131. A control system is as shown in the given figure. The maximum value of gain K for which the system is stable is______
     

1. 1. 1

   
   
   

   2. 3

   
   
   

   3. 7

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   The characteristics equation is
   1 + GH = 0
   

   ∴ 1 +	K	= 0
   	s3 + 3s2 + 2s + 1

   
   

   ⇒	s3 3s2 + 2s + K + 1	= 0
   	s3 + 3s2 + 2s + 1

   
   Routh-Hurwitz criterion can be applied,
   
   

   ∴	5 - K	> 0 & K + 1 > 0
   	3

   
   ∴ K < 5, K > – 1
   ⇒ – 1 < K < 5
   Hence maximum value = 5

   Correct Option: D

   The characteristics equation is
   1 + GH = 0
   

   ∴ 1 +	K	= 0
   	s3 + 3s2 + 2s + 1

   
   

   ⇒	s3 3s2 + 2s + K + 1	= 0
   	s3 + 3s2 + 2s + 1

   
   Routh-Hurwitz criterion can be applied,
   
   

   ∴	5 - K	> 0 & K + 1 > 0
   	3

   
   ∴ K < 5, K > – 1
   ⇒ – 1 < K < 5
   Hence maximum value = 5

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132. The system shown in the given figure has a unit step input. In order that the steady state error is 0.1, the value of K required is _______
     

1. 1. 6.0

   
   
   

   2. 9.0

   
   
   

   3. 3

   
   
   

   4. None of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   For a step input, steady state error =	1
   	(1 + Kp)

   
   where K_p is positional error constant.
   Also,
   

   ∴	1	=	1	= 0.1
   	1 + Kp		1 + K

   
   ⇒ K = 9.0

   Correct Option: B

   For a step input, steady state error =	1
   	(1 + Kp)

   
   where K_p is positional error constant.
   Also,
   

   ∴	1	=	1	= 0.1
   	1 + Kp		1 + K

   
   ⇒ K = 9.0

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133. For a unit step input, a system with forward path transfer function G(s) =	20
     	s2

     
     and feedback path transfer function H (s) = (s + 5), has a steady state output of_______

1. 1. 7.2

   
   
   

   2. 0.01

   
   
   

   3. 0.002

   
   
   

   4. 0.2

   
   
   

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1. View Hint View Answer Discuss in Forum

   C(s) =	G(s)	R(s)
   	1 + G(s) H(s)

   
   (Assuming negative feedback)
   

   C(s) =			20
   			s2				=	10
   	1 +		20		(s + 5)			s2 + 11s
   			s2

   
   
   

   G(s) =	20
   	s2 + 20(s + 5)

   
   
   

   Correct Option: D

   C(s) =	G(s)	R(s)
   	1 + G(s) H(s)

   
   (Assuming negative feedback)
   

   C(s) =			20
   			s2				=	10
   	1 +		20		(s + 5)			s2 + 11s
   			s2

   
   
   

   G(s) =	20
   	s2 + 20(s + 5)

   
   
   

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134. The z-transform of a signal is given by c(z) =	z–1 (1 - z–4)
     	4(1 - z–1)2

     
     Its final value is_______ .

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Final value, f (∞)

   Correct Option: A

   Final value, f (∞)

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135. The transfer function of a system is	10
     	1 + s

     
     When operated as a unity feedback system, the steady state error to a unit step input will be_______
     

1. 1. 1 / 11

   
   
   

   2. 4 / 7

   
   
   

   3. 11 / 7

   
   
   

   4. None of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   The given transfer function is to be taken as space open loop transfer function
   
   It is type zero system.
   The steady state error to a unit step input will be
   

   ess =	1
   	1 + K

   
   
   

   ∴ ess =	1
   	11

   
   

   Correct Option: A

   The given transfer function is to be taken as space open loop transfer function
   
   It is type zero system.
   The steady state error to a unit step input will be
   

   ess =	1
   	1 + K

   
   
   

   ∴ ess =	1
   	11

   
   

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