# Control Systems Questions and Answers – Bode Plots

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Bode Plots”.

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

Explanation: 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

Explanation: The phase angle plot in Bode diagram is not affected by the variation in the gain of the system.The variation in the gain of the system has effect on the phase margin of the system.

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°

Explanation: 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

Explanation: 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
Explanation: 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°

Explanation: Centre = (-0.5, 0)
Centre of N circle is (-1/2, 1/2N)
N =tanα
α =90°.
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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

Explanation: 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

Explanation: 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

Explanation: 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?

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: Gm (dB) = 20log⁡GM
here Gm = 6 dB
By simplifying
GM = 1.99526 = 2 (approx)
Given K (marginal) = 40
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

Explanation: Nichol’s chart is useful for the detailed study and analysis of closed loop frequency response.

15. The roots of the characteristic equation of the second order system in which real and imaginary part represents the :
a) Damped frequency and damping
b) Damping and damped frequency
c) Natural frequency and damping ratio
d) Damping ratio and natural frequency

Explanation: Real part represents the damping and imaginary part damped frequency.

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