## Info

Figure 7.24 (a) Deadtime All Variables table; (b) after initialization run.

Figure 7.24 (a) Deadtime All Variables table; (b) after initialization run.

Figure 7.25 Flowsheet with controller faceplate.

formulas are

These are loaded into the controller by clicking the Update controller button. Run the simulation out in time for a while to see how well these settings work in terms of bringing the column to steady state. In the next section we will subject the column to disturbances and evaluate the performance of several control structures.

### 7.5.2 Reflux to Feed Ratio

Before we illustrate the use of a composition controller, it might be instructive to show how a reflux to feed ratio structure is set up. In Chapter 5, steady-state calculations indicated that a R/F ratio scheme should do a pretty good job of maintaining product purities in the propane/isobutane system in the face of feed composition disturbances and, of course, feed flowrate changes.

The R/F structure is implemented by using a multiplier block. The input of this block is the mass flowrate of the feed, which is 52.513 kg/s. The properties of any stream can be found by clicking on the steam name, right-clicking, selecting Forms, and then selecting Results. Figure 7.27 gives the stream information for the feed F1.

Figure 7.26 (a) Setting up the relay-feedback test; (b) relay-feedback test results; (c) calculated controller settings.
Figure 7.26 Continued.
Figure 7.27 Results table for stream F1.
Figure 7.28 (a) Results table for column; (b) choices; (c) entering ratio constant.

The output of the multiplier block will be the mass flowrate of the reflux. To determine the design value of this variable, we can click the column icon, right-click, select Forms, and select Results. This opens the table shown in Figure 7.28a. The second line from the bottom gives the reflux mass flowrate of 61.7877 kg/s. So the multiplier block should multiply the feed mass flowrate by the number (61.7877/52.513) = 1.1766.

A Multiplier control model is placed on the flowsheet. A control signal is connected from the feed F1 (mass flowrate) to the multiplier (labeled "R/F ratio" in Figure 7.29). This is "Input1." A second control signal is connected from the multiplier output to the column and connected to the blue arrow pointing to the line below the condenser. A list

Figure 7.29 Flowsheet with R/F structure.

of alternatives opens, and the top one, Reflux.FmR, is selected (see Fig. 7.28b). To set the constant in the multiplier, the icon is clicked and right-clicked. Forms and All Variables are selected, and the window shown in Figure 7.28c opens, on which we enter the number "1.1766" for "Input2." In this example, one of the inputs is a constant. In other examples, both of the inputs can vary with time.

The final flowsheet and controller faceplates are shown in Figure 7.29. We will compare the performance of this control structure with some alternatives later in this chapter. First we want to illustrate the use of a composition controller.

### 7.5.3 Composition Control

We want to compare tray temperature control with two types of composition control. In both, the composition of the propane product is measured directly and controlled at 2 mol% isobutane. The first type is "direct composition control," in which a single PI controller is used with reboiler heat input manipulated. The second type uses a cascade composition-to-temperature control structure.

Composition measurement typically has larger deadtime and lags than does temperature control. We assume a 3-min deadtime in the composition measurement.

First, we add a PIDIncr controller to the flowsheet and make the appropriate connections and do not use a deadtime, which will be added later. The controller should be set to Reverse. The PV is the mole fraction of isobutane in the distillate stream. The OP is reboiler heat input. A composition transmitter range of 0-0.05 mF isobutane is used, as shown in Figure 7.30.

After the simulation is run, a 3-min deadtime is inserted. Initialization and Dynamic runs are made to converge to steady-state conditions. Then a relay-feedback test is run. Results are shown in Figure 7.31. Note that the timescale on the plot is very different

Figure 7.30 Ranges page tab for cascade control.
Figure 7.32 Final flowsheet with cascade control.

from that for the temperature controller. The ultimate gain is 0.58, and the ultimate period is 32.4 min. The Tyreus-Luyben settings are calculated and inserted in the composition controller. The final flowsheet is given in Figure 7.32.

7.5.4 Composition/Temperature Cascade Control

Temperature control has the advantage of being fast, but it may not hold the product purity constant. Composition control is slow, but it will drive product purity to the desired value. The final control structure studied in this chapter is a cascade combination of composition and temperature control that achieves both fast control and the maintenance of product purity.

The tray temperature controller is the secondary controller. It is set up in exactly the same way as we did in the previous section. It looks at tray temperature and manipulates reboiler heat input. However, its setpoint is not fixed. The setpoint signal is the output signal of the composition controller, which is the primary controller.

The tuning of the secondary temperature controller remains unchanged. The primary composition controller must be retuned since its ouput signal is now a temperature setpoint. With the temperature controller set on automatic, the relay-feedback test is run on the composition controller. Figure 7.33 shows the relay feedback test results. The ultimate gain and ultimate period are 0.98 and 15.9 min, respectively, compared to the direct composition results of 0.58 and 32.4 min. We can see immediately that a higher gain and smaller integral time result, which indicates tighter control with the cascade control structure. Figure 7.34 shows the cascade control structure and controller faceplates. Note that the TC7 temperature controller is "on cascade" (meaning that its setpoint signal is the output signal of the composition controller).

Figure 7.33 Cascade control relay-feedback test.

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