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SCIENCE · INVESTIGATE AND EXPLAIN

Revise a controller while retaining its failure

Compare a declared redesign on public changed conditions without claiming a hidden test.

Learning outcome: Build a traceable gain revision and separate development captures from future independently reviewed transfer evidence.

Starting recap

A scenario is a supplied deterministic condition. Reusing it after tuning is development, not independent assessment.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

Delayed gain 6 fails its first two tail samples; delayed gain 2 satisfies the full tail band in the stated run.

Open the experiment

Predict

Before changing gain, predict whether reducing it will improve delay tolerance and what nominal or energy tradeoff may remain.

Experiment

Retain delayed gain 6, write a pre-result prediction, then capture delayed gain 2. Compare every criterion and check both gains in the public nominal scenario. Document one unresolved offset or actuator failure.

Test a sampled thermal controller

Worked teaching model · synthetic values · Original fictional one-node device and assigned costs. Uniform temperature, constant heat capacity/conductance/ambient, held heater input and exact exponential propagation within each sample. No spatial gradient, evaporation, radiation law, random noise, active cooling, integral control or physical safety/efficiency/reliability certification. Public cases are exposed teaching practice. Standard hardware and zero correction are fixed; a/b select gain and scenario.

Reset keeps your prediction, captures and practice history.

Trace the observation before judging the controller

Active scenario: Nominal; matched nominal reference uses the same gain, 6 W/K. Both use standard hardware: heat capacity 100 J/K, conductance 1 W/K, initial and ambient temperature 20°C, target 30°C, cost 3 assigned tokens, and twelve 10-second intervals. Correction is fixed at zero.

  1. 1. Select an observationAt command time t, request true temperature at t − 0 s. Negative requested times use the held initial 20°C state at effective time 0; they are not measured negative-time samples.
  2. 2. Form the indication and requestAdd sensor bias 0°C; subtract zero correction. Raw and corrected indications therefore coincide, but can differ from current true temperature. Request 10 W + 6 W/K × (30°C − indication).
  3. 3. Limit and evolveClip requested power to 0–20 W, hold it for 10 s, then propagate the exact one-node thermal model. Zero power is passive cooling toward ambient, not active cooling.

The 10 W feedforward term is fixed, not integral control. A temperature difference of one degree Celsius equals one kelvin. Sensor bias changes the information used by the controller; it does not directly add heat. Delay changes which earlier state is read; clipping changes actual delivered power.

Delay timeline: read the requested and effective times in every command receipt below. In the delayed scenario, commands at 0, 10 and 20 s request −20, −10 and 0 s respectively; all use the initial state. At 30 s the request uses the state at 10 s. Commands occur at 0–110 s; the final true state at 120 s has no new sensor command.

Original fictional one-node device and assigned costs. Uniform temperature, constant heat capacity/conductance/ambient, held heater input and exact exponential propagation within each sample. No spatial gradient, evaporation, radiation law, random noise, active cooling, integral control or physical safety/efficiency/reliability certification. Public cases are exposed teaching practice.

Temperature comparison · fixed axes: 0–120 s and 15–45°C
152025303540450306090120Temperature (°C)Elapsed time (s)

Solid navy: active Nominal true temperature. Long-dashed brown: nominal true temperature at the same gain. Dotted red with circles: active raw and corrected indication at command times. Gray dashes: 30°C target. Pale band: 29–31°C criterion range, required only from 90 s onward.

Lines connect sampled states for comparison; they are not the exact curved path between samples. Indication points are plotted at the time the controller uses them, not the earlier observation time. They can differ from current true temperature; there is no terminal command at 120 s. In the nominal scenario the two true traces coincide.

Active and nominal applied heater power · fixed axes: 0–120 s and 0–20 W
051015200306090120Applied power (W)Elapsed time (s)

Solid navy: active applied power; long-dashed brown: nominal applied power; gray dotted line: active 20 W actuator ceiling. Horizontal segments are held inputs, not a smooth ramp. Requested power is tabulated rather than plotted on the applied-power scale. At least one request is outside 0–20 W; the actuator limits it.

Separate requirements at the same gain and hardware; only the operating scenario differs; judgments use full model precision
Supplied requirementActive NominalNominal reference
Temperature at 90, 100, 110 and 120 s: every value in [29,31]°C29.964, 29.988, 29.996, 29.999 °C
Meets supplied criterion
29.964, 29.988, 29.996, 29.999 °C
Meets supplied criterion
True trajectory peak ≤32°C29.999°C at 120 s
Meets supplied criterion
29.999°C at 120 s
Meets supplied criterion
Applied heater energy ≤2000 J1887.809 J
Meets supplied criterion
1887.809 J
Meets supplied criterion
Resource cost ≤6 tokens3 tokens
Meets supplied criterion
3 tokens
Meets supplied criterion
All four supplied requirementsAll met in this model runAll met in this model run

Each exact held-input interval moves monotonically toward its fixed equilibrium. Therefore interval endpoints bound the continuous peak, and the 90–120 s endpoint checks also bound the temperature between those samples in this particular model. This argument does not extend automatically to a real device or another plant model. Lower energy cannot cancel a failed temperature criterion.

All thirteen true-temperature states for the matched scenarios
Original model states; both runs begin from the same initial condition
Time (s)Active true (°C)Nominal true (°C)Active / nominal held power for next 10 s (W)
020.00000020.00000020.000000 / 20.000000
1021.90325221.90325220.000000 / 20.000000
2023.62538523.62538520.000000 / 20.000000
3025.18363625.18363620.000000 / 20.000000
4026.59359926.59359920.000000 / 20.000000
5027.86938727.86938720.000000 / 20.000000
6029.02376729.02376715.857396 / 15.857396
7029.67407329.67407311.955562 / 11.955562
8029.89118529.89118510.652888 / 10.652888
9029.96367129.96367110.217974 / 10.217974
10029.98787129.98787110.072773 / 10.072773
11029.99595129.99595110.024296 / 10.024296
12029.99864829.998648No next command
Active scenario: all twelve command and energy receipts

Requested observation time and effective sample time are separate fields. Correction is subtracted from the raw indication and is zero here. A request before 0 s uses the held initial state at effective time 0; later effective times identify actual earlier model states. Positive ambient energy is outward; a negative value would mean inward transfer. Displayed rounding may leave a tiny apparent balance difference.

Nominal · command formation and actual plant response
Step index / interval (s)True start → end (°C)Requested / effective observation (s)Raw / correction / corrected (°C)Controller error (K)Requested / applied (W)Request clippedHeater input (J)Stored change (J)To ambient (J)Balance residual (J)
0: 0–1020.000000 → 21.9032520 / 020.000 / 0.000 / 20.00010.00070.000 / 20.000Upper clipping200.000000190.3251649.6748360.00e+0
1: 10–2021.903252 → 23.62538510 / 1021.903 / 0.000 / 21.9038.09758.580 / 20.000Upper clipping200.000000172.21333027.7866700.00e+0
2: 20–3023.625385 → 25.18363620 / 2023.625 / 0.000 / 23.6256.37548.248 / 20.000Upper clipping200.000000155.82506544.1749350.00e+0
3: 30–4025.183636 → 26.59359930 / 3025.184 / 0.000 / 25.1844.81638.898 / 20.000Upper clipping200.000000140.99634959.0036510.00e+0
4: 40–5026.593599 → 27.86938740 / 4026.594 / 0.000 / 26.5943.40630.438 / 20.000Upper clipping200.000000127.57877372.4212270.00e+0
5: 50–6027.869387 → 29.02376750 / 5027.869 / 0.000 / 27.8692.13122.784 / 20.000Upper clipping200.000000115.43804784.5619530.00e+0
6: 60–7029.023767 → 29.67407360 / 6029.024 / 0.000 / 29.0240.97615.857 / 15.857No clipping158.57396365.03057893.5433850.00e+0
7: 70–8029.674073 → 29.89118570 / 7029.674 / 0.000 / 29.6740.32611.956 / 11.956No clipping119.55561621.71123497.8443820.00e+0
8: 80–9029.891185 → 29.96367180 / 8029.891 / 0.000 / 29.8910.10910.653 / 10.653No clipping106.5288767.24855499.2803210.00e+0
9: 90–10029.963671 → 29.98787190 / 9029.964 / 0.000 / 29.9640.03610.218 / 10.218No clipping102.1797432.42001699.7597270.00e+0
10: 100–11029.987871 → 29.995951100 / 10029.988 / 0.000 / 29.9880.01210.073 / 10.073No clipping100.7277330.80795199.9197820.00e+0
11: 110–12029.995951 → 29.998648110 / 11029.996 / 0.000 / 29.9960.00410.024 / 10.024No clipping100.2429620.26974499.9732180.00e+0

Active whole-run ledger: 1887.808894 J heater input = 999.864807 J stored-energy change + 887.944087 J signed transfer to ambient. Model residual: -1.14e-13 J. Energy accounting agreement does not validate the device physically.

Your comparison: predict how a changed observation or actuator limit affects true temperature, then inspect all four criteria. Compare scenarios at the same gain, or compare gains within one scenario. Use the receipt times, sensor indication and requested/applied power to explain a failure before proposing a revision. Passing one public scenario does not establish stability or reliability in other conditions. Repeating this deterministic run checks reproducibility, not field reliability or a new independent trial.

Final true temperature 29.999 degC; heater input 1887.809 J.

Peak 29.999 degC at 120 s; cost 3 assigned tokens. Tail band met; peak limit met; energy budget met; resource budget met. Synthetic model evidence, not a physical prototype or reliability estimate.

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Retain the failure before proposing a fix

Select standard hardware’s delayed scenario at gain 6 W/K. The lab fixes hardware and zero correction; you can change gain and the public operating scenario. Before trying a new setting, write what failed and what you expect a change to do. Save the original capture and add a note identifying the relevant tail samples. This workflow records development evidence; it is not the future cumulative project’s immutable candidate-freezing workflow.

The gain-6 delayed tail at 90, 100, 110 and 120 seconds is approximately 31.474386, 31.295085, 30.593203 and 29.694914°C. The first two samples exceed 31°C even though the final value is inside the band. Peak, energy and token criteria still pass. Your proposed mechanism should explain that particular failure: old sensor information keeps the heater command high after the true temperature has risen.

Predeclare a bounded revision

Propose lowering gain from 6 to 2 W/K while keeping the delayed scenario unchanged. Predict whether weaker response to an outdated error will reduce overshoot. Also predict a possible cost: reduced response strength could leave nominal tracking farther from target. Record both predictions before inspecting the revised output, then save the revised recipe and comparison note.

The current lesson prediction and reflection fields are learner-authored working records. Do not claim they create a secure hidden test or an immutable submitted design. All twelve case definitions and worked results are public, and a changed public scenario may already be familiar. Disclose that familiarity rather than erasing earlier captures to manufacture a fresh-looking sequence.

Compare all requirements on matched runs

The revised delayed gain-2 tail is approximately 30.341073, 30.359363, 30.293904 and 30.201020°C. Each value lies in the supplied inclusive 29–31°C band. Its peak is about 30.359363°C, input energy 1,922.517416 J, and cost remains three tokens. It passes all displayed requirements in this scenario.

The failed gain-6 delayed run used 1,905.207928 J, so the successful revision uses about 17.309488 J more, not less. The redesign improved the failed temperature criterion while slightly worsening input energy, still within its allowance. Preserve that tradeoff; do not describe the new setting as uniformly superior.

Now inspect the already public nominal comparison. Gain 2 ends near 29.766220°C and gain 6 near 29.998648°C. Both meet the nominal criteria, but the lower gain has a larger final error. A choice can be justified by robust performance over the stated conditions without pretending to optimize every indicator. Specify whether your priority is closer nominal tracking, delay tolerance, energy use or another supplied requirement.

Test whether the explanation addresses other failures

Changing gain does not remove the +2°C sensor offset. All three allowed gains fail that scenario’s lower tail limit. Nor can gain overcome the 8 W capacity limit: all three limited runs end near 25.590446°C. Use these counterexamples to bound the redesign claim. “Gain 2 resolves the supplied delayed-case tail failure” is supported; “gain 2 fixes the device” is too broad.

A useful failure log includes condition, violated requirement, retained receipt, proposed mechanism, change, retest result and unresolved alternative. NASA’s product-realization guidance connects verification evidence with stated requirements and distinguishes it from validation of intended use. This synthetic exercise neither demonstrates a physical prototype nor certifies operation across real environments.

Transfer: review a partial comparison

A colleague compares the original full 120-second delayed gain-6 energy with a revised gain-2 run stopped at 90 seconds. The revised energy is lower at that earlier endpoint, and its 90-second temperature is inside the band. Can the colleague conclude that the revision uses less energy and passes the original requirement? Identify what evidence is missing.

Check the unequal-duration transfer

No. The durations are unequal, so the energy totals answer different service questions. The original tail requirement also includes 100, 110 and 120 seconds, which the shortened comparison omits. Retain a full 120-second revised run, compare every specified tail sample and total energy, and report the actual tradeoff. A passing 90-second observation alone is insufficient.

For genuinely unfamiliar transfer, a human must supply a new, adequately specified failure or evidence packet and review the learner’s reasoning with help and exposure disclosed. Tuning after seeing that assignment makes subsequent comparisons developmental. The current captures remain useful public practice, not authenticated mastery. Return to prototype evidence to organize the argument or revisit sensor delay to strengthen its mechanism.

Apply

After tuning gain using the displayed delayed case, another run of that same case is:

Public practice checks a specific claim. It does not establish independent mastery.

State what the current capture workflow preserves and what still needs a human unfamiliar assignment and immutable project submission.

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

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