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.
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
| Type | Range | Accuracy | Response | Cost |
|---|---|---|---|---|
| Thermocouple | -200 to 2,300°C | ±1-2°C | Fast | Low |
| RTD (Pt100) | -200 to 850°C | ±0.1°C | Moderate | Medium |
| Thermistor | -100 to 300°C | ±0.1°C | Fast | Low |
| Infrared (IR) | -50 to 3,000°C | ±1-2% | Very fast | High |
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
| Type | Principle | Application |
|---|---|---|
| Bourdon tube | Elastic deformation of curved tube | Mechanical gauges |
| Diaphragm | Deflection of thin membrane | Process control |
| Piezoelectric | Voltage from crystal deformation | Dynamic pressure |
| Strain gauge | Resistance change with deformation | Force/load cells |
| Manometer | Hydrostatic pressure column | Calibration, lab |
Flow Measurement
| Device | Principle | Type |
|---|---|---|
| Orifice plate | Pressure drop at restriction | Differential pressure |
| Venturi meter | Pressure drop at constriction | Differential pressure |
| Rotameter | Float in tapered tube | Variable area |
| Turbine meter | Rotor speed ∝ flow rate | Velocity |
| Ultrasonic | Transit time or Doppler shift | Non-invasive |
| Coriolis | Mass flow from tube vibration | Mass flow |
Position/Motion Sensors
| Sensor | Measures | Output |
|---|---|---|
| LVDT | Linear displacement | AC voltage (analog) |
| Encoder (rotary) | Angular position/speed | Digital pulses |
| Accelerometer | Acceleration | Voltage (analog) |
| Proximity sensor | Presence/distance | Digital/analog |
| Tachometer | Rotational speed | Voltage or pulses |
Data Acquisition (DAQ)
Signal Chain
- Sensor → physical quantity to raw signal
- Signal conditioning → amplification, filtering, linearization
- Multiplexer → selects between multiple channels
- A/D converter → analog signal to digital data
- Computer/controller → processes and stores data
Sampling and Nyquist Theorem
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 Type | Purpose |
|---|---|
| Low-pass | Removes high-frequency noise |
| High-pass | Removes DC offset and low-frequency drift |
| Band-pass | Keeps 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
| Feature | Open-Loop | Closed-Loop |
|---|---|---|
| Feedback | None | Measures output, adjusts input |
| Accuracy | Lower | Higher |
| Stability | Always stable | Can become unstable |
| Cost | Lower | Higher |
| Example | Toaster timer | Thermostat |
PID Control
The most widely used control algorithm:
where e(t) = setpoint - measured value (error)
| Term | Effect | Purpose |
|---|---|---|
| P (Proportional) | Output ∝ error | Reduces error; cannot eliminate steady-state error |
| I (Integral) | Output ∝ accumulated error | Eliminates steady-state error |
| D (Derivative) | Output ∝ rate of change of error | Anticipates future error; reduces overshoot |
Logic Diagrams
Basic Logic Gates
| Gate | Symbol | Output | Truth |
|---|---|---|---|
| AND | A · B | 1 only if both inputs are 1 | 0,0→0; 0,1→0; 1,0→0; 1,1→1 |
| OR | A + B | 1 if either input is 1 | 0,0→0; 0,1→1; 1,0→1; 1,1→1 |
| NOT | Ā | Inverts input | 0→1; 1→0 |
| NAND | (A·B)' | NOT AND | 0,0→1; 0,1→1; 1,0→1; 1,1→0 |
| NOR | (A+B)' | NOT OR | 0,0→1; 0,1→0; 1,0→0; 1,1→0 |
| XOR | A⊕B | 1 if inputs differ | 0,0→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'
According to the Nyquist theorem, what is the minimum sampling rate for a signal with a maximum frequency of 500 Hz?
Which temperature sensor is generally the most accurate?
In a PID controller, which term eliminates steady-state error?
What is the output of a NAND gate when both inputs are 1?
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