Measurements and Control
Measurements and Control tests indicating instruments, bridges, transducers, error analysis and linear control-system modelling. Expect numericals on bridge balance, CT/PT loading, potentiometers, Routh stability and second-order response.
Instruments
PMMC reads average and is used for DC; moving-iron reads RMS and works on AC and DC. A CT must never be open-circuited on the secondary; a PT must not be short-circuited. Wheatstone bridge is for medium resistance, Kelvin double bridge for low resistance, and Megger for insulation. A potentiometer measures an unknown emf by comparing it with a standard cell at zero current.
Control
Closed-loop transfer function C/R = G/(1 + GH). The Routh array gives absolute stability and the number of right-half-plane poles. For a second-order system, ζ and ω_n set overshoot and settling time. In Bode plots, gain margin is measured at phase crossover and phase margin at gain crossover.
Worked example
For s³ + 4s² + 5s + 2 = 0, the Routh array is: s³: 1, 5; s²: 4, 2; s¹: (4 × 5 − 1 × 2)/4 = 4.5; s⁰: 2. All first-column entries are positive, so there are no right-half-plane roots and the system is stable. The auxiliary equation is not needed because no row of zeros occurs.
Traps
Treating a PMMC reading as RMS on AC; forgetting CT burden; reversing bridge arms; missing a sign change in Routh; and confusing gain margin with gain crossover frequency.