Keep a thermal chamber on target
Control a slow process with heating limits, sensor noise, and delayed measurements.
How much speed can a temperature loop gain before delay and saturation dominate?
Model Cth*dT/dt=q-h*(T-Ta) with Cth=600 J/K, h=5 W/K, and Ta=25 C. Heater power is limited to 0 to 100 W. The data show open-loop temperature readings. Design a PI controller for 35 C, then evaluate a 10-second sensor delay and an ambient change to 20 C. This is a simulated thermal system.
Build it, step by step
- 01
Check the equilibrium power for each reference before tuning. Estimate the 120-second time constant and 0.2 K/W gain from the CSV.
- 02
Use a 1-second controller period and an exact held-input thermal update. Compare a proportional baseline with a PI design.
- 03
Set nominal goals of error below 0.2 C, overshoot below 1 C, and 2% settling relative to the 10 C step within 600 s. Report heater energy in joules.
- 04
Add a 10-s measurement buffer and seeded 0.05 C standard-deviation sensor noise. Check the effect on stability and command variation.
- 05
Test ambient=20 C and an unreachable 50 C target followed by recovery. Compare conditional integration and back-calculation.
Your project checklist
- Energy balance and attainable equilibrium calculations.
- Temperature, heater power, and accumulated energy plots.
- Explicit delay indexing and noise seed.
- A table of nominal and adverse-case metrics with tuning recommendations.
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