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Control Systems - Stability Analysis and Frequency Response

Comprehensive test covering stability analysis, frequency response, state space representation, compensator design, and root locus techniques for GATE Electronics and Communication Engineering

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

For the polynomial P(s) = s2 + s4 + 2s3 + 3s + 15, the number of roots which lie in the right half of the s−plane is

  1. 4
  2. 2
  3. 3
  4. 1
Question 2 Multiple Choice (Single Answer)

A system has poles at 0.1 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz.
The approximate phase of the system response at 20 Hz is

  1. -900
  2. 00
  3. 900
  4. -1800
Question 3 Multiple Choice (Single Answer)

A signal flow graph of a system is given below:

The set of equalities that corresponds to this signal flow graph is

Question 4 Multiple Choice (Single Answer)

The state space representation of a separately excited DC servo motor dynamics is given as
$
\left[
\begin{array}
\ \dfrac{d\omega}{dt} \\
\dfrac{di_s}{dt}
\end{array}
\right] =
$ $
\left[
\begin{array}
-1 & 1 \\
-1 & -10
\end{array}
\right]
$ $
\left[
\begin{array}
\ \omega \\
i_s
\end{array}
\right]
$ + $
\left[
\begin{array}
\ 0 \\
10
\end{array}
\right] u
$

  1. $\dfrac{10}{s^2+11s+11}$
  2. $\dfrac{1}{s^2+11s+11}$
  3. $\dfrac{10+10}{s^2+11s+11}$
  4. $\dfrac{1}{s^2+s+1}$
Question 5 Multiple Choice (Single Answer)

The approximate Bode magnitude plot of a minimum-phase system is shown in figure. The transfer function of the system is

  1. 108 $\dfrac{(s+0.1)^3}{(s+10)^2 (s+100)}$
  2. 107 $\dfrac{(s+0.1)^3}{(s+10) (s+100)}$
  3. 108 $\dfrac{(s+0.1)^2}{(s+10)^2 (s+100)}$
  4. 109 $\dfrac{(s+0.1)^3}{(s+10)^2 (s+100)^2}$
Question 6 Multiple Choice (Single Answer)

The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

  1. 1, 0.75
  2. 2, 0.75
  3. 1, 1
  4. 2, 2
Question 7 Multiple Choice (Single Answer)

Given A= $
\left[
\begin{array}
\ 1 & 0 \\
0 & 1
\end{array}
\right]
$ the state transition matrix eAt is given by

  1. $ \left[ \begin{array} \ 0 & e^{-t} \\\\ e^{-t} & 0 \end{array} \right] $
  2. $ \left[ \begin{array} \ e^{-t} & 0 \\\\ 0 & e^t & \end{array} \right] $
  3. $ \left[ \begin{array} \ e^{-t} & 0 \\\\ 0 & e^{-t} & \end{array} \right] $
  4. $ \left[ \begin{array} \ 0 & e^{t} \\\\ e^{t} & 0 \end{array} \right] $
Question 8 Multiple Choice (Single Answer)

In the derivation of expression for peak percent overshoot, $M_p = exp
\left(
\dfrac{-\pi\xi}{\sqrt{1-\xi^2}}
\right) \times 100 %
$, which of the following conditions is not required?

  1. System is linear and time invariant.
  2. The system transfer function has a pair of complex conjugate poles and no zeroes.
  3. There is no transportation delay in the system.
  4. The system has zero initial conditions.
Question 9 Multiple Choice (Single Answer)

The state variable equations of a system are x1 = -3x1 -x2 = u, x2 = 2x1 and Y= x1+ u. The system is

  1. controllable but not observable
  2. observable but not controllable
  3. neither controllable nor observable
  4. controllable and observable
Question 10 Multiple Choice (Single Answer)

A certain system has transfer function
G (s) = $\dfrac{s+8}{s^2+\alpha s-4}$
where$\alpha$ is a parameter. Consider the standard negative unity feedback configuration as shown below:

Which of the following statements is true?

  1. The closed loop systems is never stable for any value of $\alpha$.
  2. For some positive value of $\alpha$, the closed loop system is stable, but not for all positive values.
  3. For all positive values of $\alpha$, the closed loop system is stable.
  4. The closed loop system is stable for all values of $\alpha$, both positive and negative.
Question 11 Multiple Choice (Single Answer)

The open loop transfer function of a plant is given as G(s) = $\dfrac{1}{s^2-1}$. If the plant is operated in a unity feedback configuration, the lead compensator that an stabilize this control system is

  1. $\dfrac{10(s-1)}{s+2}$
  2. $\dfrac{10(s-1)}{s+2}$
  3. $\dfrac{10(s+2)}{s+10}$
  4. $\dfrac{2(s+2)}{s+10}$
Question 12 Multiple Choice (Single Answer)

An unity feedback system is given as
$G(s) = \dfrac{K(1-s)}{s(s+3)}$
Indicate the correct root locus diagram.

Question 13 Multiple Choice (Single Answer)

The gain margin and the phase margin of a feedback system with G (s) H(s) = $\dfrac{s}{(s+100)^3}$are

  1. 0 dB, 0°
  2. $\infty$, $\infty$
  3. $\infty$, 0°
  4. 88.5 dB, $\infty$
Question 14 Multiple Choice (Single Answer)

The open-loop transfer function of a unity feedback system is

G(s) $\dfrac{K}{s(s^2+s+2)(s+3)}$

The range of K for which the system is stable is

  1. $\dfrac{21}{4} > K > 0$
  2. 13 > K > 0
  3. $\dfrac{21}{4}$< K < $\infty$
  4. – 6 < K < $\infty$
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