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FIG 6.9. The ratio of the two flows is automaticallg set in cascade to maintain composition control.
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function of the ratio of the flowing streams, apart from their total flow. A typical application is the blending of ingredients to form a mixture of controlled composition. Figure 6.9 shows the arrangement of the control loops for a two-component system. Notice that the signals are in the differential form. Although the gain of the cascade flow loop varies inversely with its flow, the gain of the multiplier varies with the wild flow squared. Thus loop gain is dX
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Direct variation of gain with flow is much preferable to inverse variation. Compare this cascade control system to the one in Fig. 6.8 where total flow was the primary manipulated variable.
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The range of adjustment available with standard ratio stations is typically 0.3 to 3.0. Using a single multiplier, a range of 0 to 2.0 is CUStomary. Occasionally an application will be encountered where these ranges are insufficient. In this event, two multipliers can be used, each setting the rate of one flowing stream. Mathematically, the system is organized to deliver a set total flow F: F=X+Y Then the percentage of X in the total is introduced as an independent setting 2:
X = Fx
The flow of the other stream Y is then the dif!erence: Y = F(l - Z) The controlled ratio X/Y can then be varied from zero to infinity as IZ: varies from zero to one:
x x -=Y l - x
(6.5)
Multiple-loop
Systems
FIG 6.10. The use of two multipliers affords an infinite ratio range.
Because the calculation is based on the sum of the two flowing streams, it will only work with linear flow signals. Independent selection of total flow and percent composition are available, as Fig. 6.10 indicates. Note. that the lower of the two multipliers has a reverse-acting input. When z is 1.0, the gain of this multiplier is zero. Both element factors are unity, which is necessary to satisfy the equation. Although infinite ratio range is theoretically possible, it must be recognized that differential meters are only accurate within a 4: 1 flow range, which will necessarily limit the actual ratio range.
Digital Blending Systems
The use of turbine and positive displacement meters has generated a new type of flow ratio system. These devices are inherently linear and are of a fairly wide range; but of most significance, they do not produce an analog output. Each rotation of their moving elements produces a discrete number of pulses representative of a particular volume of fluid that has passed through. The pulse rate or frequency is proportional to the flow rate, and the total number of pulses transmitted over a given length of time is a measure of the volume of fluid delivered. To take advantage of the discrete nature of the measurements, a special type of control system has been developed. In the digital blending system, the volume delivered through each meter is continuously compared with the volume desired for that stream. An error between the two generates a control signal that manipulates the valve in that stream. Functionally, the loops are arranged similarly to what was shown in Fig. 6.7. A master set station transmits a pulse rate that paces the entire system, demanding a certain total flow rate. This pulse rate is multiplied by the ratio setting for each flow loop, thus producing a rate set point for each loop. There the similarity to an analog system ends.
Pulse Current
FIG 6.11. The output of the controller is the only analog signal in a typical digital blending system.
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The object of the controller is to maintain the set volume delivery. This allows a temporary reduction of flow in any loop, to be made up to the correct total once its cause has been removed. The basic control mechanism is a digital up-down counter. Set-point pulses cause an increase in the register, while measurement pulses bring about a decrease. .The difference between the number of pulses from the two sources is stored and convert,ed to an analog signal which may be used to drive a valve. The valve would then be driven proportionally to the volume error or integrated flow error. Thus the control mode is int.egral (reset only). Let the volume error required for 100 percent change in output be identified as I/ and the maximum flow rate as F. The percent output to the valve in terms of percent demanded and measured flow is then 1 m=V IF(r - c) dt
(6.6)
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