51. The step error coefficient of a system G(s) = 1/(s + 6) (s + 1) with unity feedback is—
    

1. 1. 1/6
      

   
   
   

   2. ∞
      

   
   
   

   3. 0
      

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Step error coefficient also called positional error coefficient i.e.,
   K_p = _{s → 0}Lim G(s)H(s)
   = _{s → 0}Lim 1/(s + 6) (s + 1)
   = 1/6

   Correct Option: A

   Step error coefficient also called positional error coefficient i.e.,
   K_p = _{s → 0}Lim G(s)H(s)
   = _{s → 0}Lim 1/(s + 6) (s + 1)
   = 1/6

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52. A lead compensating network—
    (i) improves response time
    (ii) increases resonant frequency
    (iii) stabilizes the system with low phase margin
    (iv) enables moderate increase in gain without affecting stability The correct statements are—
    

1. 1. All
      

   
   
   

   2. (i) and (iv)
      

   
   
   

   3. (ii) and (iii)
      

   
   
   

   4. (ii) and (iv)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Refer synopsis.

   Correct Option: A

   Refer synopsis.

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53. In the signal flow graph of figure shown below y/x equal to—
    
    
    
    

1. 1. 3
      

   
   
   

   2. 5/2
      

   
   
   

   3. 2
      

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   From figure y = 5 × 2 × x – 2 × 2 × y
   or
   y + 4y = 10x
   or
   5y = 10x
   or
   y/x = 2

   
   

   Correct Option: C

   From figure y = 5 × 2 × x – 2 × 2 × y
   or
   y + 4y = 10x
   or
   5y = 10x
   or
   y/x = 2

   
   

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54. A certain linear time invariant system has the state and the output equations given below
    

    	x1		=		1	-1			x1		+		0		u
    	x2				0	1			x2				1

    
    

    y = [1 1]			x1
    			x2

    
    If X₁(0) = 1,
    X₂(0) = – 1,
    u (0) = 0
    then | dy/dt |_{t = 0} is—
    

1. 1. 1
      

   
   
   

   2. – 1
      

   
   
   

   3. 0
      

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   From given data y = x₁ + x₂
   y |_{t = 0} = 1 – 1
   or
   y |_{t = 0} = 0
   or dy/dx| _{t = 0} = 0
   

   Correct Option: C

   From given data y = x₁ + x₂
   y |_{t = 0} = 1 – 1
   or
   y |_{t = 0} = 0
   or dy/dx| _{t = 0} = 0
   

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55. Consider a unit feedback control system with open-loop transfer function
    G (s) = K/ [s (s + 1)].
    The steady state error of the system due to a unit step input is—
    

1. 1. zero
      

   
   
   

   2. K
      

   
   
   

   3. 1/ K
      

   
   
   

   4. ∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   e_ss = _{s → 0}Lim sE(s)
   

   = s → 0Lims.	s.R(s)
   	1 + (K/s(s+1))1

   
   = H(s) = 1 and if r(t) = u(t)
   then R(s) = 1/s
   

   = s → 0Lim	s(s + 1)
   	s(s + 1) + K

   
   = 0

   Correct Option: A

   e_ss = _{s → 0}Lim sE(s)
   

   = s → 0Lims.	s.R(s)
   	1 + (K/s(s+1))1

   
   = H(s) = 1 and if r(t) = u(t)
   then R(s) = 1/s
   

   = s → 0Lim	s(s + 1)
   	s(s + 1) + K

   
   = 0

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