FA-93611 / Solar tracker geometry / Open access
Torque-tube inclinometer rotation: angle normalisation · case 01
Angles past the flip point are reported beyond +-180.
ROOT CAUSE
The rotation is not wrapped after subtracting the offset.
VERIFIED REPAIR
Normalise to (-180, 180].
Unsuccessful approach: Wrapping to [0, 360) turns every eastward angle into a large positive one.
Case contract
ax (across-axis) and az (normal) are gravity components in g. The magnitude must be within [0.8, 1.2] g, else [None, 'fault']. Rotation = atan2(ax, az) in degrees, negated for a sensor mounted on the west side, then minus the calibration offset, normalised to (-180, 180]. Return [angle rounded 2, 'ok'].
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
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
mag = math.hypot(ax, az)
if not 0.8 <= mag <= 1.2:
return [None, 'fault']
ang = math.degrees(math.atan2(ax, az))
if mount == 'west':
ang = -ang
ang -= offset
if ang == -180:
ang = 180.0
return [round(ang, 2), 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [-0.014, -0.7999, 'west', -3], [-178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.7778, -0.7778, 'west', 5],
[-140.0, 'ok']],
['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.2, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.8485, 0.8485, 'west', 0], [-45.0, 'ok']],
['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.0, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.9526, 0.55, 'east', 0], [-60.0, 'ok']],
['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -0.8, 'west', 2], [178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.9526, 0.55, 'west', 0], [-60.0, 'ok']],
['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.1, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.5657, 0.5657, 'east', -3],
[-42.0, 'ok']],
['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
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: magnitude at lower bound | [0.0, 'ok'] | [0.0, 'ok'] | Passed |
| boundary: magnitude at upper bound | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| boundary: upside-down reading | [180.0, 'ok'] | [180.0, 'ok'] | Passed |
| regression: angle normalisation | [182.0, 'ok'] | [-178.0, 'ok'] | Failed |
| regression: angle normalisation (partial repair) | [-140.0, 'ok'] | [-140.0, 'ok'] | Passed |
| control 1 | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| control 2 | [None, 'fault'] | [None, 'fault'] | Passed |
SHA-256 / 9a3a7a42cb8062f32411a88d2f2b6d7a4ac956a95625cacfad2de208634a79ef
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
mag = math.hypot(ax, az)
if not 0.8 <= mag <= 1.2:
return [None, 'fault']
ang = math.degrees(math.atan2(ax, az))
if mount == 'west':
ang = -ang
ang -= offset
ang = ang % 360
if ang == -180:
ang = 180.0
return [round(ang, 2), 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [-0.014, -0.7999, 'west', -3], [-178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.7778, -0.7778, 'west', 5],
[-140.0, 'ok']],
['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.2, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.8485, 0.8485, 'west', 0], [-45.0, 'ok']],
['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.0, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.9526, 0.55, 'east', 0], [-60.0, 'ok']],
['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -0.8, 'west', 2], [178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.9526, 0.55, 'west', 0], [-60.0, 'ok']],
['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.1, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.5657, 0.5657, 'east', -3],
[-42.0, 'ok']],
['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
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: magnitude at lower bound | [0.0, 'ok'] | [0.0, 'ok'] | Passed |
| boundary: magnitude at upper bound | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| boundary: upside-down reading | [180.0, 'ok'] | [180.0, 'ok'] | Passed |
| regression: angle normalisation | [182.0, 'ok'] | [-178.0, 'ok'] | Failed |
| regression: angle normalisation (partial repair) | [220.0, 'ok'] | [-140.0, 'ok'] | Failed |
| control 1 | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| control 2 | [None, 'fault'] | [None, 'fault'] | Passed |
SHA-256 / c2de6afb8762cf4b23ec403c73b1fe0341fdf81fa006caaa576c05fce87a188e
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
mag = math.hypot(ax, az)
if not 0.8 <= mag <= 1.2:
return [None, 'fault']
ang = math.degrees(math.atan2(ax, az))
if mount == 'west':
ang = -ang
ang -= offset
ang = (ang + 180) % 360 - 180
if ang == -180:
ang = 180.0
return [round(ang, 2), 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [-0.014, -0.7999, 'west', -3], [-178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.7778, -0.7778, 'west', 5],
[-140.0, 'ok']],
['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.2, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.8485, 0.8485, 'west', 0], [-45.0, 'ok']],
['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.0, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.9526, 0.55, 'east', 0], [-60.0, 'ok']],
['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -0.8, 'west', 2], [178.0, 'ok']],
['regression: angle normalisation (partial repair)', [0.9526, 0.55, 'west', 0], [-60.0, 'ok']],
['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
['regression: angle normalisation', [0.0, -1.1, 'east', -3], [-177.0, 'ok']],
['regression: angle normalisation (partial repair)', [-0.5657, 0.5657, 'east', -3],
[-42.0, 'ok']],
['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
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: magnitude at lower bound | [0.0, 'ok'] | [0.0, 'ok'] | Passed |
| boundary: magnitude at upper bound | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| boundary: upside-down reading | [180.0, 'ok'] | [180.0, 'ok'] | Passed |
| regression: angle normalisation | [-178.0, 'ok'] | [-178.0, 'ok'] | Passed |
| regression: angle normalisation (partial repair) | [-140.0, 'ok'] | [-140.0, 'ok'] | Passed |
| control 1 | [90.0, 'ok'] | [90.0, 'ok'] | Passed |
| control 2 | [None, 'fault'] | [None, 'fault'] | Passed |
SHA-256 / 7885cc3ecb8683e3fe35435a836316632ae67b3f8dde6b98bfbc01e6cd7d3899
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 2026-09-29T14:51:56.787387+00:00.
Case digest / 9e51b65ee35dfcd74a99108babde5092760cdd9e43f33ac609665026ff74039a