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2003 & 1997 Course Process Modeling & Optimization

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Total No. of Questions : 12] P1166 [Total No. of Pages : 3 [3664]-256 B.E. (Instrumentation & Control) PROCESS MODELING AND OPTIMIZATION (1997 & 2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer three questions from Section-I and three questions from Section-II. 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, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. 7) All questions are compulsory. SECTION - I Q1) a) Obtain the model for armature controlled D.C. shunt motor. [8] b) Fit the given data to the model y = mx + c using least square method.[8] x y 200 400 600 800 1000 1200 1400 1600 0.846 0.573 0.401 0.288 0.199 0.153 0.111 0.078 OR Q2) a) Obtain the model for field controlled D.C. shunt motor. [8] b) Obtain the model for gravity flow tank. [8] Q3) a) Obtain the model for non isothermal C.S.T.R. [8] b) Obtain the model for ideal binary distillation column. [8] OR P.T.O. Q4) Obtain the model of heat exchanger. [16] Q5) Explain the sine wave test and pulse test of system identification in detail.[18] OR Q6) Explain ATV identification and its models in detail. [18] SECTION - II Q7) List various methods of stability analysis of multivariable systems. Explain Niederlinsky index. Find Niederlinsky index of the system, [16] 12 .8e s X D 1 + 16 .7s X = 6.6e 7 s B 1 + 10 .9s 18 .9e 3s 1 + 21s R 19 .4e 3s V 1 + 14.4s and comment on stability. Repeat the procedure for XD V and XB R pairing. OR Q8) Write short notes on : [16] a) Relative gain array. b) Inverse Nyquist array. Q9) a) Define and explain the following : [12] i) Continuity of a function. ii) Convexity of a function. iii) Concavity of a function. b) Determine the optimum values of x1 and x2 for the function y= [6] 2 x12 + + 4 x2 . 4 x1 x2 OR Q10) a) Find the optimum values of f(x) = 12x5 45x4 + 40x3 + 5 b) Find the minimum value of y if, y= [3664]-256 x1 1 12 x + + x2 + 3 . x2 x1 x3 2 16 2 [6] [12] Q11) Explain the procedure of scanning and bracketing for single variable optimization in detail. [16] OR 2 Q12) a) Minimize f(x1, x2) = x1 x2 + 2 x12 + 2x1x2 + x2 using Newton s method 0 if starting point is x = . 0 [8] b) Explain conjugate gradient method for multivariable optimization with the help of algorithm and flow chart. [8] xxxx [3664]-256 3

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