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

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

Answer

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

Answer

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

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

Outside the unit circle

Answer

On the unit circle

Answer

On the real axis only

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

All poles in the left half-plane

Answer

All poles and zeros in the left half-plane

Answer

Damping ratio greater than 1

Question 4

The Mason's gain formula is used to find:

Accepted Answer

Transfer function from a signal flow graph

Answer

Characteristic roots of a system

Answer

Stability margins from a Bode plot

Answer

Controllability of a state-space system

Question 5

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

Accepted Answer

4 / (ζωn)

Answer

π / ωd

Answer

1 / (ζωn)

Answer

2π / ωd

Question 6

The transfer function representation of a system is LESS general than the state-space representation because:

Accepted Answer

Transfer functions assume zero initial conditions

Answer

Transfer functions cannot represent MIMO systems

Answer

Transfer functions are only valid for nonlinear systems

Answer

Transfer functions require time-domain analysis

Question 7

A lead compensator in frequency domain primarily improves:

Accepted Answer

Phase margin and transient response

Answer

Steady-state accuracy

Answer

Gain margin only

Answer

Low-frequency gain