76. The transfer function C/ R of the system shown in the figure is—
    
    
    
    

1. 1. G1G2H2

      H1(1 + G1G2H1)

   
   
   

   2. G1H2

      H1(1 + G1G2H2)

   
   
   

   3. G2H2

      H1(1 + G1G2H2)

   
   
   

   4. G2H1

      H1(1 + G1G2H2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   From given figure
   

   C(s)R(s) =	1	×	H2G1
   	H1		H2G1G2

   
   or
   

   T.F. =	C(s)	=	H2G1
   	R(s)		H1(1 + G2G2H2)

   
   

   Correct Option: B

   From given figure
   

   C(s)R(s) =	1	×	H2G1
   	H1		H2G1G2

   
   or
   

   T.F. =	C(s)	=	H2G1
   	R(s)		H1(1 + G2G2H2)

   
   

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77. The Nyquist plot for a control system is shown in figure. The Bode plot for the same system will be as in—
    
    
    
    

1. 1. Fig:- A
      

   
   
   

   2. Fig:- B
      

   
   
   

   3. Fig:- C
      

   
   
   

   4. Fig:- D
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   From given figure we observe that at ω = 0 phase of the function is –90° and at ω = ∞ phase of the function is – 270°.
   Hence, Nyquist plot shown corresponds to a function of the type,
   

   C(s)	=	K
   R(s)		s(1 + sT1) (1 + sT2)

   
   The Bode-plot for such a function is of type shown in option (D).

   
   

   Correct Option: D

   From given figure we observe that at ω = 0 phase of the function is –90° and at ω = ∞ phase of the function is – 270°.
   Hence, Nyquist plot shown corresponds to a function of the type,
   

   C(s)	=	K
   R(s)		s(1 + sT1) (1 + sT2)

   
   The Bode-plot for such a function is of type shown in option (D).

   
   

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78. The root locus of a unity feedback system is shown in the above figure. The open-loop transfer function is given by—
    
    
    
    

1. 1. K

      s (s + 1) (s + 2)

      
      

   
   
   

   2. K(s + 1)

      s (s + 2)

   
   
   

   3. K(s + 2)

      s (s + 1)

   
   
   

   4. Ks

      (s + 1)(s + 2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Refer synopsis.

   Correct Option: C

   Refer synopsis.

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79. The characteristic equation of a closed loop system is given by— s⁴ + 6s³ + 11s² + 6s + K = 0 Stable closed loop behaviour can be ensured when gain K is such that—
    

1. 1. 0 < K < 10
      

   
   
   

   2. K > 10
      

   
   
   

   3. – ∞ ≤ K < ∞
      

   
   
   

   4. 0 < K ≤ 20

   
   
   

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1. View Hint View Answer Discuss in Forum

   Try yourself.

   Correct Option: A

   Try yourself.

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80. Which one of the following transfer function represents the Bode plot shown in the given figure?
    
    
    
    

1. 1. G(s) = 1– s/1 + s
      

   
   
   

   2. G(s) = 1/(1 + s)²
      

   
   
   

   3. G(s) = 1/s²
      

   
   
   

   4. G(s) = 1/s(1 + s)

   
   
   

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1. View Hint View Answer Discuss in Forum

   It can be easily checked that the corresponding function is G(s) = 1 – s/1 + s
   Since |G(jω)| = 1 and gain in dB = 0 is given.

   
   

   Correct Option: A

   It can be easily checked that the corresponding function is G(s) = 1 – s/1 + s
   Since |G(jω)| = 1 and gain in dB = 0 is given.

   
   

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