6. Given that the transfer function G (s) is

   K

   s2(1 + sT)

   State the type and order of the system—
   

1. 1. 2 and 3
      

   
   
   

   2. 3 and 2
      

   
   
   

   3. 3 and 3
      

   
   
   

   4. 2 and 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Type = 2, Order = 3
   

   Correct Option: A

   Type = 2, Order = 3
   

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7. The forward transfer function of a system is 10/1 + s. The steady state error to unit step input when operated as a unity feedback system is—
   

1. 1. 10
      

   
   
   

   2. 0
      

   
   
   

   3. 1/11
      

   
   
   

   4. ∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that
   

   G(s) =	10	, H(s)=	1
   	1 + s		s

   
   r (t) = u (t)
   then R (s) = 1/s
   

   ess = s → 0Lim .sE (s) =s → 0Lim	s.R(s)
   	1 + G(s) H(s)

   
   

   =s → 0Lim	s.1/s	=	1
   	1 + 10/1 + s.1		11

   Correct Option: C

   Given that
   

   G(s) =	10	, H(s)=	1
   	1 + s		s

   
   r (t) = u (t)
   then R (s) = 1/s
   

   ess = s → 0Lim .sE (s) =s → 0Lim	s.R(s)
   	1 + G(s) H(s)

   
   

   =s → 0Lim	s.1/s	=	1
   	1 + 10/1 + s.1		11

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8. Consider the following statements with reference to the block diagram of a control system given in the figure
   1. For G₂ = 0, the system is open-loop.
   2. For G₁ = 0, the system is closed-loop.
   3. For G₂ = H = 1, the system is closed-loop Of these statements—
   
   
   
   

1. 1. 1, 2 and 3 are correct
      

   
   
   

   2. 1 and 2 are correct
      

   
   
   

   3. 2 and 3 are correct
      

   
   
   

   4. 1 and 3 are correct

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   
   

   Correct Option: C

   NA

   
   

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9. For a standard feedback control loop, the sensitivity of the closed-loop transfer function T to forward path gain G and feedback path gain H are—
   

   SGT	SHT
   A. -1/(1 + GH)	-1(1 + GH)
   B. -GH/(1 + GH)	-H/(1 + GH)
   C. G/(1 + GH)	1/(1 + GH)
   D. 1/(1 + GH)	-GH/(1 +GH)

1. 1. A

   
   
   

   2. B

   
   
   

   3. C

   
   
   

   4. D

   
   
   

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1. View Hint View Answer Discuss in Forum

   For more detail refer synopsis.

   Correct Option: D

   For more detail refer synopsis.

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10. The second order system defined by
    

    25

    s2 + 5s + 25

    
    is given a step input. The time taken for the output to settle within ± 2% of input is—
    

1. 1. 1.2 sec
      

   
   
   

   2. 1.6 sec
      

   
   
   

   3. 2 sec
      

   
   
   

   4. 0.4 sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   Settling time =	4	for ± 2% of input
   	ξωn

   
   from the given C.E. ⇒ s² + 5s + 25 = 0
   ω²_n = 25
   2ξ ω_n = 5
   

   ξ =	5	=	5	= 0·5
   	2 × ωn		2 × 5

   
   

   so, settling time =	4	=	4	=	4
   	ξωn		0·5 × 5		2·5

   
   = 1.6 sec.

   Correct Option: B

   Settling time =	4	for ± 2% of input
   	ξωn

   
   from the given C.E. ⇒ s² + 5s + 25 = 0
   ω²_n = 25
   2ξ ω_n = 5
   

   ξ =	5	=	5	= 0·5
   	2 × ωn		2 × 5

   
   

   so, settling time =	4	=	4	=	4
   	ξωn		0·5 × 5		2·5

   
   = 1.6 sec.

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