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2003 & 1997 Course Process Modeling & Optimization

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Total No. of Questions : 12] P1852 [Total No. of Pages : 3 [3764]- 295 B.E. (Instrumentation) PROCESS MODELING AND OPTIMIZATION (1997 & 2003 Course) (406270) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer three questions from each section as per the instructions. 2) Answers to the two sections should be written in separate answer books. 3) Neat diagrams must be drawn, wherever necessary. 4) Figures to the right indicate full marks. 5) Use of electronic pocket calculator is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) Derive the model of the field controlled DC shunt motor. [8] b) Fit the following data to the model y = a0 + a1x + a2x2 using Lagrange interpolation formula. [8] x 1 3 6 8 y 9.8 13.0 9.1 0.6 OR Q2) Fit the following data to the model y = a0 + a1x + a2x2 using least square method. [16] x 20 20 30 40 40 50 50 60 70 y 73 78 85 90 91 87 86 90 65 Q3) Develop the model of the ideal distillation column. [16] OR Q4) Develop the model of the non isothermal CSTR with first order reaction dynamics for the reaction. [16] A k B P.T.O. Q5) Write short note on : [18] a) Sine wave testing for system Identification. b) Pulse test for system Identification. OR Q6) Explain the advantage pf the ATV identification over pulse test. Explain the ATV identification method and its five models. [18] SECTION - II Q7) a) Define the term Niederlinsky index. Obtain the Niderlinski Index for the system and comment on the stability of the system. [10] 12.8e s 16.7 s + 1 G (s ) = 7 s 6 .6 e 10.9 s + 1 18.9e 3 s 21s + 1 19.4e 3 s 14.4 s + 1 b) Define the relative gain array. Obtain the RGA of the system whose transfer function matrix is [8] 22.89 e 0.2 s 4.572 s + 1 G (s ) = 0.2 s 4.689 e 2.174 s + 1 11.64 e 0.4 s 1.807 s + 1 5.8 e 0.4 s 1.801 s + 1 OR Q8) Define the resiliency index and determine the Morari Resiliency index of the systems given in Q.7 (a) and Q.7 (b). [18] Q9) Explain the following terms : [16] a) Concave function. b) Convex function. c) Local minimum and global minimum. d) Hessian matrix for function f (x). OR [3764]-295 -2- Q10) a) Find the optimum values f (x) = 12x5 45x4 + 40x3 + 5 of function. [8] b) Find the minimum value of the y for 2 1 x1 x2 x3 y= + + + 2 16 x2 x1x3 [8] x with bracket 2 < x < 3 and 0.01 log 2 x Q11) a) Minimize the function f ( x) = using Secant method. [8] b) Explain the Newton s method of function minimization [8] OR Q12) a) Explain the steepest decent method with the help of algorithm and flowchart. [8] 2 2 b) Minimize f (x1,x2) = x1 x2 + 2 x1 + 2x1x2 + 2 x2 using Newton s method. 0 Assume starting point is x = . 0 xxxx [3764]-295 -3- [8]

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