41. Equivalent of the block diagram in the figure is
    
    

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 
      

   
   
   

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   NA

   Correct Option: D

   NA

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42. A unity feedback control system has a forward path transfer function equal to
    

    	42.25
    	s2(s + 6.5)

    
    The unit step response of this system starting from rest, will have its maximum value at a time equal to
    

1. 1. 0 sec

   
   
   

   2. 0.56 sec

   
   
   

   3. 5.6 sec

   
   
   

   4. infinity

   
   
   

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   Step response transform is
   

   	42.25	=	1	+	6.5	-	1
   	s2(s + 6.5)		s + 6.5		s2		s

   
   c (t) = e ^-6.5t + 6.5 t u (t) – u (t)
   At t → ∞, c (t) → ∞
   

   Correct Option: D

   Step response transform is
   

   	42.25	=	1	+	6.5	-	1
   	s2(s + 6.5)		s + 6.5		s2		s

   
   c (t) = e ^-6.5t + 6.5 t u (t) – u (t)
   At t → ∞, c (t) → ∞
   

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43. Consider a system shown in the given figure
    

    U(s) →	2	→ C(s)
    	s

    
    If the system is disturbed so that C(0) = 1, then C (t) for a unit step input will be
    

1. 1. 1 + t

   
   
   

   2. 1 – t

   
   
   

   3. 1 + 2t

   
   
   

   4. 1 – 2t

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   The system represent an integrator, therefore, if a step function is applied, we get ramp output. This will be enhanced by the initial value present, i.e. by 1.
   Thus, c (t) = 1 + 2t; t ≥ 0.

   Correct Option: C

   
   The system represent an integrator, therefore, if a step function is applied, we get ramp output. This will be enhanced by the initial value present, i.e. by 1.
   Thus, c (t) = 1 + 2t; t ≥ 0.

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44. What will be the closed loop transfer function of a unity feedback control system whose step response is given by
    c(t) = K [1 – 1.66e^{– 8 t} sin (6t + 37°)]
    

1. 1. 	100 K
      	s2 + 16s + 100

      
      

   
   
   

   2. 	10 K
      	s2 + 16s + 100

      
      

   
   
   

   3. 	K
      	s2 + 16s + 100

      
      

   
   
   

   4. 	10 K
      	s2 + 8s + 10

      
      

   
   
   

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   M(s) =	C(s)
   	R(s)

   
   

   But R(s) =	1	=
   	c

   
   ∴ M (s) = s C (s)
   
   (ω_n √1 - δ² t - φ)
   Thus, 8 = δω_n
   and 6 = ω_n √1 - δ²
   ⇒ δ = 0.8
   and since ω_n = 10 satisfy these equations,
   therefore
   

   ≤ K [1 + 1.66 e– 8t sin (6t – 143°)] =	100 K
   	s(s2 + 16s + 100)

   
   

   ∴ M(s) = s C(s) =	100 K
   	s2 + 16s + 100

   Correct Option: A

   M(s) =	C(s)
   	R(s)

   
   

   But R(s) =	1	=
   	c

   
   ∴ M (s) = s C (s)
   
   (ω_n √1 - δ² t - φ)
   Thus, 8 = δω_n
   and 6 = ω_n √1 - δ²
   ⇒ δ = 0.8
   and since ω_n = 10 satisfy these equations,
   therefore
   

   ≤ K [1 + 1.66 e– 8t sin (6t – 143°)] =	100 K
   	s(s2 + 16s + 100)

   
   

   ∴ M(s) = s C(s) =	100 K
   	s2 + 16s + 100

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45. The feedback control system shown in the given figure represents a
    
    

1. 1. Type 0 system

   
   
   

   2. Type 1 system

   
   
   

   3. Type 2 system

   
   
   

   4. Type 3 system

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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