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GATE EC 2021: National Champion Quiz 2 (App update required to attempt this test)

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Question 1

Find the value of the transfer function of the signal flow graph (SFG) given below. (Round off to two decimal point).

Question 2

Find the resonant peak value of a system whose damping ratio is 0.5 (Give your answer upto 2 decimal places)

Question 3

Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation as
S5+S4+4S3+4S2+4S+4=0

Question 4

Which of the following is true for the Signal Flow Graph (SFG) given below?

Question 5

A unity-feedback servo-driven instrument has an open loop transfer function given as . It is given that the peak overshoot of the system on step input is 35.1 %. Find the steady state error to an input (1 + 4t)u(t).

Question 6

An unforced system is characterised by the following state equation,

The sum of all elements of the state transition matrix is given by . Find the value of [Give the answer in two decimal places]

Question 7

The feedback system shown below oscillates at 2 rad/s when

Question 8

The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20 log|G(s)| ) is 32 dB and –8 dB at 1 rad/s and 10 rads/s respectively. The phase is negative for all ω. Then G(s) is

Question 9

A unity feedback system has an open loop transfer function. The phase margin in degrees will be ________.

Question 10

A linear second-order single-input continous-time system is described by the following set of differential equations:
1(t)= -2 X1(t)+ 4 X2(t)
2(t)= 2 X1(t) – X2(t) +u(t)
Where X1(t) and X2(t) are the state variables and u(t) is the control variable.
The system is

Question 11

G(s) = (s+a)/(s+b) is a lead controller to obtain maximum phase lead of 30⁰. The values of a and b are

Question 12

Study the standard negative feedback configuration with G(s) = and H(s) =0.5. Find the number of clockwise encirclements of (-1, 0) in the Nyquist of the Loop transfer function G(s) H(s) will be
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Nov 9ESE & GATE EC