151. In the signal flow diagram given in the figure, u₁ and u₂ are possible inputs whereas y₁ and y₂ are possible outputs.When would the SISO system derived from this diagram be controlable and observable?
     
     

1. 1. When u₁ is the only input and y₁ is the only output

   
   
   

   2. When u₂ is the only input and y₁ is the only output

   
   
   

   3. When u₁ is the only input and y₂ is the only output

   
   
   

   4. When u₂ is the only input and y₂ is the only output

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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152. Find the transfer function	Y(s)	of the system given below.
     	X(s)

     
     

1. 1. 	G1	+	G2
      	1 - HG1		1 - HG2

   
   
   

   2. 	G1	+	G2
      	1 + HG1		1 + HG2

   
   
   

   3. 	G1 + G2
      	1 + H(G1+ G2)

   
   
   

   4. 	G1 + G2
      	1 - H(G1+ G2)

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Y(s) = Y₁ (s) + Y₂ (s)
   Y₁ (s) = (X – HY)G₁ = XG₁ – HG₁ Y
   Y₂ (s) = (X – HY)G₂ = XG₂ – HG₂ Y
   Y(s) = XG₁ – HG₁ Y + XG₂ – HG₂ Y
   Y = X(G₁ + G₂) – H(G₁ + G₂ )Y
   Y + Y(G₁ + G₂ )H = (G₁ + G₂ )X
   Y(1 + (G₁ + G₂ )H) = (G₁ + G₂ )X
   

   	Y(s)	=	G1 + G2
   	X (s)		1 + H(G1 + G2)

   
   

   Correct Option: C

   
   Y(s) = Y₁ (s) + Y₂ (s)
   Y₁ (s) = (X – HY)G₁ = XG₁ – HG₁ Y
   Y₂ (s) = (X – HY)G₂ = XG₂ – HG₂ Y
   Y(s) = XG₁ – HG₁ Y + XG₂ – HG₂ Y
   Y = X(G₁ + G₂) – H(G₁ + G₂ )Y
   Y + Y(G₁ + G₂ )H = (G₁ + G₂ )X
   Y(1 + (G₁ + G₂ )H) = (G₁ + G₂ )X
   

   	Y(s)	=	G1 + G2
   	X (s)		1 + H(G1 + G2)

   
   

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153. The R-L-C series circuit shown is supplied from a variable frequency voltage source. The admittance - locus of the R-L-C network at terminals AB for increasing frequency ω is
     

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   By rationalization and varying frequency ω , then locus is
   
   

   Correct Option: A

   
   By rationalization and varying frequency ω , then locus is
   
   

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154. The transfer functions of two compensators are
     

     C1 =	10(s + 1)	, C2 =	s + 10
     	(s + 10)		10(s + 1)

     
     Which one of the following statements is correct?

1. 1. C₁ is a lead compensator and C₂ is a lag compensator
      

   
   
   

   2. C₁ is a lag compensator and C₂ is a lead compensator

   
   
   

   3. Both C₁ and C₂ are lead compensators

   
   
   

   4. Both C₁ and C₂ are lag compensators

   
   
   

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1. View Hint View Answer Discuss in Forum

   C1 =	10(s + 1)	, C2 =	s + 10
   	(s + 10)		10(s + 1)

   
   
   Hence C₁ is lead compensator and C₂ is lag compensator.
   Alternately
   

   ∠ φ for G = tan-1 ω - tan-1	ω
   	10

   
   

   or ∠ φ for G = tan-1	ω	ω - tan-1 ω
   	10

   
   Hence C₁ is lead compensator and C₂ is lag compensator.
   

   Correct Option: A

   C1 =	10(s + 1)	, C2 =	s + 10
   	(s + 10)		10(s + 1)

   
   
   Hence C₁ is lead compensator and C₂ is lag compensator.
   Alternately
   

   ∠ φ for G = tan-1 ω - tan-1	ω
   	10

   
   

   or ∠ φ for G = tan-1	ω	ω - tan-1 ω
   	10

   
   Hence C₁ is lead compensator and C₂ is lag compensator.
   

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155. The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure
     
     This transfer function has
     

1. 1. Three poles and one zero

   
   
   

   2. Two poles and one zero

   
   
   

   3. Two poles and two zeros

   
   
   

   4. One pole and two zeros

   
   
   

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1. View Hint View Answer Discuss in Forum

   Transfer function of given plot is of the form
   

   T(s) =	k(1 + s T1)(1 + s T2)
   	s2

   
   so, it will have two poles and two zeroes.
   First – 40 dB/decade slope indicates 2 pole in system.
   Next – 20 dB/decade slope indicates 1 zero is added.
   Next – dB/decade slope indicates 1 more zero is added.
   Alternately
   At ω = 0.1, slope changes from – 40 dB/decade to – 20 dB/decade, then, zero at ω = 0.1
   At, ω > 0.1, slope changes from – 20dB/decade to 0 dB/decade, then one more zero at ω > 0.1
   Since, for ω < 0.1, slope is – 40 dB/decade there is alveag two poles. Hence (c) is the correct option.
   

   Correct Option: C

   Transfer function of given plot is of the form
   

   T(s) =	k(1 + s T1)(1 + s T2)
   	s2

   
   so, it will have two poles and two zeroes.
   First – 40 dB/decade slope indicates 2 pole in system.
   Next – 20 dB/decade slope indicates 1 zero is added.
   Next – dB/decade slope indicates 1 more zero is added.
   Alternately
   At ω = 0.1, slope changes from – 40 dB/decade to – 20 dB/decade, then, zero at ω = 0.1
   At, ω > 0.1, slope changes from – 20dB/decade to 0 dB/decade, then one more zero at ω > 0.1
   Since, for ω < 0.1, slope is – 40 dB/decade there is alveag two poles. Hence (c) is the correct option.
   

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