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FIG 6.5. Using the ratio of two variables as the input to a controller is not recommended.
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FIG 6.6. In the recommended sgstern, the ratio calculation is outside the loop.
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circuit, making I = KY if X is controlled, or r = X/K if Y is controlled. Figure 6.6 shows the set-point calculation. In this configuration, one of the variables becomes controlled and the other serves to generate a set point. The wild variable is multiplied by the adjustable coefficient K in a device called a ratio station.
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By far the most common application of ratio control is in flow systems. Ingredients for a reactor, for example, are introduced in precise proportions. Any number of streams can be set in ratio to one independent flow, allowing the plant to be started or shut down by the manipulation of that key variable alone-all others must follow. Or, if all flows are under control, total plant throughput can be commanded through a single master set station, as shown in Fig. 6.7. Up to this point, the ratio stations have all been outside the closed loops. But a natural extension to the configuration in Fig. 6.7 is the automatic repositioning of a master set point by the output of another controller. Consider the example of a chemical reactor which is to be operated consistently at maximum throughput, as determined by its heat-removal capability. The only control system which could satisfy this specification would feature a temperature controller setting the flow rates of all ingredients into the reactor, as shown in Fig. 6.8. Because this configuration places the ratio stat,ions within the primary loop, loop gain varies with their settings. In such an arrangement, constant loop gain can ordinarily be assured if the sum of the ratio settings is constant. Thus a percentage increase in one ingredient should be accompanied by a corresponding decrease in the others. This is often done for accounting purposes anyway, by making the sum of the ratios
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FIG 6.7. A single master station can set all the plant streams through ratio stations.
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To flow controllers
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station
Individual rotio stations
1 Multiple-loop Systems
Secondary
FIG 6.8. Several secondary loops can be set in cascade from one primary controller.
always equal 100 percent. Then the master station or primary controller sets the true total flow. Since the prime manipulated variable in Fig. 6.8 is total flow, the prime controlled variable must be a function of total flow and be relatively independent of the individual ratio settings. Most ratio stations have a gain range of about 10: 1. Since the normal ratio setting for most applications is in the vicinity of 1.0, this is selected as the midscale position. (Th is assumes that the flowmeters for the various streams are sized in proper proportion, so that under normal operation they will all read about the same percentage flow.) Thus the gain of a typical ratio station would be adjustable from 0.3 to 3.0. But most flowmeters are of the differential type, in which case flow squared is the transmitted variable. Then, X2 = K2Y2 The gain of the ratio station is the square of the ratio setting; in other words, the ratio setting is the square root of the gain. The ratio scale for differential meters is compared with a linear scale below :
Gain K2 0.3 1.o 3.0
Ratio X 0.6 1 1.7
Setting the Ratio Remotely
The ratio stations discussed thus far are nothing more than amplifiers with adjustable gain. The ratio setting was introduced manually. If it is desired that the ratio setting be introduced as a control signal, a different device must be used. The device is, in fact, defined as a multiplier, because its output is the product of two analog signals. The gain of a multiplier is directly proportional to each of its inputs. If a midscale ratio of 1.0 is desired, the gain range of the multiplier must be 0 to 2.0. The multiplier is then said to have an element factor of 2.0. Linear and differential flowmeter ratio scales for the multiplier are compared below:
Linear flow ratio 0 M Differential flow ratio 0
The use of a multiplier permits setting of the ratio by the output of a primary controller. This is desirable where the primary variable is a
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