Instrumentation, Measurement and Control: Meters, Bridges, Transducers and Response
This domain tests measurement principles (meter types, bridges, CT/PT burden, transducers) and elementary control theory (transfer functions, second-order response, stability).
Meters and bridges
- PMMC responds to average value, is DC-only, has a uniform scale and is used with rectifiers for AC.
- Moving-iron instruments work on AC and DC, read RMS, and have a non-uniform scale.
- A dynamometer wattmeter has a high-resistance pressure coil and a current coil; pressure-coil inductance causes error at low power factor and is compensated by a capacitor.
- Wheatstone bridge for medium resistance, Kelvin double bridge for low resistance, Maxwell bridge for inductance, Schering bridge for capacitance and tan δ.
Transducers and control
- LVDT gives a linear AC output proportional to displacement; strain gauge gauge factor is typically about 2; RTDs and thermocouples cover temperature.
- Second-order system: overshoot = 100·e^(−πζ/√(1−ζ²)), 2% settling time ≈ 4/(ζω_n).
- Routh–Hurwitz gives absolute stability; steady-state error depends on system type and input.
Worked example
For ζ = 0.5 and ω_n = 10 rad/s: exponent = −π(0.5)/√(0.75) = −1.814, so overshoot = 100·e^(−1.814) ≈ 16.3%. Settling time (2% band) = 4/(0.5 × 10) = 0.8 s.
Traps
Assuming a PMMC meter reads AC (it reads zero), ignoring wattmeter power-factor error, and using the 5% settling formula 3/(ζω_n) when the question specifies 2%.