Sensors, Data Acquisition, and Control Systems

FE Exam Weight: Instrumentation and Controls is 4–6 questions (~5%) on the FE Other Disciplines exam — the lowest-weighted topic, but the questions are usually conceptual and quick. Definitions and the relevant equations are in the searchable NCEES FE Reference Handbook.

Sensors and Transducers

A sensor detects a physical quantity; a transducer converts one form of energy into another, almost always producing an electrical signal proportional to the measured variable. The output may be a voltage, a current (the 4–20 mA industrial standard, where the 4 mA "live zero" lets you distinguish a true zero reading from a broken wire), a resistance change, or digital pulses.

Temperature Sensors

A thermocouple joins two dissimilar metals; the junction produces a small temperature-dependent voltage (the Seebeck effect). It is rugged and spans the widest range but is the least accurate; common types are J (iron–constantan), K (chromel–alumel), and T (copper–constantan). An RTD exploits the nearly linear rise of platinum's resistance with temperature (Pt100 = 100 Ω at 0°C); it is the most accurate and stable choice. A thermistor is a semiconductor whose resistance changes dramatically (and nonlinearly) with temperature, giving high sensitivity over a narrow range; negative-temperature-coefficient (NTC) types are most common.

Pressure, Flow, and Motion Sensors

Pressure is measured by elastic-deformation devices — a Bourdon tube (a curved tube that straightens with pressure, driving a mechanical gauge), a diaphragm, a piezoelectric crystal (best for fast, dynamic pressures), or a strain gauge bonded to a flexing element. A manometer balances pressure against a liquid column and is used for calibration.

Strain gauges deserve special attention: a metal foil grid changes resistance as it stretches, quantified by the gauge factor GF = (ΔR/R)/ε, where ε is strain. Because ΔR is tiny, strain gauges are wired into a Wheatstone bridge that converts the small resistance change into a measurable voltage and cancels temperature drift. Strain gauges are the heart of load cells for force and weight.

Flow devices include differential-pressure types — the orifice plate and Venturi meter create a pressure drop that scales with flow (via Bernoulli); the rotameter (variable-area float in a tapered tube); the turbine meter (rotor speed ∝ flow); non-invasive ultrasonic meters (transit-time or Doppler); and the Coriolis meter, which measures true mass flow from the deflection of a vibrating tube.

Position and motion: an LVDT gives analog AC output proportional to linear displacement; a rotary encoder outputs digital pulses for angular position and speed; an accelerometer outputs voltage proportional to acceleration; a proximity sensor detects presence; a tachometer measures rotational speed.

Measurement Error, Accuracy, and Precision

Accuracy is how close a reading is to the true value; precision (repeatability) is how consistently the instrument returns the same reading. The two are independent: a sensor can be precise but inaccurate (tight cluster, wrong center — a systematic/bias error) or accurate on average but imprecise (scattered — random error). Resolution is the smallest change a device can detect, and calibration is the procedure of comparing an instrument against a traceable standard and adjusting it to remove bias. Hysteresis is a different reading for the same input depending on whether the input was increasing or decreasing.

Data Acquisition (DAQ)

The signal chain converts a physical quantity into stored digital data: sensor → signal conditioning (amplification, filtering, linearization) → multiplexer → analog-to-digital (A/D) converter → computer/controller.

Sampling and the Nyquist theorem. A continuous signal must be sampled fast enough to be reconstructed: $f_s \geq 2 f_{max}$ The sampling rate must be at least twice the highest frequency present. Sample too slowly and aliasing occurs — high-frequency content masquerades as a false low frequency that cannot be removed afterward. In practice engineers sample at 5–10× the highest frequency and use an anti-aliasing low-pass filter before the A/D converter.

Resolution of an A/D converter. An n-bit converter divides its full-scale range into 2ⁿ discrete levels, so resolution = (full-scale range)/2ⁿ. Worked example: a 12-bit converter on a 0–10 V range has 2¹² = 4,096 levels, so resolution = 10 V/4,096 = 2.44 mV per step.

Control Systems

An open-loop controller acts on its input without checking the result (a toaster timer); a closed-loop controller measures the output and feeds it back to correct the input, comparing the measured process variable to the setpoint and acting on the error e(t) = setpoint − measured. Feedback gives accuracy and disturbance rejection but can become unstable if poorly tuned. Block diagrams represent these paths; each block's input–output ratio is its transfer function.

The dominant algorithm is PID control: $u(t) = K_p\,e(t) + K_i\!\int e(t)\,dt + K_d\frac{de(t)}{dt}$

The key fact tested: only the integral term drives the steady-state error to zero, while too much derivative gain amplifies noise. Calibrating sensors and tuning these gains (e.g., by the Ziegler–Nichols method) make the loop both accurate and stable.