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2003 Course Process Modeling & Optimization

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Total No. of Questions : 6] [Total No. of Pages : 2 [3864] - 295 P 1277 B.E. (Instrumentation) PROCESS MODELING & OPTIMIZATION (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer any three questions from each section. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables, is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) Explain uses of mathematical model, principles of formulation and types of models. [18] OR Q1) a) b) Find the mathematical model of field control DC motor. [18] Find the model of liquid systems shown in Fig. 1 Assume : L = length of exit line; Ap = Exit line cross-sectional area and At = tank cross-sectional area. Q2) Obtain the model of ideal binary distillation column. [16] OR Q2) Obtain the model of non isothermal C.S.T.R. [16] P.T.O. Q3) Explain pulse testing, sine wave testing in system identification. [16] OR Q3) Write short note on a) ATV identification method. b) Off-line and On-line identification. [16] SECTION - II Q4) Explain Niederlinski index for analysis of stability. Consider a system. [18] 12.8. e s x D 1 + 16.7 s x = B 6.6. e 7 s 1 + 10.9 s 18.9. e 3s 1 + 21s 3 s 19.4. e 1 + 14.4 s R V Find RGA and NI. OR Q4) Write short notes on : a) Resiliency and Morari resiliency index. b) Inverse Nyquist array. [18] Q5) Explain the following : a) Concave, convex functions and continuity of a function. b) Gradient of a function and Hessian matrix. [16] OR Q5) Determine the optimum values of the following functions and state whether they are minimum or maximum. [16] 2 a) f ( x ) = 3 x1 4 x1 x 2 + 2 x 2 . b) Q6) a) b) x12 2 f (x) = + + 4 x2 . 4 x1 x 2 Explain the procedure of scanning and bracketing for optimization. [8] Explain Newtons method for optimization of multivariable functions with the help of flow chart. [8] OR Q6) Explain Newton, Quasi-Newton and secant methods for single variable optimization. [16] [3864] - 295 -2-

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