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GATE 2023 control system Champion Quiz 3
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Question 1
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 2
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).
. 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 3
The feedback system shown below oscillates at 2 rad/s when 
Question 4
A unity feedback system has an open loop transfer function
. The phase margin in degrees will be ________.
. The phase margin in degrees will be ________.Question 5
A linear second-order single-input continous-time system is described by the following set of differential equations:
Ẋ1(t)= -2 X1(t)+ 4 X2(t)
Ẋ2(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
Ẋ1(t)= -2 X1(t)+ 4 X2(t)
Ẋ2(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 6
The transfer function 
of the linear time variant system show in figure below is
of the linear time variant system show in figure below is
Question 7
Consider the Bode magnitude plot shown in the figure. The transfer function H(s) is
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Nov 9ESE & GATE EC
