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

3 Monitoring and Control

3.1 Monitoring and measurement technologies

Monitoring systems convert a physical quantity into an electrical signal using a sensor. The table below lists the sensor types required by the Cambridge AS & A‑Level syllabus (9626), together with typical ranges, accuracies, output signals and common applications.

3.2 Control technologies

Control systems act on the information supplied by the sensors. The main elements are:

• Actuators – convert an electrical command into a physical action.
  • Linear: solenoid, stepper, pneumatic cylinder
  • Rotary: servo motor, DC motor, stepper motor
  • Hydraulic & pneumatic power units
• Controllers – micro‑processor / micro‑controller based devices that execute control algorithms, read sensor inputs and drive actuators (e.g., Arduino, Raspberry Pi, PLC).
• Communication networks
  • Wired (RS‑485, CAN, Ethernet)
  • Wireless (Zigbee, LoRa, Bluetooth, Wi‑Fi)
• IoT / Smart‑home platforms – cloud services, mobile apps and voice assistants for remote monitoring and control.

Typical exam‑style examples (useful for Paper 1/3):

1. Temperature‑controlled greenhouse – temperature sensor → controller → heating element (linear actuator).
2. Traffic‑light controller – photo‑sensor detects vehicle presence → micro‑controller → relay‑driven LEDs (binary actuator).
3. Smart‑irrigation system – soil‑moisture sensor → wireless node → solenoid valve (linear actuator) powered by a battery‑operated controller.

3.3 Calibration – importance and techniques

Why calibrate?

• Removes systematic (bias) errors that would otherwise accumulate in a control loop.
• Provides traceability to a recognised standard (e.g., NIST, IEC).
• Improves reliability, safety and regulatory compliance.

Types of error addressed by calibration

• Offset error – constant difference between measured and true value.
• Gain (scale) error – proportional deviation across the range.
• Non‑linearity – deviation that varies with the magnitude of the measurement.

Calibration techniques

One‑point calibration

• Assumption: sensor response is perfectly linear over the required range.
• Procedure
  1. Apply a single known reference (e.g., 100 °C for a temperature sensor).
  2. Record the raw output R_ref.
  3. Calculate a scaling factor k = V_true / R_ref and store it in firmware.
• Units: k has units of “true value per sensor unit”. Residual error is due to non‑linearity.

Two‑point calibration

• Purpose: correct both offset and gain for an approximately linear sensor.
• Procedure
  1. Select a low reference point R_low with true value V_low.
  2. Select a high reference point R_high with true value V_high.
  3. Measure the raw outputs R_low and R_high.
  4. Compute
     Gain = (V_high – V_low) / (R_high – R_low)
     Offset = V_low – Gain·R_low
  5. Apply the linear conversion to any future reading R_meas:
     V_actual = Gain·R_meas + Offset
• Units: Gain – “true value per sensor unit”; Offset – same units as the true value.
• Uncertainty propagation:
  u_V = √[(u_gain·R_meas)² + u_offset²]

Multi‑point calibration

• When required: sensor exhibits noticeable non‑linearity or the operating range is wide.
• Procedure
  1. Choose n (≥ 3) reference points (R_i, V_i) covering the full range.
  2. Record the raw output R_i at each known true value V_i.
  3. Fit an appropriate model:
     • Polynomial (e.g., V = aR² + bR + c) – coefficients obtained by least‑squares regression.
     • Piece‑wise linear interpolation using a lookup table.
  4. Implement the model in controller firmware or as a table‑lookup routine.
• Advantages: compensates for non‑linearity, delivers the highest accuracy.
• Disadvantages: longer calibration time, greater storage and processing requirements.

3.4 Comparison of calibration techniques

3.5 Advantages & disadvantages of sensor and actuator technologies

3.6 Example algorithm and flowchart – simple thermostat control

Pseudocode (algorithm)

SET setpoint = 22.0               // °C
READ T_raw FROM temperature_sensor
V_actual = Gain * T_raw + Offset // two‑point calibrated temperature

IF V_actual < setpoint - 0.5 THEN
    TURN heater ON
ELSE IF V_actual > setpoint + 0.5 THEN
    TURN heater OFF
END IF

WAIT 1 second
REPEAT

Flowchart symbols (Cambridge syllabus reference)

• Oval – Start / End
• Parallelogram – Input / Output (read sensor, display value)
• Rectangle – Process (apply calibration, compare with set‑point)
• Diamond – Decision (temperature too low?, too high?)
• Arrows – Flow direction

3.7 Practical activity – two‑point calibration of a temperature sensor