Because the dynamics of the 5/10/5 and 5/13/5 designs are similar, only the results of the case with 10 reactive trays will be discussed. We found that adding more reactive trays did not solve the problem of a drop in product purities for the CS7-R structure. Thus, we consider only the CS7-RR structure.
Figure 10.8 shows how the steady-state gains and the SVD results change as more reactive trays are added. The curves for the different cases look similar superficially, but closer inspection reveals important differences. Although there is a small shift in the location of the most sensitive tray for fresh feedstream F0A with an increase in the number of reactive trays, it stays in the stripping section for all three design cases. The magnitude of steady-state gains for input F0A (KF0A) decreases, but this can be compensated for by larger controller gains.
However, the differences between optimum (5/7/5) and suboptimum (5/10/5 and 5/13/ 5) designs regarding KF0B and U2 are more important. The trays in the rectifying section and upper part of the reactive zone have negative steady-state gains when more trays are added to the reactive zone. Their magnitudes are bigger compared to the very small negative gain of the optimum design (NRX = 7) at tray 10. Another difference is that the most sensitive trays from the SVD analysis shift to the rectifying section with an increase in the number of reactive trays. Note that there are also other sensitive regions (second negative peaks that are smaller) in reactive zones for the 5/10/5 and 5/13/5 designs.
The steady-state gains and the SVD analysis of the 5/10/5 case suggest using tray 18 in the rectifying section by manipulating fresh feed flowrate F0B and the temperature of tray 2 in the stripping section is controlled by manipulating fresh feed flowrate F0A. Figure 10.9 gives relay-feedback test results for both loops using these trays. As given in Table 10.2, the controller gain and reset times calculated from the relay-feedback test data have reasonable values for tray 2. However, the controller for tray 18 has a reset time of 347 min. This occurs because the T18/F0B open-loop transfer function has an inverse response. The shape of the tray 18 temperature response shown in Figure 10.9 (shark's tooth appearance) is characteristic of a process with an inverse response. This
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