ME or MEng Master of Engineering Control Systems and Dynamics 3

Question 1

According to the Routh-Hurwitz stability criterion, a system is stable if and only if:

Accepted Answer

All elements in the first column of the Routh array are positive

Answer

The Routh-Hurwitz criterion requires all entries in the first column of the Routh array to be positive (same sign) for the system to be stable.

Question 2

Gain margin is best defined as the additional open-loop gain that can be applied before the system becomes:

Accepted Answer

Marginally stable or unstable

Answer

Gain margin quantifies how much the loop gain can be increased beyond its current value before the closed-loop system reaches the verge of instability.

Question 3

On a root locus diagram, open-loop poles and zeros are marked by convention as:

Accepted Answer

Poles as crosses (X), zeros as circles (O)

Answer

By standard convention, poles are denoted by × (crosses) and zeros by ○ (circles) on a root locus plot.

Question 4

In state-space representation, the standard system matrices are labeled:

Accepted Answer

A, B, C, D

Answer

State-space equations use A (system/state matrix), B (input matrix), C (output matrix), and D (feedthrough matrix): ẋ = Ax + Bu, y = Cx + Du.

Question 5

Phase margin is measured at which frequency on a Bode plot?

Accepted Answer

The gain crossover frequency where magnitude = 0 dB

Answer

Phase margin is the additional phase lag (above −180°) present at the gain crossover frequency, where the open-loop magnitude is exactly 0 dB (unity gain).

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Control Systems and Dynamics 3