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2003 Course Digital Control

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Total No. of Questions : 12] P1004 [Total No. of Pages : 4 [3664]-245 B.E. (Instrumentation & Control) DIGITAL CONTROL Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) Answer any three questions from each section. 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) All questions carry equal marks. 6) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 7) Assume suitable data, if necessary. SECTION - I Q1) a) Derive the pulse transfer function of the system shown in Figure No. 1 by first principle. [6] b) Examine the stability of the system with closed loop characteristic equation F(z) given below using Jury stability test. F(z) = z4 1.2z3 + 0.22z2 + 0.066z 0.008 = 0 [10] OR Q2) a) Obtain the pulse transfer function of the system shown in Figure No. 2. Also obtain output response y(k) if r(k) is step input. [6] P.T.O. b) Find the range of k for the closed loop stability of the system shown in Figure No. 3 using bilinear transformation and Routh array. [10] Q3) a) Find the state transition matrix of the system with state equation. 1 0 x (k + 1) = x (k ) 0.12 0.7 1 Also find solution of state equation if x(0)= . 1 [8] b) Using Liapunov stability test, investigate the stability of the system with state equation. [8] 0 0.81 x (k + 1) = x(k ) . Also find Liapunov function v(x). 1 0 OR Q4) a) Diagonalise the plant matrix given below: 2 G = 0 0 [8] 1 4 2 0 3 1 b) Obtain the state model in i) Controllable canonical form. ii) Jordon canonical form. for the pulse transfer function. G(z) = [3664]-245 (z + 0.5) (z 0.3) z (z + 1)2 [8] -2- Q 5) For a system with continuous time transfer function. G(S) = 1 (1 + 3S) (1 + 7S) Design a continuous time controller such that the desired closed loop response is described by, Q(S) = 1 using controller synthesis formula. (1 + 2S) (1 + 4S) List the controller tuning parameters KC, TI, TD and filter time constant. Also convert the continuous time controller filter structure into discrete time form using Bilinear transformations, S = 2 z 1 with T = 0.5 sec. T z +1 [18] OR Q6) For a system shown in Figure No. 4 design a deadbeat controller such that error is zero after two sampling instants, that is , Q(z) = a1z 1 + a2z 2. Where, T = 1sec, r(t) = step input, G(S) = 1 . S (S + 5) [18] SECTION - II Q7) a) Define the term state observability and state the condition for complete state observability. Investigate for the complete state observability of system. 0 1 1 0 x(k + 1) = x(k ) + u(k ) 2 3 0 1 2 0 y (k ) = x( k ) . 0 2 [8] b) What is State Observer? List and define its types. State necessary and sufficiency condition for the design of state observer. List the steps in state observer design. [10] OR [3664]-245 -3- Q 8) Derive the formula for state variable feedback gain matrix K. Determine the state feedback gain matrix K for the system 1 0 0 0.25 x(k + 1) = 1 0 0 x(k ) + 0 u(k ) 1 0 1 0.5 such that the desired closed loop poles are placed at, z1 = 0.2, z2, 3 = 0.4 j 0.5 [18] Q9) Explain the internal model control (IMC) strategy and its design procedure. Design IMC controller for the system with transfer function, G(S) = Also convert it into conventional controller. 1 5S . 1 + 10S [16] OR Q10) Explain the concept of adaptive control, necessity of adaptive control. With the help of suitable block diagrams discuss the following: [16] a) Model Reference Adaptive Control. b) Self Tuning Regulator. Q11) For the system with state model 0 1 0 1 x(k + 1) = x (k ) + u (k ) with x (0) = 1 1 1 1 Find optimal control sequence u(k) = k(k)x(k) such that the following performance index is minimised. 12 1 J = x1 (3) + 2 2 [x12 (k ) + u 2 (k )] 2 k =0 Also find Jmin. [16] OR Q12) Explain the system identification procedure with the help of neat flow chart. Obtain the parameter vector for the ARX model with e(t) = 0 using least square method. [16] rrrr [3664]-245 -4-

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