Control Systems and Instrumentation
Core concepts
Understand transfer functions, block-diagram reduction, and signal-flow graphs. Master time response (first and second order: damping ratio, natural frequency, overshoot, settling time) and steady-state error via system type. Study Routh-Hurwitz stability, root locus rules, Bode plots (gain margin, phase margin, crossover), and Nyquist criterion. For instrumentation, know bridge circuits, transducers, error analysis, and calibration.
Traps examiners set
- Steady-state error is zero for a type-1 system under step input, but finite under ramp.
- Gain margin is measured where phase crosses -180 degrees, not at gain crossover.
- A system can be stable with negative phase margin only if the Nyquist plot encircles correctly; do not assume.
- Damping ratio less than one means underdamped and overshoot; equal to one is critically damped with no overshoot.
- Bridge balance conditions depend on both magnitude and phase for AC bridges.
Worked rule of thumb
For a standard second-order system, percent overshoot = 100exp(-pizeta/sqrt(1-zeta^2)). Example: zeta = 0.5 gives exp(-pi0.5/0.866) = exp(-1.814) is about 0.163, so overshoot about 16.3 percent. Settling time (2 percent) is approximately 4/(zetaomega_n).
Practice strategy
Always compute the closed-loop characteristic equation before judging stability.