66. The characteristic equation of a unity feedback control system is given by s³ + K₁s² + s + K₂ = 0. Consider the following statements in this regard
    1. For a given of K₁, all the root-locus branches will terminate at infinity for K₂ in the positive direction.
    2. For a given value of K₂, all the root-locus branches will terminate at infinity for variable K₁ in the positive direction.
    3. For a given value of K₂, only one root-locus branch will terminate at infinity for variable K₁ in the positive direction. Of these statements—
    

1. 1. 1 and 2 are correct
      

   
   
   

   2. 3 alone is correct
      

   
   
   

   3. 2 alone is correct
      

   
   
   

   4. 1 and 3 are correct

   
   
   

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1. View Hint View Answer Discuss in Forum

   Refer synopsis.

   Correct Option: A

   Refer synopsis.

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67. Which of the following is the transfer function of a system having the Nyquist plot in figure below?
    
    
    
    

1. 1. K

      s(s + 2)2(s + 5)

      
      

   
   
   

   2. K

      s2(s + 2)(s + 5)

   
   
   

   3. K(s + 1)

      s2(s + 2)(s + 5)

   
   
   

   4. K(s + 1)(s + 3)

      s2(s + 2)(s + 5)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Try yourself.
   

   Correct Option: B

   Try yourself.
   

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68. A lag compensation network
    (i) increases the gain of the original network without affecting stability
    (ii) reduces the steady state error
    (iii) reduces the speed of response
    (iv) permits the increase of gain if phase margin is acceptable. In the above, correct statements are—
    

1. 1. All
      

   
   
   

   2. (i) and (ii)
      

   
   
   

   3. (ii), (iii) and (iv)
      

   
   
   

   4. (iii) and (ii)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Refer synopsis

   Correct Option: A

   Refer synopsis

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69. A system is described by X = [] 0 1 2 – 3 X + [] 0 1 u y = [1 0] X The system is—
    

    X =		0	1		X +		0		u
    		2	-3				1

    
    y = [1 0] X

1. 1. controllable and observable

   
   
   

   2. uncontrollable and observable

   
   
   

   3. controllable and unobservable

   
   
   

   4. uncontrollable and unobservable

   
   
   

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1. View Hint View Answer Discuss in Forum

   Try yourself, procesure is same as done in solution 197.

   Correct Option: A

   Try yourself, procesure is same as done in solution 197.

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70. A linear discrete-time system has the characteristic equation, z³ – 0.81z = 0
    The system—
    

1. 1. is stable
      

   
   
   

   2. is marginally stable
      

   
   
   

   3. is unstable
      

   
   
   

   4. stability cannot be assessed from the given information.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given equation z³ – 0·81z = 0
   z(z – 0·81) = 0
   z(z – ·9) (z + ·9) = 0
   z = 0, 0·9, – 0·9
   since all the roots lies inside the unit circle.
   Hence the given system is stable.

   Correct Option: A

   Given equation z³ – 0·81z = 0
   z(z – 0·81) = 0
   z(z – ·9) (z + ·9) = 0
   z = 0, 0·9, – 0·9
   since all the roots lies inside the unit circle.
   Hence the given system is stable.

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