Download AKTU B-Tech 5th Sem 2017-2018 NEE503 Control System Question Paper

SECTION-A

Attempt all questions in brief. 2 x 10 = 20

1. What are the major types of control systems? Explain them in detail with examples.
2. Define the P, PI and PID controllers.

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3. Determine the stability of the system whose characteristics equation is given by 2S4 + 2S³ + S² +3S+2=0.
4. Derive the transfer function Eo(S)/Ei(S) of network shown below:
   

SECTION - B

Attempt any three of the following: 10 x 3 = 30

1. For the system shown in figure, determine the type of system, error coefficient and the error for the following inputs: (i) r(t)=6, (ii) r(t) = 8t (iii) r(t) = 10+4t+1.5t²
   

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2. A linear time invariant system is characterized by the state variable model. Examine the controllability and observability of the system
   A= 0 0 0 1 0 -3 0 1 -4 ; B= 4 1 0 ; C= [0 0 1]
3. Consider a unity feedback system with a forward path transfer function
   G(s) = k(s-4) / (s+2)(s-1)
   

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   Draw the root locus.
4. Write short note on:
   1. Centroid
   2. Breakaway points
   3. Steady state error

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5. For a unity feedback system having
   G(s)= 35(s+4) / s(s+2)(s+5)'
   find (i) the type of the system, (ii) all error coefficients and (iii) errors for ramp input with magnitude 5.

SECTION - C

Attempt any one part of the following: 10 x 1 = 10

1. 1. A system is described by the following differential equation. Represent the system in the state space.
      

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      d³x/dt³ + 3 d²x/dt² + 4 dx/dt + 4x = u1(t) + 3u2(t) + 4u3(t)
      and outputs are
      Y1 = 4x + 3u1,
      Y2 = dx/dt + 4u2 + u3
   2. Define state and state variable? What are the advantage of state space techniques?

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4.Attempt any one part of the following: 10 x 1 = 10

1. 1. Define stability? State the necessary conditions for system to be absolutely stable?
   2. What are the limitations of Routh Hurwitz criterion?

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5.Attempt any one part of the following: 10 x 1 = 10

1. 1. The characteristics equation of a system is given by (s4+20s³+15s²+2s+k=0), determine the range of the k, for system to stable.
   2. Construct the RL for a unity feedback system with OLTF G(s)= k(s+1) / (s+9)

6.Attempt any one part of the following: 10 x 1 = 10

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1. 1. Sketch the RL for a unity feedback system with OLTF G(s)=k(s²+2s+10) / (s²+4s+5)
   2. A unity feedback system shown in figure find the K_c and K_a so that the closed loop poles are placed at s=-15±j20.

7.Attempt any one part of the following: 10 x 1 = 10

1. 1. A unity feedback system has an OLTF
      

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      G(s)=(s+2) / s(s+7s²+4s+3)
      Find the static error constant and e_ss due to an input r(t)=t²u(t).
   2. Sketch the polar plot for (i) G(s)= 32 / (s+4)(s²+4s+8) and find its points of intersection with the real and imaginary axes.