Q4. A distillation column is subjected to a unit step change in feed flow rate F. Response data for the overhead product composition xD are shown below. Previous experience has indicated that the transfer function, F(s)XD(s)=10s+15 provides an accurate dynamic model. Filter these data using an exponential filter with two different values of alpha, 0.5 and 0.8 . Graphically compare the noisy data, the filtered data, and the analytical solution for the transfer function model for a unit step input. Using Eq. 17-9, the filtered values of xD are shown in Table S17.1 Table S17.1. Unfiltered and filtered data. To obtain the analytical solution for xD, set F(s)=s1 in the given transfer function, so that XD(s)=10s+15F(s)=s(10s+1)5=5(s1s+1/101) Taking inverse Laplace transform xD(t)=5(1et/10) A graphical comparison is shown in Fig. S17.1 Fig S17,1. Graphical comparison for noisy data, filtered data and anabytical solurion. As deereases, the filtered data give a smoother curve compared to the no-filter (1) case, but this noise reduetion is traded off with an increase in the deviation of the curve from the analytieal solution