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PSet_04

# PSet_04 - 1 Ł 1 B ł Therefore an expedient is to...

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Spring 2003 10.450 Process Dynamics, Operations, and Control Problem Sets - 4 In PSet 3, we worked with a third-order system. * t 1 dT 1 + T 1 * = 1 + 1 B T i * + 1 + B B T o * T 1 * (0) = 0 dt * t 2 dT 2 + T 2 * = T 1 * + CQ * T 2 * (0) = 0 dt * dT * 1 * B * * o t 3 dt + T o = 1 + B T 2 + 1 + B T 1 T o (0) = 0 t j = F (1 V + j B ) j = 1,3 t 2 = V F 2 B = UA C = F r 1 C F r C p p 1. Is it stable? Or that is to say, can B and C be chosen to make it unstable? Judge that from the poles of the transfer function. An analytic solution would tell all, of course, but there’s not much hope of factoring the denominator: * * * T o ( s ) = G i ( s ) T i ( s ) + G Q ( s ) Q ( s ) B t 2 s + 1 + B G i ( s ) = ( 1 + B ) D ( s ) C t 1 s + C G Q ( s ) = D ( s ) D ( s ) = ( 1 + B ) t 1 t 2 t 3 s 3 + ( 1 + B ) ( t 1 t 2 + t 2 t 3 + t 1 t 3 ) s 2 + ( 1 + B ) ( t 1 + t 2 + t 3 ) - B 2 t 2 s +
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Unformatted text preview: 1 Ł 1 + B ł Therefore, an expedient is to calculate them numerically. Matlab does this conveniently by the commands p = [ c3 c2 c1 1 ] r = roots(p) where the vector p represents the coefficients of the cubic polynomial and r will be a vector of the 3 roots. Your job is to look for positive roots. What are the vessel volumes and physical properties? You’re the engineer - pick something realistic. 2. Now, how does our recycle system handle step disturbances? Adapt the sample Matlab files to compute the temperatures T 1 , T 2 , and T o for some values of the parameters you explored in part (1). Submit the best plots. 1...
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