To gain some insight into the problem, singular value decomposition analysis was used. There are three manipulated variables: reflux, reboiler heat input, and sidestream flowrate. The steady-state gains between tray temperatures and the three inputs were obtained numerically. The resulting singular values are 119, 15.8, and 2.68. The large condition number indicates that the control of more than one temperature in the column will be difficult. This was found to be the case. Trying to use two temperature controllers resulted in severe interaction.
Therefore we assume that an analyzer is available to measure sidestream MeOH composition. A 3-min deadtime is used in this loop. Stage 17 temperature is controlled (the location of the steepest part of the temperature profile) by reboiler heat input through a heat input to feed ratio (see Fig. 10.32). The temperature control loop is tuned first with the composition loop on manual (KC = 0.159 and tj = 7.9 min). Then the composition loop is tuned with the temperature loop on automatic. Note that the flow controller on the sidestream flow is on "cascade" with its setpoint coming from the composition controller. A reflux to feed ratio is also used.
Unfortunately the relay-feedback test on the composition loop gives very erratic results, as shown in Figure 10.33a with no symmetric switches of the controller output and rapid oscillatory response of the process variable (sidestream methanol composition). The reason for this strange behavior remains a mystery. The resulting controller tuning constants (KC = 6.8 and tj = 26 min) gave unstable responses. Empirical tuning constants
of KC = 1 and tj = 30 min give stable response but poor transient control of product purities. For example, Figure 10.33b gives the response of the system when the methanol feed composition is increased from 1 to 2 mol%. Note that there is a huge transient increase in the methanol impurity in the distillate (upper right graph in Fig. 10.33b), which lasts for over 7 h. Clearly this performance is unacceptable.
A revised control structure was developed. Instead of controlling the methanol composition of the sidestream, the methanol composition of the distillate is controlled by manipulating the sidestream flowrate (see Fig. 10.34). The relay-feedback test of this loop gives reasonable responses (Kv = 1.16 and Pv = 70 min). If the Tyreus-Luyben settings are used (KC = 0.363 and tj = 156 min), the response is somewhat oscillatory when the methanol feed composition increases from 1 to 2 mol%, as shown in Figure 10.35. However, if the Ziegler-Nichols settings are used (KC = 0.527 and tj = 59 min), the response is quite good, as shown in Figure 10.36. The transient disturbance in the distillate purity is reduced because the sidestream is increased more quickly because of the higher gain and smaller reset time.
Figure 10.37 gives responses for 20% increase and decrease in feed flowrate, using Ziegler-Nichols settings in the distillate composition controller. Figure 10.38 gives responses when the DME in the feed is increased from 49 to 54 mol% and when it is decreased from 49 to 44 mol% (with a corresponding change in the water composition). The modified control structure handles all these disturbances quite well.
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