Polar Plot MCQ | Nyquist Plot MCQ

1. By adding a pole at the origin of s-plane, the Nyquist plot of a system will rotate by

1. 180° in clockwise direction
2. 180° in anti-clockwise direction
3. 90° in clockwise direction
4. 90° in anti-clockwise direction

2. If the s-plane contour encloses 3 zeros and 2 poles of q(s), the corresponding q(s) plane contour will encircle the origin of q(s) plane

1. once in clockwise direction
2. once in counter-clockwise direction
3. thrice in clockwise direction
4. twice in counter-clockwise direction

3. If the phase margin of a unity feedback control system is zero then the Nyquist plot of the system passes through

1. in between origin and (-1, j0) point in the GH plane.
2. exactly on (-1, j0) point in the GH plane.
3. left-hand side of (-1, j0) point in the GH plane.
4. the origin in the GH plane.

4. A unity feedback system has an open-loop transfer function as

$G(s)=\frac{K}{s(1+0.2s)(1+0.05s)}$

The phase crossover frequency of the nyquist plot is given by

1. 100 rad/sec
2. 50 rad/sec
3. 10 rad/sec
4. 5 rad/sec

5. The open-loop transfer function of a system has one pole in the right half of s-plane. If the system is to be closed-loop stable, then (-1 + j0) point should have how many encirclements in the GH-plane?

1. -2
2. -1
3. +1
4. +2

6. Consider the following:

1. Phase margin
2. Gain margin
3. Maximum overshoot
4. Bandwidth

Which of the above are the frequency domain specifications required to design a control system?

1. i and ii only
2. i and iii only
3. i, iii and iv
4. i, ii and iv

7. Which one of the following is correct?

If the open-loop transfer function has one pole in the right half of s-plane, the closed-loop system will be stable if the Nyquist plot of GH

1. does not encircle the (-1 + j0) point
2. encircles the (-1 + j0) point once in the counter-clockwise direction
3. encircles the (-1 + j0) point once in the clockwise direction
4. encircles the origin once in the counter-clockwise direction

8. The Nyquist plot of a system passes through (-1, j0) point in the G(jω)H(jω) plane, the phase-margin of the system is

1. ∞
2. greater than zero but not ∞
3. zero
4. less than zero

9. Which one of the following is the correct statement?

For the minimum phase system to be stable

1. phase margin should be negative and gain margin positive
2. phase margin should be positive and gain margin negative
3. both gain margin and phase margin should be positive
4. both gain margin and phase margin should be negative

10. Consider the following statements in connection with frequency domain specifications of a control system:

1. resonant peak and peak overshoot are both functions of the damping ratio ξ only.
2. the resonant frequency ω_r = ω_n for ξ > 0.707
3. higher the resonant peak, higher is the maximum overshoot of the step response

Which of the statements given above are correct?

1. i and ii
2. ii and iii
3. i and iii
4. i, ii and iii

11. Which one of the following is correct?

A unity feedback system with a forward path transfer function

$G(s)=\frac{K}{s(1+sT_1)(1+sT_2)}$

is stable provided the value of K is given by

1. $K < \frac{T_1+T_2}{T_1T_2}$
2. $K < \frac{T_1T_2}{T_1+T_2}$
3. $K > \frac{T_1+T_2}{T_1T_2}$
4. $K > \frac{T_1T_2}{T_1+T_2}$

12. Consider the following statements:

The gain cross-over point is the point where

1. the magnitude |G(jω)| = 1 in polar plot
2. the magnitude curve of G(jω) crosses zero dB line in Bode plot
3. magnitude vs phase plot touches the zero dB loci in Nichol’s chart

Which of the statements given above are correct?

1. only i and ii
2. only i and iii
3. only ii and iii
4. i, ii and iii

13. Encirclement of origin of 1 + G(s) plane corresponds to the encirclement of a point in the -1 + G(s) plane, given by

1. 1 + j0
2. 0 + j0
3. -2 + j0
4. -1 + j0

14. The constant M-circles corresponding to the magnitude (M) of the closed-loop transfer function of a linear system for values of M greater than one lie in the G-plane and to the

1. right of the M = 1 line
2. left of the M = 1 line
3. upper side of the M = ± j1 line
4. lower side of the M = −j1 line

15. For a unity feedback system, the origin of the s-plane is mapped in the z-plane by transformation z = e^sT to which one of the following?

1. origin
2. 1 + j0
3. -1 + j0
4. 0 + j1

16. Consider the following statements for a counterclockwise Nyquist path:

1. For a stable loop system, the Nyquist plot of G(s)H(s) should encircle (-1, j0) point as many times as there are poles of G(s)H(s) in the right half of the s-plane, the encirclements, if there are any, must be made in the counter-clockwise direction.
2. If the loop gain function G(s)H(s) is a stable function, the closed-loop system is always stable.
3. If the loop gain function G(s)H(s) is a stable function, for a stable closed-loop system, the Nyquist plot of G(s)H(s) must not enclose the critical point (-1, j0).

Which of these statements is/are correct?

1. only i
2. i and ii
3. i and iii
4. only iii

17. The Nyquist plot for the closed-loop control system with the loop transfer function $G(s)H(s)=\frac{100}{s(s+10)}$ is plotted. Then, the critical point (-1, j0) is

1. never enclosed
2. enclosed under certain conditions
3. just touched
4. enclosed

18. A second-order control system has

$M(j \omega)=\frac{100}{100- (\omega)^{2}+10 \sqrt{2} j \omega}$

Its M_p (peak magnitude) is

1. 0.5
2. 1
3. 1.414
4. 2

19. If the Nyquist plot cuts the negative real axis at a distance of 0.4, then the gain margin of the system is

1. 0.4
2. -0.4
3. 4
4. 2.5

 

20. The phase angle of the system

$G(s)=\frac{s+5}{s^2+4s+9}$, varies between

1. 0° and 90°
2. 0° and -90°
3. 0° and -180°
4. -90° and -180°