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2003 Course Digital Control Systems

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Total No. of Questions : 12] [Total No. of Pages : 4 P1342 [3764]-212 B.E. (Electrical) DIGITAL CONTROL SYSTEMS (403149) (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) Answer any one question from each pair of questions Q. 1 & Q. 2, Q. 3 & Q. 4, Q. 5 & Q. 6, Q. 7 & Q. 8, Q. 9 & Q. 10, Q. 11 & Q. 12. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, electronic unprogrammable pocket calculator is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) Discuss the advantages and limitations of Digital Control System. [8] b) A discrete system is given as : [8] y(n) = x( n + 2). Check whether the system is. i) Static or Dynamic. ii) Linear or Nonlinear. iii) Shift invariant or Shift varying. iv) Causal or Non-causal. OR Q2) a) State and explain sampling theorem. Also describe reconstruction process. [8] b) Sketch a D.T. signal x(n) = 3 n for 1 n 3 and obtain i) y(n) = x(2n) ii) [8] y(n) = 2x(n) + (n) P.T.O. Q3) a) Explain the term Convolution Sum as used in Discrete Time System. Discuss the various methods of computation of convolution in D.T. System. [8] b) Obtain linear convolution of following sequences by multiplication method and then verify the result by Tabulation method : x(n) = {1, 2, 3, 1} h (n) = {1, 2 , 1, 1} [8] OR Q4) a) Draw a neat block diagram for digital speed control of a turbinegenerator unit and explain function of each block. [8] b) Prove that LTI system is completely characterised by Unit Impulse Response h(n). [8] Q5) a) State and prove the Real Translational (Right Shifting) theorem of Z-transform. [6] b) Find the Z-transform of the sequence : [12] k i) 1 f(k) = for k = 0, 1, 2, ............... 2 ii) f(t) = e at.sin t. OR Q6) a) Explain any two methods of obtaining the Inverse Z-transform. b) Obtain Inverse Z-transform of the following : i) 1 1 z 1 1 2 x(z) = , | z | > -- using partial fraction method. 1 2 1 z 1 4 ii) x(z) = [3764]-212 1 --- using Residue Method. ( z 1) ( z 3) -2- [6] [12] SECTION - II Q7) a) Show how a mapping of Left Half of the S-plane is done into the Z-plane with stable and unstable regions. [8] b) Examine the stability of the following characteristic equation using Jury s criteria : P(z) = z4 1.2z3 + 0.07z2 + 0.3z 0.08 = 0 [8] OR Q8) a) Describe Schurchon s Stability Test as applied to Discrete Time Systems. [8] b) Open-loop transfer function of unity feed-back discrete-time control system with sampling. [8] Period T = 1 sec, is given by : G( z ) = k (0.3679z + 0.2642) ( z 0.3679) (z 1) Determine the range of gain K for stability by use of the Jury s stability test. Q9) a) Derive the expression of pulse transfer function from discrete time state space model, with usual notations : x(k + 1) = Gx(k) + Hu(k) y(k) = Cx(k) + Du(k) [8] b) Obtain STM of following difference eq n using Cayley Hamilton 1 1 0 theorem: x(k + 1) = Gx(k) + Hu(k) where G = ; H = [8] 1 0.2 1 OR Q10) a) Derive the solution of a non-homogeneous state equation of a discrete time system from first principles. [8] b) It is desired to place the closed loop poles at S = 3 and S = 4 by a state feedback controller with the control u = kx. Determine the state feed back gain matrix K and the control signal. [8] 1 0 0 x= x + 2 u ; y = [1 0]x 1 3 [3764]-212 -3- Q11) a) Explain precisely the concept of controllability and observability in case of discrete time state space representation. Discuss the methods of determining these values. [9] b) A state space model is given by 0 1 0 0 2 0 ; H = G= 0 0 3 1 0 1 2 ; C = 2 1 1 1 2 3 1 5 ; D = [0] Determine the controllability and observability of this system. [9] OR Q12) a) Write a detail note on Digital PID controller. [8] b) Consider the system represented by 1 0 0 0 x (k + 1) = 0 0 1 x (k ) + 0 u(k ); y(k) = [1 0 0] x(k) 6 11 6 1 Design a full order observer such that the observer eigen values are at 2 j 2 3 and 5 . [10] rrrr [3764]-212 -4-

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