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# Multiple choice question for engineering

## Set 1

1. A minimum phase unity feedback system has a bode plot with a constant slope of -20dB/decade for all frequencies. What is the value of the maximum phase margins of the system?
a) 0°
b) 90°
c) -90°
d) 180°

Answer: b [Reason:] For given Bode plot, G(s) H(s) =K/jw As H(s) =1 PM (maximum) =90°.

2. The range of K for the stability of system is 0<K<100. For K =10, The gain Margin of the system
a) 10
b) 5
c) 0.1
d) 0.5

Answer: a [Reason:] Gain margin of the system is 10.

3. The frequency at which the Nyquist diagram cuts the unit circle is known as:
a) Gain crossover frequency
b) Phase crossover frequency
c) Damping frequency
d) Corner frequency

Answer: a [Reason:] The frequency at which the Nyquist diagram cuts the unit circle is known as gain cross over frequency.

4. The forward path transfer function of a unity feedback system is given by G(s) = 1/(1+s)^2.
What is the phase margin of the system?

Answer: d [Reason:] Magnitude at gain cross over frequency is 1 and PM is π rad.

5. Consider the following statements:
1. The delay time is the time required to reach 50% of the final value in the first time.
2. The rise time is the time required for the response to rise from 10% to 90% of its final value for underdamped systems.
3. The rise time is the time required for the response to rise from 0 to 100% for the underdamped systems.
Which of these statements are correct?
a) 1,2 and 3 only
b) 1 and 2 only
c) 1 and 3 only
d) 2 and 3 only negative real axis

Answer: c [Reason:] The rise time is the time required for the response to rise from 10% to 90% of its final value for overdamped systems.

6. For minimum phase systems:
a) Pole must lie on left plane
b) Zeroes must lie on left plane
c) Poles and zeroes must lie on left plane
d) Both must lie on right plane

Answer: c [Reason:] For minimum phase systems poles and zeroes must lie on the right s-plane.

7. For non-minimum phase systems:
a) Poles and zeroes must lie on the right s-plane
b) Zeroes must lie on right of s-plane
c) Both lie on left of s-plane
d) Poles must be on the left and zeroes can be on the right s –plane.

Answer: d [Reason:] For non-minimum phase systems poles must be on the left and zeroes can be on the right s –plane.

8. For all-pass systems:
a) Poles must lie on right of the s-plane
b) Zeroes must lie on the left of s-plane
c) Poles must lie on the left and zeroes on the mirror image of the pole can be on the right
d) None of the mentioned

Answer: c [Reason:] For all-pass systems poles must lie on the left and zeroes on the mirror image of the pole can be on the right.

9. All pass system and minimum phase system constitute_________________
a) Pole must lie on left plane
b) Minimum phase system
c) Non-minimum phase system
d) Both must lie on right plane

Answer: c [Reason:] All pass system and minimum phase system constitute non-minimum phase system.

10. Minimum phase systems have unique relationship between its phase and magnitude curves
a) True
b) False

Answer: a [Reason:] Minimum phase system has the least phase angle range for a given magnitude curve.

## Set 2

1. The output of a feedback control system must be a function of
a) Reference and output
b) Reference and input
c) Input and feedback signal
d) Output and feedback signal

Answer: a [Reason:] The output from the feedback control system must be a function of the reference input and output.

2. A control system with excessive noise, is likely to suffer from?
a) Saturation in amplifying stages
b) Loss of gain
c) Vibrations
d) Oscillations

Answer: a [Reason:] A control system with excessive noise suffers from the saturation due to multiple inputs and outputs present and high gain of the system.

3. Zero initial condition for a system means?
a) Input reference signal is zero
b) Zero stored energy
c) Initial movement of moving parts
d) System is at rest and no energy is stored in any of its components

Answer: d [Reason:] Zero initial condition for a system means it has stored energy and system is at rest.

4. Transfer function of a system is used to calculate which of the following?
a) The order of the system
b) The time constant
c) The output for any given input

Answer: c [Reason:] The output of any given system can be calculated by the transfer function of the system and this is the ratio of Laplace output to the Laplace input considering zero initial conditions.

5. The band width, in a feedback amplifier.
a) Remains unaffected
b) Decreases by the same amount as the gain increase
c) Increases by the same amount as the gain decrease
d) Decreases by the same amount as the gain decrease

Answer: c [Reason:] The bandwidth of closed loop system increases hence increasing the noise due to increased bandwidth.

6. On which of the following factors does the sensitivity of a closed loop system to gain changes and load disturbances depend?
a) Frequency
b) Loop gain
c) Forward gain
d) All of the mentioned

Answer: d [Reason:] The sensitivity depends upon the frequency, loop gain and forward gain of the closed loop control system.

7. The transient response, with feedback system,
a) Rises slowly
b) Rises quickly
c) Decays slowly
d) Decays quickly

Answer: d [Reason:] The transient response of the system is improved with the help of the feedback and hence the transient response decays slowly.

8. The second derivative input signals modify which of the following?
a) The time constant of the system
b) Damping of the system
c) The gain of the system
d) The time constant and suppress the oscillations

Answer: d [Reason:] The second derivative of the input signal modify the time constant and suppress the oscillations.

9. Which of the following statements is correct for any closed loop system?
a) All the co-efficient can have zero value
b) All the co-efficient are always non-zero
c) Only one of the static error co-efficient has a finite non-zero value
d) Only two of the static error co-efficient has a finite non-zero value

Answer: c [Reason:] Closed loop system has one of the static error constant for any input that can be position, velocity or acceleration error constant.

10. Which of the following statements is correct for a system with gain margin close to unity or a phase margin close to zero?
a) The system is relatively stable
b) The system is highly stable
c) The system is highly oscillatory
d) The system is stable

Answer: c [Reason:] The system is highly oscillatory or unstable as the value of phase margin must be finite for the stable system.

## Set 3

1. The phase margin (in degrees) of a system having the loop transfer function G(s) H(s)=2√3/s(s+1) is:
a) 45°
b) -30°
c) 60°
d) 30°

Answer: d [Reason:] Phase margin is calculated at gain cross over frequency where magnitude of the transfer function is 1.

2. The system with the open loop transfer function G(s) H(s) =1/s(s^2+s+1) has the gain margin of :
a) -6 dB
b) 0 dB
c) 3.5 dB
d) 6 dB

Answer: b [Reason:] Gain margin is calculated at phase cross over frequency where the phase is 180°.

3. The phase angle of the system, G(s) =s+5/s2+4s+9, varies between :
a) 0° and 90°
b) 0° and -90°
c) 0° and -180°
d) -90° and -180°

Answer: a [Reason:] As it is the type 0 system so the phase angle can be 0° and 90°.

4. The polar plot of the transfer function G(s) = 10(s+1)/s+10 will be in the :

Answer: d [Reason:] Polar plot of the given transfer function lies in the fourth quadrant.

5. As the polar plot moves toward the point (-1, 0) then the system becomes :
a) Stable
b) Marginally stable
c) Conditionally stable
d) Unstable

Answer: d [Reason:] As the polar plot moves toward the point (-1, 0) then the system becomes unstable.

6. Polar plots moving toward the imaginary axis makes the system:
a) Stable
b) Marginally stable
c) Conditionally stable
d) Unstable

Answer: d [Reason:] Polar plots moving toward the imaginary axis makes the system unstable.

7. The concepts used to measure relative stability are:
a) Phase margin
b) Gain margin
c) Phase and Gain margin
d) Stable

Answer: c [Reason:] The concepts used to measure relative stability are phase margin and gain margin.

8. Phase and gain margin are applicable to open and closed loop systems both.
a) True
b) False

Answer: b [Reason:] Phase and gain margin are applicable only to open loop systems.

9. Gain margin is:
a) It is a factor by which the system gain can be increased to drive it to the verge of instability
b) It is calculated at gain cross over frequency
c) It is calculated at phase cross over frequency
d) Both a and c

Answer: d [Reason:] Gain margin is a factor by which the system gain can be increased to drive it to the verge of instability and is calculated at phase cross over frequency.

10. Phase margin is:
a) It is amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability
b) It is always positive for stable feedback systems
c) It is calculated at gain cross over frequency
d) All of the mentioned

Answer: d [Reason:] Phase margin is the measure of relative stability which is always positive for stable systems.

## Set 4

1. Consider the block diagram shown below:

If the transfer function of the system is given by T(s)=G1G2+G2G3/1+X. Then X is:
a) G2G3G4
b) G2G4
c) G1G2G4
d) G3G4

Answer: b [Reason:] Use the technique of making two different block diagram by dividing two summers and use the approaches of shifting take off point and blocks.

2. For the block diagram given in the following figure, the expression of C/R is:

a) G1G2G3/1-G2G1
b) G1G2/1-G1G2G3
c) G1G2G3/1-G1G2G3
d) G1G2/G3(1-G1G2)

Answer: a [Reason:] Block diagram is being converted into signal flow graphs by considering each take off point as a node and each forward transfer function as forward gain.

3. The transfer function from D(s) to Y(s) is :

a) 2/3s+7
b) 2/3s+1
c) 6/3s+7
d) 2/3s+6

4. The closed loop gain of the system shown in the given figure is :

a) -9/5
b) -6/5
c) 6/5
d) 9/5

5. The advantage of block diagram representation is that it is possible to evaluate the contribution of each component to the overall performance of the system.
a) True
b) False

Answer: a [Reason:] The advantage of the block diagram is that it is possible to get the contribution of each block to the overall performance of the system.

6. The overall transfer function from block diagram reduction for cascaded blocks is :
a) Sum of individual gain
b) Product of individual gain
c) Difference of individual gain
d) Division of individual gain

Answer: b [Reason:] Gain of block get multiplied when they are cascaded where cascaded means that the blocks are in series combination with no summer in between.

7. The overall transfer function of two blocks in parallel are :
a) Sum of individual gain
b) Product of individual gain
c) Difference of individual gain
d) Division of individual gain

Answer: a [Reason:] The gains get added as the blocks are connected in parallel with the summer in between and they are connected with the same sign.

8. Transfer function of the system is defined as the ratio of Laplace output to Laplace input considering initial conditions________
a) 1
b) 2
c) 0
d) infinite

Answer: c [Reason:] By definition transfer function is the ratio of the laplace output to the input but the initial conditions mainly the stored energy is zero.

9. In the following block diagram, G1=10/s G2=10/s+1 H1=s+3, H2=1. The overall transfer function is given by :

a) 10/11s2+31s+10
b) 100/11s2+31s+100
c) 100/11s2+31s+10
d) 100/11s2+31s

10. Oscillations in output response is due to :
a) Positive feedback
b) Negative feedback
c) No feedback
d) None of the mentioned

Answer: a [Reason:] Oscillations are the unwanted sinuoidal signals with high gain in positive feedback and s the damping factor is absent in the positive feedback system entirely oscillations are present.

## Set 5

1. Assertion (A): Relative stability of the system reduces due to the presence of transportation lag.
Reason (R): Transportation lag can be conveniently handled by Bode plot.
a) Both A and R are true but R is correct explanation of A
b) Both A and R are true but R is correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: b [Reason:] Transportation lag can be conveniently handled on Bode plot as well without the need to make any approximation.

2. Assertion (A): The phase angle plot in Bode diagram is not affected by the variation in the gain of the system.
Reason(R): The variation in the gain of the system has no effect on the phase margin of the system.
a) Both A and R are true but R is correct explanation of A
b) Both A and R are true but R is correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: c [Reason:] The variation in the gain of the system has effect on the phase margin but phase plot is not affected.

3. A system has poles at 0.01 Hz, 1 Hz and 80Hz, zeroes at 5Hz, 100Hz and 200Hz. The approximate phase of the system response at 20 Hz is :
a) -90°
b) 0°
c) 90°
d) -180°

Answer: a [Reason:] Pole at 0.01 Hz gives -180° phase. Zero at 5Hz gives 90° phase therefore at 20Hz -90° phase shift is provided.

4. The constant M-circle represented by the equation x^2+2.25x+y^2=-1.25 has the value of M equal to:
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] Comparing with the M circle equation we have the value of M =3.

5. What is the value of M for the constant M circle represented by the equation 8x2+18x+8y2+9=0?
a) 0.5
b) 2
c) 3
d) 8

Answer: c [Reason:] Comparing with the M circle equation we have the value of M =3.

6. The constant N loci represented by the equation x^2+x+y^2=0 is for the value of phase angle equal to:
a) -45°
b) 0°
c) 45°
d) 90°

Answer: d [Reason:] Centre = (-0.5, 0) Centre of N circle is (-1/2, 1/2N) N =tanα α =90°.

7. All the constant N-circles in G planes cross the real axis at the fixed points. Which are these points?
a) -1 and origin
b) Origin and +1
c) -0.5 and 0.5
d) -1 and +1

Answer: a [Reason:] Centre of N circle is (-1/2, 1/2N) N =tanα Constant –N circles always pass through (-1, 0) and (0, 0).

8. Consider the following statements:
i. Closed loop frequency response.
ii. The value of the peak magnitude of the closed loop frequency response Mp.
iii. The frequency at which Mp occurs.
Which of the above statements are correct?
a) 2 and 3
b) 1 and 2
c) 1 and 3
d) 1,2 and 3

Answer: d [Reason:] Nichol’s chart gives information about closed loop frequency response, value of the peak magnitude of the closed loop frequency response Mp and the frequency at which Mp occurs.

9. Which one of the following statements is correct? Nichol’s chart is useful for the detailed study analysis of:
a) Closed loop frequency response
b) Open loop frequency response
c) Close loop and open loop frequency responses
d) None of the above

Answer: a [Reason:] Nichol’s chart is useful for the detailed study analysis of closed loop frequency response.

10. In a bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

Answer: a [Reason:] A 4th order all pole system means that the system must be having no zero or s-term in numerator and s4 terms in denominator. One pole exhibits -20dB/decade slope, so 4 pole exhibits a slope of -80 dB /decade.

11. Frequency range of bode magnitude and phases are decided by :
a) The lowest and higher important frequencies of dominant factors of the OLTF
b) The lowest and highest important frequencies of all the factors of the open loop transfer function
c) Resonant frequencies of the second factors
d) None of the above

Answer: d [Reason:] T. F. = Kp (1+Tds) There is only one zero which will give slope of +20dB/decade.

12. OLTF contains one zero in right half of s-plane then
a) Open loop system is unstable
b) Close loop system is unstable
c) Close loop system is unstable for higher gain
d) Close loop system is stable

Answer: c [Reason:] OLTF contains one zero in right half of s-plane then Close loop system is unstable for higher gain.

13. The critical value of gain for a system is 40 and gain margin is 6dB. The system is operating at a gain of:
a) 20
b) 40
c) 80
d) 120

Answer: a [Reason:] Gm (dB) = 20log⁡GM GM =2 As we know, GM =K (marginal)/K (desired) K desired =40/2 =20.

14. Nichol’s chart is useful for the detailed study and analysis of:
a) Closed loop frequency response
b) Open loop frequency response
c) Close loop and open loop frequency responses
d) open loop and Close loop frequency responses