A process consists of two stirred tanks with input q and outputs T1 and T2 (see Fig. E7.3). To test the hypothesis that the dynamics in each tank are basically first-order, a step change in q is made from 82 to 85 L!min, with output responses given in Table E7.3. (a) Find the transfer functions Tl(s)!Q'(s) and T'z(s)IT!(s). Assume that they are of the form K/( Tis + 1 ). Figure E7.3 Exercises 131 Process Control, M.A. Henson and D. E. Seborg (Eds.), Prentice Hall, Upper Saddle River, NJ, 1997. Sundaresan, K. R., and R. R. Krishnaswamy, Estimation of Time Delay, Time Constant Parameters in Time, Frequency, and Laplace Domains, Can. J. Chern. Eng., 56,257 (1978). Table E7.3 t(min) TlCC) Tz (0C) t(min) TlCC) Tz (0C) 0 10.00 20.00 11 17.80 25.77 1 12.27 20.65 12 17.85 25.84 2 13.89 21.79 13 17.89 25.88 3 15.06 22.83 14 17.92 25.92 4 15.89 23.68 15 17.95 25.94 5 16.49 24.32 16 17.96 25.96 6 16.91 24.79 17 17.97 25.97 7 17.22 25.13 18 17.98 25.98 8 17.44 25.38 19 17.99 25.98 9 17.60 25.55 20 17.99 25.99 10 17.71 25.68 50 18.00 26.00 (b) Calculate the model responses to the same step change in q and plot with the experimental data.
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