Explain calibration techniques (one-point, two-point, multi-point)

🔧 3 Monitoring and Control – Calibration Techniques

🎯 One‑Point Calibration

Think of it like tuning a single note on a guitar. You set the instrument to a known reference value and adjust the sensor so it reads that value exactly.

1. Place the sensor in a known environment (e.g., a 25 °C water bath).
2. Record the sensor output V_out.
3. Apply a correction factor: offset = V_ref – V_out.
4. Store the offset in the device’s calibration table.

Result: V_corrected = V_out + offset.

📏 Two‑Point Calibration

Now imagine tuning a guitar to two notes. You adjust both the offset and the gain so the sensor matches two known points.

• Take two reference measurements: (x₁, y₁) and (x₂, y₂).
• Compute the slope (gain): m = (y₂ – y₁) / (x₂ – x₁) .
• Compute the intercept (offset): b = y₁ – m·x₁.
• Apply the linear correction: y_corrected = m·x + b.

Mathematically:

$$y_{\text{corrected}} = m \cdot x + b$$

🧮 Multi‑Point Calibration

For complex sensors, a single line may not be enough. Think of it as tuning a full chord on a piano – you need multiple notes to capture the whole sound.

1. Collect a set of N reference points: {(x_i, y_i)_i=1…N}.
2. Use linear regression to find the best fit line: minimize Σ(y_i – (m·x_i + b))².
3. Compute m and b using the formulas:
• m = (N Σx_iy_i – Σx_i Σy_i) / (N Σx_i² – (Σx_i)²)
• b = (Σy_i – m Σx_i) / N
4. Store the regression parameters and use them for all future readings.

Result: y_corrected = m·x + b, but now m and b are derived from many points, giving higher accuracy.

📊 Comparison Table

💡 Quick Tips for Students

• Always use a known reference – a calibrated standard.
• Record multiple readings at each reference point to reduce random error.
• Check the linearity of your sensor: if the plot of raw vs. reference values is not a straight line, consider multi‑point calibration.
• Keep a calibration log – date, reference values, calculated parameters.

🎓 Summary

Calibration is like fine‑tuning a musical instrument: one‑point is a quick pitch check, two‑point adjusts both pitch and volume, and multi‑point ensures the whole orchestra sounds harmonious. Choose the technique that balances effort with the accuracy your project needs.