146. The characteristic equation of a feedback system is s ³ + Ks ² + 5s + 10 = 0
     For the system to be critically stable, the value of K should be_______

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   By Routh criterion
   
   For stable system, 10 – 5K > 0
   ⇒ K ≤ 2

   Correct Option: B

   By Routh criterion
   
   For stable system, 10 – 5K > 0
   ⇒ K ≤ 2

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147. In a synchro error detector, the output voltage is proportional to [ω(t)]ⁿ, where ω(t) is the rotor velocity and n equals_______

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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148. A phase-lead compensator has the transfer function ______ rad/sec
     

     GC(s) =	10(1 + 0.4s)
     	(1 + 0.01s)

     
     The maximum phase angle lead provided by this compensator will occur at a frequency ω_m is equal to
     

1. 1. 50

   
   
   

   2. 5

   
   
   

   3. 125

   
   
   

   4. 150

   
   
   

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1. View Hint View Answer Discuss in Forum

   G(s) =	10(1 + 0.04s)	=	10(1 + aTs)
   	(1 + 0.01 s)		(1 + Ts)

   
   Taking T = 0.01, “a” is seen to be equal to 4.
   The maximum phase lead occurs at the frequency,
   

   ωn =	1	=	1	= 50 rad / sec
   	√a T		√4 × 0.01

   
   

   Correct Option: A

   G(s) =	10(1 + 0.04s)	=	10(1 + aTs)
   	(1 + 0.01 s)		(1 + Ts)

   
   Taking T = 0.01, “a” is seen to be equal to 4.
   The maximum phase lead occurs at the frequency,
   

   ωn =	1	=	1	= 50 rad / sec
   	√a T		√4 × 0.01

   
   

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149. The minimum number of states necessar y to describe the network shown in the figure in a state variable form is _______
     

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   The minimum number of states necessary to describe a network is the number of independent energy storing elements in the network.
   

   Correct Option: C

   The minimum number of states necessary to describe a network is the number of independent energy storing elements in the network.
   

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150. A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?
     

1. 1. 	1000(s + 10)
      	s + 1000

      
      

   
   
   

   2. 	10(s + 10)
      	s(s + 1000)

   
   
   

   3. 	s + 1000
      	10s (s + 10)

   
   
   

   4. 	s + 1000
      	10 (s + 10)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Initial slope is zero
   It is type ‘0’ system
   (No pole at origin)
   Starting gain = 20 log K db
   20 log K = 20 K = 10
   Given T/F
   

   G(s) =	s + 1000
   	10 (s + 10)

   
   

   =	1000		1 +	s
   				1000
   	10 × 10		1 +	s
   				10

   
   

   G(s) =	10		1 +	s
   				1000
   			1 +	s
   				10

   
   

   Correct Option: D

   Initial slope is zero
   It is type ‘0’ system
   (No pole at origin)
   Starting gain = 20 log K db
   20 log K = 20 K = 10
   Given T/F
   

   G(s) =	s + 1000
   	10 (s + 10)

   
   

   =	1000		1 +	s
   				1000
   	10 × 10		1 +	s
   				10

   
   

   G(s) =	10		1 +	s
   				1000
   			1 +	s
   				10

   
   

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