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# GATE SUBJECT REVISION QUIZ

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Question 1

The system with the open loop transfer function G(s)H(s)=has a gain margin of

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

S

S

^{5}+S^{4}+4S^{3}+4S^{2}+4S+4=0Question 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:

Ẋ1(t)= -2 X

Ẋ2(t)= 2 X

Where X

The system is

Ẋ1(t)= -2 X

_{1}(t)+ 4 X_{2}(t)Ẋ2(t)= 2 X

_{1}(t) – X_{2}(t) +u(t)Where X

_{1}(t) and X_{2}(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

Question 13

The transfer function of the linear time variant system show in figure below is

Question 14

Consider the Bode magnitude plot shown in the figure. The transfer function H(s) is

Question 15

Find the value of the Transfer function of the Signal Flow Graph (SFG) given below:

[Write the answer upto two decimal point]

[Write the answer upto two decimal point]

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Aug 28ESE & GATE EC

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