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Equation (8.15), like (8.14), is a single relationship containing two unknowns. Yet some definite conclusions can be drawn which will be useful in making preliminary adjustments: 1. If 71 must exceed r2, based upon the direction of the uncompensated transient, r2 can safely be set in the vicinity of 0.7t,. If 71 must be less than Q, Q should be about 1.5t,. 2. Initially, 71 can be set at about 2T2 in the former case, or 0.572 in the latter. Once these preliminary adjustments have been introduced, the load response should be repeated, from which finer adjustments may be made. Figure 8.13 compares the load response, with varying degrees of compensation, to the uncompensated response of a typical process. Notice that curve (b) in Fig. 8.13 lacks area compensation. Curve (c), on the other hand, shows adequate compensation with respect to area, in that it is distributed equally about the set point. In this case, the difference between T1 and T2 is correct, but their individual values are not. Once the correct area compensation has been found, Tl and 72 should both be adjusted in the same direction, to maintain their difference. In the example shown in Fig. 8.13c, Tl and TX need to be reduced; this will make their ratio increase, which will move the centroid of the lead-lag area to the left. Curve (a ) is the result of such an adjustment: it crosses the set point at approximately time t,. Perfect compensation is unattainable. For one thing, any process sufficiently problematic to warrant feedforward control can be expected to display some dead time in addition to capacity. This is true of the heat exchanger. But compensation for dead time is, at best, approximate. Second, the dynamics of most processes are subject to change.
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FIG 8.13. Curve (a) is the uncompensated loop response; curves (b) and (c) reveal incorrect compensation; curve (d) is nearly perfect.
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FIG 8.14. Feedforward control.is capable of reducing both the area and the duration of the load-response transients.
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This is also true for the heat exchanger, whose dead time varies with the rate of flow through t.he tubes. It might be possible to construct an extremely complete dynamic model of a process, but any compensator with more than three terms to adjust would be unrea,sonably difficult to cope with. Furthermore, the purpose of dynamic compensation is to minimize an error which is already transient, so perfection is not really warranted. In most cases, a simple lead-lag function will be perfectly adequate and will be able to reduce the absolute area of the response curve by tenfold or more, distributed uniformly. Figure 8.14 compares the load response of the heat exchanger under dynamically compensated feedforward control with that encountered under feedback control. For processes whose uncompensated load-response curves cross the set point, lead-lag may be inadequate. For these applications, an additional lag is useful in canceling the first part of the curve, while the lead-lag function compensates the balance. Distillation columns typically exhibit this characteristic. Further discussion of the problem will be found in Chap. 11 and in reference (3).
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ADDING FEEDBACK
The only serious failing of the feedforward technique is its dependency on accuracy. To provide perfect control, a system must model the plant exactly; otherwise whatever error may exist in positioning the manipulated variable causes offset. Errors may arise from several sources: 1. Inaccuracy in the measurement of load and manipulated variables 2. Errors in the computing components 3. Failure of the computing system to adequately represent the characteristics of the plant 4. Exclusion of significant load components from the feedforward system The first and second items alone limit the accuracy of practical systems to the vicinity of 1 to 2 percent.
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