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

All poles are located in the right-half s-plane

Answer

The determinant of the system matrix is zero

Answer

All coefficients of the characteristic polynomial alternate in sign

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

Overdamped

Answer

Critically damped

Answer

Underdamped

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

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

Answer

Both marked as filled squares

Answer

Both marked as filled triangles

Question 4

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

Accepted Answer

A, B, C, D

Answer

P, Q, R, S

Answer

K, L, M, N

Answer

X, Y, Z, W

Question 5

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

Accepted Answer

The gain crossover frequency where magnitude = 0 dB

Answer

The phase crossover frequency where phase = −180°

Answer

The natural frequency ωn of the closed-loop system

Answer

The resonant peak frequency of the closed-loop response

Question 6

A linear system of order n is fully controllable if and only if its controllability matrix has:

Accepted Answer

Full row rank equal to n

Answer

Full column rank equal to the number of inputs

Answer

A determinant of zero

Answer

All eigenvalues with negative real parts

Question 7

The Nyquist-Shannon sampling theorem requires the sampling frequency fs for a signal with highest frequency fmax to satisfy:

Accepted Answer

fs ≥ 2fmax

Answer

fs = fmax

Answer

fs ≥ 10fmax

Answer

fs < fmax