BEE Control Systems Theory 3

Question 1

The phase margin of a stable feedback system is measured at the frequency where the open-loop magnitude is:

Accepted Answer

0 dB (unity gain)

Answer

Phase margin is the additional phase lag at the gain crossover frequency (where |G(jω)H(jω)| = 1, or 0 dB) before the system becomes unstable.

Question 2

Which of the following statements about the root locus is correct?

Accepted Answer

Branches start at open-loop poles and end at open-loop zeros (or infinity)

Answer

Root locus branches begin at open-loop poles (K=0) and terminate at open-loop zeros or travel to infinity along asymptotes as K→∞.

Question 3

A second-order system with ζ = 0.5 and ωn = 10 rad/s has a damped natural frequency (ωd) of:

Accepted Answer

8.66 rad/s

Answer

The damped natural frequency is ωd = ωn√(1−ζ²) = 10√(1−0.25) = 10√0.75 ≈ 8.66 rad/s.

Question 4

In the Nyquist stability criterion, encirclements of the −1+j0 point in the clockwise direction are counted to determine:

Accepted Answer

The number of unstable closed-loop poles

Answer

By the Nyquist criterion, N = Z − P, where N is clockwise encirclements of −1, P is open-loop RHP poles, and Z is closed-loop RHP poles (instability count).

Question 5

A system is said to be observable if:

Accepted Answer

The initial state can be determined from the output over a finite time interval

Answer

Observability means that every initial state x(0) can be uniquely determined by observing the output y(t) over a finite time interval.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

BEE Control Systems Theory 3