Download AKTU B-Tech 6th Sem 2016-2017 NEN011 Digital Control System Question Paper

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B. TECH.

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THEORY EXAMINATION (SEM–VI) 2016-17

DIGITAL CONTROL SYSTEM

Time: 3 Hours Max. Marks : 100

Note: Be precise in your answer. In case of numerical problem assume data wherever not provided.

SECTION-A

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1. Attempt the following : (10×2=20)
   1. Explain state space representation of digital Control System.
   2. Design a controller from continuous to digital system.
   3. Explain acquisition time for sample and hold operation.
   4. Write shifting property of Z transform.
   5. If X(z) = 2+3Z¯¹+4Z¯² then find the initial and final value of the corresponding sequence.

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   6. State Cayley-Hamilton theorem.
   7. Calculate the pulse transfer function of zero order hold whose transfer function is Gho(s) = (1-e^-Ts)/S
   8. Find out the equilibrium points of the following nonlinear system.
      x₁(k+1) = x₁(k) - x₁(k)
      x₂(k+1) = -x₂(k)

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   9. Write Euler-Lagrange equation.
   10. Define Asymptotic Stability.

SECTION-B

2. Attempt any five of the following: (10×5=50)
   1. (i) Draw the basic digital control system and explain the function of each block.
      

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      (ii) Discuss the relationship between Laplace transform and Z transform.
   2. (i) Explain the Concepts of controllability and observability.
      (ii) Describe the sample and hold operations.
   3. A plant is described by the transfer function shown in the below block diagram. With the help of Jury stability test find the range of K for the system to be stable.
      [Block Diagram Description: A forward path with gain K and transfer function G(s) = 1/(S(S+2)), closed-loop system with unity negative feedback]

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   4. (i)Write the Controllability and Observability conditions for Pulse Transfer Function.
      (ii) Explain the relation between bilinear transformation and W-plane.
   5. Explain the stability criteria. Calculate the characteristic equation below by using jury stability criteria:
      F(z) = z³ – 1.25z² – 1.375z – 0.25= 0
   6. Find the pulse transfer function of the zero order hold and the relation between G(s) and G(z).

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   7. Explain the principle of optimality and dynamic programming.
   8. Explain the design procedure in the W-plane.

SECTION-C

3. Attempt any two of the following : (15×2=30)

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4. Find the optimal control u°(k), k = 0,1,2,.....10, such that the performance index
   J= S[x²(k) +2u² (k)] from k=0 to 10
   Is minimized, subject to the equality constraint
   x(k+1) = x(k) + 2u(k)
   i. The initial state is x(0) = 1 and the final state is x(11) = 0
   

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   ii. The initial state is x(0) = 1 and the final state x(11) is free.
5. (i) find the Z transform of the sequence f(k)=(1/2)^k
   (ii) compute the state transition matrix using Caley Hamilton Theorem for the given A.
   A = [[0, 0, -2], [0, 1, 0], [1, 0, 3]]
6. State and explain Liapunov stability criteria and test the stability of the discrete-data system
   

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   described by
   X₁(k+1) = -0.5 X₁(k)
   X₂(k+1) = -0.5X₂(k)

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