### GATE 2009 ECE Control Systems - Complete Video Solutions with Answers

2009

1. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensator has such a magnitude plot?

b) Lag compensator
c) PID compensator

2. If the transfer function of the following circuit is Vo(s)/Vi(s) = 1/(2+sCR), then the value of the load resistor RL is

a) R/4
b) R/2
c) R
d) 2R

3. consider the system,
where p and q are arbitrary real numbers, which one of the following statements about the controllability of the system is TRUE?
a) the system is completely state controllable for any non zero values of p and q
b) only p=0 and q=0 result in controllability
c) the system is uncontrollable for all values of p and q
d) we cannot conclude about controllability from the given data

4. the feedback configuration and the pole-zero locations of G(s) = (s2 – 2s + 2)/(s2 + 2s +2), are shown below.
The root locus for negative values of k, i.e. for –∞ < k < 0, has break away/break in points and angle of departure at pole P (w.r.t. the positive real axis) equal to
a) ± √2 and 0o
b) ± √2 and 45o
c) ± √3 and 0o
d) ± √3 and 45o

5. The unit step response of an under damped second order system has steady state value of – 2. Which of the following transfer functions has these properties?

Common Data Questions: (6 & 7)
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.

6. Which of the following statements is TRUE?
a) G(s) is an all pass filter
b) G(s) has a zero in the right half plane
c) G(s) is the impedance of a passive network
d) G(s) is marginally stable

7. The gain and phase margin of G(s) for closed loop stability are
a) 6 dB and 180o
b) 3 dB and 180o
c) 6 dB and 90o
d) 3 dB and 90o