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

For a Type-1 system, the velocity error constant Kv is finite, so the steady-state error to a ramp is 1/Kv.

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

Gain margin in dB is -20 log|G(jω)H(jω)| evaluated at the phase crossover frequency where the phase is -180°.

Question 3

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

Accepted Answer

Damping ratio only

Answer

Peak overshoot Mp = exp(-πζ/√(1-ζ²)) × 100%, which is a function of the damping ratio ζ only.

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

The damped natural frequency ωd is the imaginary part of the complex poles, which equals 2 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

A pure integrator 1/s has a gain of -20 dB/decade and a constant phase of -90° across all frequencies.

(GATE) Graduate Aptitude Test in Engineering Practice Test