Sensors, Data Acquisition, and Control Systems

Key Takeaways

  • Sensors convert physical quantities (temperature, pressure, flow, position) into electrical signals.
  • Common temperature sensors: thermocouples (wide range, rugged), RTDs (most accurate), thermistors (high sensitivity).
  • Data acquisition involves sampling, filtering, amplification, and analog-to-digital (A/D) conversion.
  • Nyquist theorem: sampling rate must be at least 2× the highest frequency in the signal to avoid aliasing.
  • Control systems use feedback to maintain a process variable at a setpoint: PID control is the most common.
  • Logic diagrams (AND, OR, NOT, NAND, NOR) represent digital control logic for automated systems.
Last updated: March 2026

Sensors, Data Acquisition, and Control Systems

FE Exam Weight: Instrumentation and Controls accounts for 4-6 questions (~5% of the exam). While the lowest-weighted topic, these are often straightforward conceptual questions.

Sensors and Transducers

A sensor detects a physical quantity. A transducer converts one form of energy to another (usually to an electrical signal).

Temperature Sensors

TypeRangeAccuracyResponseCost
Thermocouple-200 to 2,300°C±1-2°CFastLow
RTD (Pt100)-200 to 850°C±0.1°CModerateMedium
Thermistor-100 to 300°C±0.1°CFastLow
Infrared (IR)-50 to 3,000°C±1-2%Very fastHigh

Thermocouple: Two dissimilar metals joined at a junction; voltage proportional to temperature difference (Seebeck effect). Types: J (iron-constantan), K (chromel-alumel), T (copper-constantan).

RTD: Resistance changes with temperature (most commonly platinum, Pt100 = 100 Ω at 0°C). Most accurate and stable.

Thermistor: Semiconductor whose resistance changes dramatically with temperature. High sensitivity but narrow range. NTC (negative temperature coefficient) is most common.

Pressure Sensors

TypePrincipleApplication
Bourdon tubeElastic deformation of curved tubeMechanical gauges
DiaphragmDeflection of thin membraneProcess control
PiezoelectricVoltage from crystal deformationDynamic pressure
Strain gaugeResistance change with deformationForce/load cells
ManometerHydrostatic pressure columnCalibration, lab

Flow Measurement

DevicePrincipleType
Orifice platePressure drop at restrictionDifferential pressure
Venturi meterPressure drop at constrictionDifferential pressure
RotameterFloat in tapered tubeVariable area
Turbine meterRotor speed ∝ flow rateVelocity
UltrasonicTransit time or Doppler shiftNon-invasive
CoriolisMass flow from tube vibrationMass flow

Position/Motion Sensors

SensorMeasuresOutput
LVDTLinear displacementAC voltage (analog)
Encoder (rotary)Angular position/speedDigital pulses
AccelerometerAccelerationVoltage (analog)
Proximity sensorPresence/distanceDigital/analog
TachometerRotational speedVoltage or pulses

Data Acquisition (DAQ)

Signal Chain

  1. Sensor → physical quantity to raw signal
  2. Signal conditioning → amplification, filtering, linearization
  3. Multiplexer → selects between multiple channels
  4. A/D converter → analog signal to digital data
  5. Computer/controller → processes and stores data

Sampling and Nyquist Theorem

fs2fmaxf_s \geq 2 f_{max}

The sampling frequency must be at least twice the highest frequency component in the signal. If undersampled, aliasing occurs (high frequencies appear as false low frequencies).

In practice: Use sampling rates 5-10× the highest frequency for good signal reconstruction.

Resolution

A/D converter resolution:

  • n-bit converter has 2ⁿ discrete levels
  • Resolution = full-scale range / 2ⁿ
  • Example: 12-bit converter with 0-10 V range: resolution = 10/4,096 = 2.44 mV

Filtering

Filter TypePurpose
Low-passRemoves high-frequency noise
High-passRemoves DC offset and low-frequency drift
Band-passKeeps only frequencies in a specific range
Notch (band-stop)Removes a specific frequency (e.g., 60 Hz hum)

Control Systems

Open-Loop vs. Closed-Loop Control

FeatureOpen-LoopClosed-Loop
FeedbackNoneMeasures output, adjusts input
AccuracyLowerHigher
StabilityAlways stableCan become unstable
CostLowerHigher
ExampleToaster timerThermostat

PID Control

The most widely used control algorithm:

u(t)=Kpe(t)+Kie(t)dt+Kdde(t)dtu(t) = K_p e(t) + K_i \int e(t) \, dt + K_d \frac{de(t)}{dt}

where e(t) = setpoint - measured value (error)

TermEffectPurpose
P (Proportional)Output ∝ errorReduces error; cannot eliminate steady-state error
I (Integral)Output ∝ accumulated errorEliminates steady-state error
D (Derivative)Output ∝ rate of change of errorAnticipates future error; reduces overshoot

Logic Diagrams

Basic Logic Gates

GateSymbolOutputTruth
ANDA · B1 only if both inputs are 10,0→0; 0,1→0; 1,0→0; 1,1→1
ORA + B1 if either input is 10,0→0; 0,1→1; 1,0→1; 1,1→1
NOTĀInverts input0→1; 1→0
NAND(A·B)'NOT AND0,0→1; 0,1→1; 1,0→1; 1,1→0
NOR(A+B)'NOT OR0,0→1; 0,1→0; 1,0→0; 1,1→0
XORA⊕B1 if inputs differ0,0→0; 0,1→1; 1,0→1; 1,1→0

Boolean Algebra Laws

  • Commutative: A + B = B + A; A · B = B · A
  • Associative: (A + B) + C = A + (B + C)
  • Distributive: A · (B + C) = A·B + A·C
  • De Morgan's: (A·B)' = A' + B'; (A+B)' = A' · B'
Test Your Knowledge

According to the Nyquist theorem, what is the minimum sampling rate for a signal with a maximum frequency of 500 Hz?

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Test Your Knowledge

Which temperature sensor is generally the most accurate?

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Test Your Knowledge

In a PID controller, which term eliminates steady-state error?

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D
Test Your Knowledge

What is the output of a NAND gate when both inputs are 1?

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D
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