21. NA

1. 1. Phase margin φ_PM is directly proportional to damping ratio ξ
      

   
   
   

   2. Phase margin φ_PM is inversely proportional to damping ratio ξ
      

   
   
   

   3. Phase margin φ_PM and damping ratio ξ are unrelated.
      

   
   
   

   4. When phase margin φ_PMis 0, damping ratio ξ is 0.

   
   
   

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1. View Hint View Answer Discuss in Forum

   The phase margin, φ_PM and damping ratio, ξ is related by equation
   

   ξ =	tan φPM√cos φPM
   	2

   
   thus, from this relation we conclude that
   ● Phase margin φPM is directly proportional to damping ratio.
   ● When phase margin, is 0, damping ratio, ξ is 0.

   Correct Option: A

   The phase margin, φ_PM and damping ratio, ξ is related by equation
   

   ξ =	tan φPM√cos φPM
   	2

   
   thus, from this relation we conclude that
   ● Phase margin φPM is directly proportional to damping ratio.
   ● When phase margin, is 0, damping ratio, ξ is 0.

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22. The frequency at which the Nyquist diagram crosses the negative real axis is known as—
    

1. 1. gain crossover frequency
      

   
   
   

   2. phase crossover frequency
      

   
   
   

   3. damping frequency
      

   
   
   

   4. natural frequency

   
   
   

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1. View Hint View Answer Discuss in Forum

   The frequency at which the Nyquist diagram crosses the negative real axis is known as phase cross-over frequency.

   Correct Option: B

   The frequency at which the Nyquist diagram crosses the negative real axis is known as phase cross-over frequency.

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23. The frequency at which the Nyquist diagram cuts (– 1, 0) circle is known as—
    

1. 1. gain crossover frequency
      

   
   
   

   2. phase crossover frequency
      

   
   
   

   3. damping frequency
      

   
   
   

   4. natural frequency

   
   
   

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1. View Hint View Answer Discuss in Forum

   The frequency at which the Nyquist diagram cuts (–1, 0) circle is known as gain cross-over frequency.

   Correct Option: A

   The frequency at which the Nyquist diagram cuts (–1, 0) circle is known as gain cross-over frequency.

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24. System has phase margin φPM = 45°. The damping ratio ξ is—
    

1. 1. 1
      

   
   
   

   2. 0.5
      

   
   
   

   3. 0
      

   
   
   

   4. 0.42

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given, φ_PM = 45°
   ξ = ?
   

   ξ =	tan φPM√cos φPM
   	2

   
   

   =	tan 45°√cos 45°
   	2

   Correct Option: D

   Given, φ_PM = 45°
   ξ = ?
   

   ξ =	tan φPM√cos φPM
   	2

   
   

   =	tan 45°√cos 45°
   	2

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25. Match List-I with List-II and select the correct answer using the codes given below the lists:
    
    
    

1. 1. a b c d
      3 4 2 1
      

   
   
   

   2. a b c d
      4 3 1 2
      

   
   
   

   3. a b c d
      3 2 4 1
      

   
   
   

   4. a b c d
      4 1 2 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   K1s + K2	=	K1s	+	K2	→ PD—controller
   K3		K3		K3

   
   

   K1s2 + K2s + K3	=	K1s	+	K2	+	K3	1	→ PID—controller
   K4s		K4		K4		K4	s

   
   

   K1s + K2	=	K1	+	K2	→ PI—controller
   K3s		K3		K3

   
   

   K1s K2s	=	K1	→ P—controller
   K2s		K2

   
   Hence alternative (A) is the correct choice.
   

   Correct Option: A

   K1s + K2	=	K1s	+	K2	→ PD—controller
   K3		K3		K3

   
   

   K1s2 + K2s + K3	=	K1s	+	K2	+	K3	1	→ PID—controller
   K4s		K4		K4		K4	s

   
   

   K1s + K2	=	K1	+	K2	→ PI—controller
   K3s		K3		K3

   
   

   K1s K2s	=	K1	→ P—controller
   K2s		K2

   
   Hence alternative (A) is the correct choice.
   

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