Control Systems Test 2

Question 1
2 / -0.33

Consider the polynomial

P(s) = s⁵ + 5s⁴ + 11s³ + 23s² + 28s + 12

Using the Routh Hurwitz criteria, which of the following is/are true?

A
The system has no roots on the imaginary axis

B
The system has multiple roots at the origin

C
The system is stable

D
The system has three poles on the left half of s-plane

Question 2
2 / -0.33

The open-loop transfer function of a unity feedback system is given by
\(G\left( s \right) = \frac{{10}}{{s\left( {\frac{s}{5} + 1} \right)\left( {\frac{s}{{20}} + 1} \right)}}\)
In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point

A
(-0.4, 0)

B
(-2.5, 0)

C
(-4, 0)

D
(-0.25, 0)

Question 3
2 / -0.33

A unity feedback control system has an open-loop transfer function
\(G\left( s \right) = \frac{A}{{s\left( {s + a} \right)}}\)
The sensitivity of the closed-loop transfer function to the changes in the parameter is

A
\(\frac{{ - A}}{{{{\left( {s + a} \right)}^2}}}\)

B
\(\frac{{ - a}}{{\left( {s + a} \right)}}\)

C
\(\frac{{ - As}}{{{{\left( {{s^2} + as + A} \right)}^2}}}\)

D
\(\frac{{ - as}}{{\left( {{s^2} + as + A} \right)}}\)

Question 4
2 / -0.33

The system matrix of a continuous time system, described in the state variable from is
\(\left[ {\begin{array}{*{20}{c}}x&0&0\\0&y&{ - 1}\\0&1&{ - 2}\end{array}} \right]\)
The range of x and y so that the system is stable is

A
x > 0, y > 2

B
x < 0, y < 0.5

C
x < 0, y > 2

D
x > 0, y < 0.5

Question 5
2 / -0.33

A system is represented by the following equation
\(\ddot y\left( t \right) + 6\dot y\left( t \right) + 5y\left( t \right) = u\left( t \right)\)
For the unit response of the system, the steady state value of the output is _______

A
0.2-0.2

B
0.24-0.21

C
0.27-0.26

D
0.29-0.22

Question 6
2 / -0.33

The transfer function of a control system is given by
\(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{25}}{{{s^2} + 6s + 25}}\)
The first maximum value of the response occurs at a time t_max given by

A
\(\frac{\pi }{8}\)

B
\(\frac{\pi }{4}\)

C
\(\frac{\pi }{2}\)

D
π

Question 7
2 / -0.33

For the transfer function, \(G\left( s \right) = \frac{{5\left( {s + 4} \right)}}{{s\left( {s + 0.25} \right)\left( {{s^2} + 10s + 25} \right)}}\), the values of the constant gain term and the highest corner frequency of the Bode plot respectively are:

A
3.2, 5.0

B
16.0, 4.0

C
3.2, 4.0

D
16.0, 5.0

Question 8
2 / -0.33

Consider the open-loop transfer function \(G\left( s \right)H\left( s \right) = \frac{K}{{s\left( {{s^2} + 6s + 25} \right)}}\). The angle of departure at the complex pole with positive imaginary part (angle measured in the anticlockwise direction and to be answered in between 0 and 360) in degrees is _______

A
319-327

B
3194-3271

C
3197-3276

D
3199-3272

Question 9
2 / -0.33

A certain linear time invariant system has the state and the output equations given below
\(\left[ {\begin{array}{*{20}{c}}{{{\dot x}_1}}\\{{{\dot x}_2}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{{x_1}}\\{{x_2}}\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}0\\1\end{array}} \right]u\)
\(y = \left[ {1\;\;1} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right]\)
If \(\left[ {\begin{array}{*{20}{c}} {{x_1}\left( 0 \right)}\\ {{x_2}\left( 0 \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1\\ { - 1} \end{array}} \right]\)and u(0) = -1, then \(\frac{{dy}}{{dt}}\;at\;t = 0\) is ______

A
0-0

B
04-01

C
07-06

D
09-02

Question 10
2 / -0.33

Consider a plant whose transfer function is \(\frac{2}{{s\left( {s + 4} \right)}}\). It is desired that a lead compensator is used to design a negative feedback closed loop system with this plant.
The lead compensator needs to provide a maximum phase lead of 40° and this maximum phase lead angle should be provided at a frequency of 5 rad/sec.
It is desired that the static velocity error constant of the compensated system to be 10.
Then the transfer function of the lead compensator is

A
\({G_c}\left( s \right) = \frac{{93\left( {s + 2.3} \right)}}{{\left( {s + 10.7} \right)}}\)

B
\({G_c}\left( s \right) = \frac{{10\left( {s + 10.7} \right)}}{{\left( {s + 2.3} \right)}}\)

C
\({G_c}\left( s \right) = \frac{{10\left( {s + 2.3} \right)}}{{\left( {s + 10.7} \right)}}\)

D
\({G_c}\left( s \right) = \frac{{93\left( {s + 10.7} \right)}}{{\left( {s + 2.3} \right)}}\)

Question 11
2 / -0.33

The unity feedback system has forward path transfer function.
\(G\left( s \right) = \frac{K}{{s\left( {s + 1} \right)\left( {s + 2} \right)}}\)
What is the maximum value of K that will make its gain margin zero?

A
6-6

B
64-61

C
67-66

D
69-62

Submit Test

Control Systems...

Question 1

The system has no roots on the imaginary axis

The system has multiple roots at the origin

The system is stable

The system has three poles on the left half of s-plane

Question 2

(-0.4, 0)

(-2.5, 0)

(-4, 0)

(-0.25, 0)

Question 3

\(\frac{{ - A}}{{{{\left( {s + a} \right)}^2}}}\)

\(\frac{{ - a}}{{\left( {s + a} \right)}}\)

\(\frac{{ - As}}{{{{\left( {{s^2} + as + A} \right)}^2}}}\)

\(\frac{{ - as}}{{\left( {{s^2} + as + A} \right)}}\)

Question 4

x > 0, y > 2

x < 0, y < 0.5

x < 0, y > 2

x > 0, y < 0.5

Question 5

0.2-0.2

0.24-0.21

0.27-0.26

0.29-0.22

Question 6

\(\frac{\pi }{8}\)

\(\frac{\pi }{4}\)

\(\frac{\pi }{2}\)

π

Question 7

3.2, 5.0

16.0, 4.0

3.2, 4.0

16.0, 5.0

Question 8

319-327

3194-3271

3197-3276

3199-3272

Question 9

0-0

04-01

07-06

09-02

Question 10

\({G_c}\left( s \right) = \frac{{93\left( {s + 2.3} \right)}}{{\left( {s + 10.7} \right)}}\)

\({G_c}\left( s \right) = \frac{{10\left( {s + 10.7} \right)}}{{\left( {s + 2.3} \right)}}\)

\({G_c}\left( s \right) = \frac{{10\left( {s + 2.3} \right)}}{{\left( {s + 10.7} \right)}}\)

\({G_c}\left( s \right) = \frac{{93\left( {s + 10.7} \right)}}{{\left( {s + 2.3} \right)}}\)

Question 11

6-6

64-61

67-66

69-62

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