This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Correlation between Time and Frequency Response”.

1. Assertion (A): All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.

Reason (R): Large resonance peak in frequency response corresponds to a large overshoot in transient response.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true and R is not the correct explanation of A

c) A is true but R is false

d) A is false but R is true

2. The transfer function of a system is given by Y(s)/X(s) = e^{−0.1}s/1+s. If x(t) is 0.5sint, then the phase angle between the output and the input will be:

a) -39.27°

b) -45°

c) -50.73°

d) -90°

3. The forward path transfer function of a unity feedback system is given by G(s) = 100/(s^{2}+10s+100). The frequency response of this system will exhibit the resonance peak at:

a) 10 rad/sec

b) 8.66 rad/sec

c) 7.07 rad/sec

d) 5rad/sec

4. The critical value of gain for the system is 40. The system is operating at a gain of 20. The gain margin of the system is :

a) 2 dB

b) 3 dB

c) 6 dB

d) 4 dB

5. The open loop transfer function of a system is :

G(s) H(s) =K/ (1+s) (1+2s) (1+3s)

The phase crossover frequency wpc is:

a) √2

b) 1

c) Zero

d) √3

6. In a feedback control system, phase margin(PM) is

1. Directly proportional to G

2. Inversely proportional to G

3. Independent of G

4. Zero when G =0

Which of the above statements are correct?

a) 1 and 2

b) 2 and 3

c) 3 and 4

d) 1 and 4

7. The phase angle of the system G(s) =s+5/s^{2}+4s+9;varies between

a) 0° and 90°

b) 0° and -90°

c) 0° and -180°

d) -90° and -180°

8. Which one of the following statements is correct for gain margin and phase margin of two closed-loop systems having loop functions G(s) H(s) and exp(-s) G(s) H(s)?

a) Both gain and phase margins of the two systems will be identical

b) Both gain and phase margins of G(s) H(s) will be more

c) Gain margins of the two systems are the same but phase margins of G(s) H(s) will be more

d) Phase margins of the two systems are the same but gain margin of G(s) H(s) will be less

9. The gain margin in dBs of a unity feedback control system whose open loop transfer function, G(s) H(s) =1/s(s+1) is

a) 0

b) 1

c) -1

d) ∞

10. The loop transfer function of a system is given by G(s) H(s) =10e^{-Ls}/s. The phase crossover frequency is 5rad/s. The value of the dead time L is

a) π/20

b) π/10

c) -π/20

d) Zero