Preserve a failed design and justify a revision

Make the failure useful

A prototype comparison is more informative when a failed design remains visible. Begin with the insulated hardware at gain 2 W/K. Record a prediction, capture the entire run and identify the violated criterion before changing anything. Its tail temperatures at 90, 100, 110 and 120 seconds are approximately 30.798, 31.091, 31.313 and 31.481°C. The last three exceed the 31°C limit. This is a specific failure, not a vague statement that the design “looks unstable.”

Its input energy, about 1,624.625 J, is below 2,000 J. Its peak is below 32°C, and its five-token cost is below six. Retain those successes alongside the failure. A design does not pass a hard requirement merely because three other indicators look favorable.

Write a reproducible failure log

Use five headings: requirement, observed model symptom, mechanism hypothesis, proposed change and retest result. Under requirement, write the inclusive tail band and the exact times being checked. Under symptom, record the failing rows rather than only the final temperature. Under hypothesis, explain that the lower-conductance hardware needs less steady power near the target while the controller retains its ten-watt feedforward contribution.

Propose changing only gain from 2 to 6 W/K. Before running, predict the direction of the temperature change and whether hardware cost can change. Keep the same initial temperature, ambient, capacity, conductance, heater limit, sampling interval and duration. This is a controlled revision of the controller for the same hardware, not a new insulation experiment.

Retest every criterion

The revised insulated gain-6 run has tail temperatures approximately 30.735, 30.757, 30.765 and 30.768°C. Its peak is about 30.768°C, total heater input about 1,558.581 J, and cost remains five tokens. It meets the listed nominal criteria. The energy reduction from the failed candidate is approximately 66.044 J; calculate that subtraction without calling it measured electrical savings from a real product.

Do not stop the successful run early and compare its shorter energy total against the original 120-second result. Preserve both full traces. The visual presents a fixed time axis so you can compare behavior at the same times. Check the requested/applied power ledger when explaining a plateau: the actuator may clip a command, and a clipped request is not delivered energy.

The peak calculation has a special justification here. During each held-input interval, the one-node temperature moves monotonically toward that interval’s equilibrium. Therefore the interval maximum occurs at an endpoint. This property lets the model check the continuous peak from its endpoints. It does not mean sparse samples bound every real device’s temperature; unmodeled dynamics can violate that argument.

State what has been verified

Write a conclusion that names hardware, gain, scenario, model version, time horizon and criteria. The result supports a passing candidate in the nominal simulated conditions. NASA’s product-realization guidance distinguishes checking requirements from establishing that a product fulfills its intended use. Here no actual enclosure, sensor or user setting has been measured, so physical validation remains absent.

The six selectable hardware/gain combinations are deterministic teaching cases. Repeating one a hundred times does not create a hundred independently manufactured devices or establish a field reliability percentage. Public solutions, worked examples and captured traces also remain exposed practice. A later independently reviewed assignment must record what the learner already saw and what help was available.

Transfer: a stricter input-energy criterion

On paper, keep the original temperature and cost requirements but lower the input-energy ceiling to 1,500 J. Compare the insulated gain-6 result, 1,558.581 J, with the insulated gain-12 result, approximately 1,515.221 J. The latter has a peak near 30.407°C and satisfies the original tail band. Is either now feasible, and should the model turn its heater off when it crosses the new ceiling?

Check the stricter-energy transfer

Neither meets the new energy criterion: they exceed it by about 58.581 J and 15.221 J. Lower input is an improvement without being sufficient. The ceiling is an acceptance criterion, not an implemented energy cutoff, so changing the paper brief does not change the recorded trajectories. A cutoff would require a new operating rule and a new temperature calculation.

Keep the failed and revised captures, your before-result prediction and the transfer conclusion together. A genuinely new test might change ambient conditions or reveal a sensor scale error; first specify the evidence and model needed rather than pretending those changes are controls in this six-state lab. Return to design requirements or calibration comparison to repair a weak part of the argument.