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

- 180° in clockwise direction
- 180° in anti-clockwise direction
- 90° in clockwise direction
- 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

- once in clockwise direction
- once in counter-clockwise direction
- thrice in clockwise direction
- 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

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

- 100 rad/sec
- 50 rad/sec
- 10 rad/sec
- 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?

- -2
- -1
- +1
- +2

6. Consider the following:

- Phase margin
- Gain margin
- Maximum overshoot
- Bandwidth

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

- i and ii only
- i and iii only
- i, iii and iv
- 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

- does not encircle the (-1 + j0) point
- encircles the (-1 + j0) point once in the counter-clockwise direction
- encircles the (-1 + j0) point once in the clockwise direction
- 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

- ∞
- greater than zero but not ∞
- zero
- less than zero

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

For the minimum phase system to be stable

- phase margin should be negative and gain margin positive
- phase margin should be positive and gain margin negative
- both gain margin and phase margin should be positive
- both gain margin and phase margin should be negative

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

- resonant peak and peak overshoot are both functions of the damping ratio ξ only.
- the resonant frequency ω
_{r}= ω_{n}for ξ > 0.707 - higher the resonant peak, higher is the maximum overshoot of the step response

Which of the statements given above are correct?

- i and ii
- ii and iii
- i and iii
- 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

- $K < \frac{T_1+T_2}{T_1T_2}$
- $K < \frac{T_1T_2}{T_1+T_2}$
- $K > \frac{T_1+T_2}{T_1T_2}$
- $K > \frac{T_1T_2}{T_1+T_2}$

12. Consider the following statements:

The gain cross-over point is the point where

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

Which of the statements given above are correct?

- only i and ii
- only i and iii
- only ii and iii
- 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 + j0
- 0 + j0
- -2 + j0
- -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

- right of the M = 1 line
- left of the M = 1 line
- upper side of the M = ± j1 line
- 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?

- origin
- 1 + j0
- -1 + j0
- 0 + j1

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

- 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.
- If the loop gain function G(s)H(s) is a stable function, the closed-loop system is always stable.
- 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?

- only i
- i and ii
- i and iii
- 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

- never enclosed
- enclosed under certain conditions
- just touched
- 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

- 0.5
- 1
- 1.414
- 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

- 0.4
- -0.4
- 4
- 2.5

20. The phase angle of the system

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

- 0° and 90°
- 0° and -90°
- 0° and -180°
- -90° and -180°