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unsw ceic3000 tutorial w1 process modeling and analysis

# unsw ceic3000 tutorial w1 process modeling and analysis -...

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School of Chemical Engineering CEIC3000 Process Modelling and Analysis Tutorial 1 1. Using the cylinder surge tank example discussed in class to explain what is a mathematical dynamic model and the concepts of input, output and state variables. Assume the liquid level is unknown variable of interest. What are the input, output and state variables in this case? 2. Consider the distillation column discussed in class. At the steady-state, the tray temperatures at trays 7 and 21 ( T 7 and T 21 ) are related to liquid reﬂux ( L ) and vapour boilup rates ( V ). y = A u , (1) where A = [ - 33 . 89 32 . 63 - 18 . 85 34 . 84 ] , y = [ T 7 T 21 ] , u = [ L V ] (a) Is matrix A i. square? ii. diagonally dominant? Why/why not? (b) What are the eigenvalues and eigenvectors of matrix
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Unformatted text preview: A ? (c) For a given u = ± 1-1 ² T , represent y in the form of the linear combi-nation of the eigenvectors of Matrix A . (d) Re-deﬁne a new set of input and output variables such that the input output relationship is decoupled (that is, there is no interactions between diﬀerent inputs). (e) Find the inverse mapping from y to u such that you can calculator corre-sponding u from given y . 3. For a given matrix A and its eigenvalues λ 1 , λ 2 . . . λ n , prove that the eigenvalues of A-1 would be 1 /λ 1 , 1 /λ 2 , . . . 1 /λ n if A-1 exists. 1...
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