[16985, -285]],
['regression: step truncation direction (partial repair)',
[60232, -13012, 500, 500, 300, -60000, 55000], [-12712, 1]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [60001, 143] | [59994, 142] | Failed |
| normal: negative move truncation | [-2100, -7] | [-1800, -6] | Failed |
| regression: step truncation direction | [3362, -6] | [3452, -5] | Failed |
| regression: step truncation direction (partial repair) | [1289, 17] | [989, 16] | Failed |
| control 1 | [-54017, 7] | [-54317, 6] | Failed |
| control 2 | [-34789, -17] | [-34489, -16] | Failed |
SHA-256 / 6af45ef7d68f86f4cf010618838167592c8fdfc1ae0f19d2f41ec34dafbb5438
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(err) < deadband:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = abs(move) // dps
if move < 0:
steps = -steps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [87, 3902, 250, 500, 90, -52000, 55000], [3452, -5]],
['regression: step truncation direction (partial repair)',
[1899, -3811, 250, 5000, 300, -60000, 60000], [989, 16]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-54271, -9833, 0, 2000, 90, -52000, 52000],
[-11813, -22]],
['regression: step truncation direction (partial repair)',
[-47305, -34773, 1000, 5000, 300, -60000, 55000], [-39573, -16]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [25571, 48224, 500, 2000, 90, -52000, 55000],
[46244, -22]],
['regression: step truncation direction (partial repair)',
[-24432, -36322, 1000, 5000, 300, -60000, 52000], [-31522, 16]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [-50922, -33896, 1000, 2000, 7, -52000, 60000],
[-35891, -285]],
['regression: step truncation direction (partial repair)',
[56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: step truncation direction', [3491, 18980, 250, 2000, 7, -55000, 60000],
[16985, -285]],
['regression: step truncation direction (partial repair)',
[60232, -13012, 500, 500, 300, -60000, 55000], [-12712, 1]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [59994, 142] | [59994, 142] | Passed |
| normal: negative move truncation | [-1800, -6] | [-1800, -6] | Passed |
| regression: step truncation direction | [3452, -5] | [3452, -5] | Passed |
| regression: step truncation direction (partial repair) | [989, 16] | [989, 16] | Passed |
| control 1 | [-54317, 6] | [-54317, 6] | Passed |
| control 2 | [-34489, -16] | [-34489, -16] | Passed |
SHA-256 / 347a4e041f03e82829a5ed59082d82ba908ab91c1a4b4fa082f1bacc5b3bd9ab
Verification & scope
Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:51:56.152532+00:00.
Case digest / b0e79c9d6639198b817863db04d6e91c65d224e3e00a38ab5555c3071d6f40cf