GATE Control Systems 4

Question 1

The centroid of asymptotes in the root locus is given by:

Accepted Answer

(Sum of poles - Sum of zeros) / (P - Z)

Answer

The centroid σ = (Σpoles - Σzeros) / (P - Z), giving the real-axis intersection of the asymptotes.

Question 2

For a discrete-time system to be BIBO stable, the poles of its z-transfer function must lie:

Accepted Answer

Inside the unit circle

Answer

Discrete-time BIBO stability requires all poles of the z-transfer function to be strictly inside the unit circle |z| < 1.

Question 3

Which of the following conditions is NECESSARY for a system to be minimum-phase?

Accepted Answer

All zeros in the left half-plane

Answer

A minimum-phase system has all its zeros (and poles for stability) in the left half-plane, giving the minimum possible phase lag.

Question 4

The Mason's gain formula is used to find:

Accepted Answer

Transfer function from a signal flow graph

Answer

Mason's gain formula computes the overall transfer function of a signal flow graph using forward paths, loops, and cofactors.

Question 5

In the time-domain analysis of a second-order system, the settling time (2% criterion) is approximately:

Accepted Answer

4 / (ζωn)

Answer

The 2% settling time is approximately ts ≈ 4/(ζωn), derived from the envelope of the exponentially decaying oscillation.

(GATE) Graduate Aptitude Test in Engineering Practice Test