GATE Control Systems 2

Question 1

The steady-state error of a Type-1 system to a unit ramp input is:

Accepted Answer

1/Kv

Answer

Zero

Answer

1/Ka

Answer

Infinite

Question 2

Which of the following is the correct expression for the Gain Margin (GM) of a system?

Accepted Answer

GM = -20 log|G(jω_pc)H(jω_pc)|

Answer

GM = 20 log|G(jω_pc)H(jω_pc)|

Answer

GM = 20 log(1/|G(jω_gc)H(jω_gc)|)

Answer

GM = |G(jω_pc)H(jω_pc)|

Question 3

For a second-order underdamped system, the peak overshoot depends on:

Accepted Answer

Damping ratio only

Answer

Natural frequency only

Answer

Both damping ratio and natural frequency

Answer

Neither damping ratio nor natural frequency

Question 4

A system has poles at s = -1 ± j2 and a zero at s = -3. The damped natural frequency is:

Accepted Answer

2 rad/s

Answer

1 rad/s

Answer

√5 rad/s

Answer

3 rad/s

Question 5

In a Bode plot, a pure integrator (1/s) contributes a slope of:

Accepted Answer

-20 dB/decade and -90° phase

Answer

+20 dB/decade and +90° phase

Answer

-40 dB/decade and -180° phase

Answer

-20 dB/decade and +90° phase

Question 6

The number of asymptotes in the root locus of a system with 4 poles and 1 zero is:

Accepted Answer

3

Answer

1

Answer

4

Answer

5

Question 7

The transfer function of an ideal proportional-integral (PI) controller is:

Accepted Answer

Kp(1 + 1/(Tis))

Answer

Kp(1 + Tds)

Answer

Kp(1 + Tds + 1/(Tis))

Answer

Kp/(1 + Tis)