Instrumentation, Measurement, and Control Systems
Instrumentation questions test whether you can quantify what a measurement means; control questions test loop structure, tuning, and stability.
Core rules
- Accuracy is closeness to the true value; precision is repeatability. Error sources include bias (offset and gain), random noise, hysteresis, and drift.
- Uncertainty propagation: for R = f(x,y), worst-case absolute errors add linearly, while independent random relative errors add in quadrature: (u_R/R)² = (u_x/x)² + (u_y/y)².
- Sensors: a thermocouple needs cold-junction compensation; an RTD has a positive, near-linear response; strain gauges use a Wheatstone bridge; an LVDT measures displacement; piezoelectric sensors measure dynamic quantities.
- Sampling: the Nyquist criterion requires f_s > 2f_max to avoid aliasing.
- Control: negative feedback reduces sensitivity to disturbances. PID output = K_p e + K_i∫e dt + K_d de/dt. Integral action removes steady-state offset; derivative action amplifies noise. Stability is assessed with Routh–Hurwitz, root location, or gain and phase margins.
Worked example
R = V/I with V = 10 ± 0.1 V and I = 2 ± 0.02 A, so R = 5 Ω. The relative errors are 0.01 and 0.01; in quadrature the combined relative uncertainty is √(0.01² + 0.01²) = 0.0141, giving u_R = 0.071 Ω. Worst-case linear addition would give 0.1 Ω. Read the question to see which convention it expects.
Traps
- Omitting cold-junction compensation on a thermocouple reading.
- Sampling exactly at f_max and aliasing higher-frequency content.
- Assuming more integral gain always improves response; excess causes overshoot and windup.
- Reporting more significant figures than the instrument resolution supports.