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Dynamic Elements in the Flow Loop
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1 . P r o c e s s . 2 . T r a n s m i t t e r . 3. Transmission line: 7.......................... 7d......................... 5 . T r a n s m i s s i o n l i n e 7d. + 6. Valve 7.. _. Loop minus controller.. 4. Controller reset, Loop minus proportional.
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To determine what the proportional band will be, valve and kansmitter gain must be combined with the dynamic loop gain of 0.33, calculated above. In the given esample, 200 ft of pipe and fittings produce about an &psi drop at 10 gpm, leaving 12 psi across the valve. A l.O-in. valve has a C, rating of 10. At 12-psi drop, the gain of the linear valve nould be G 21 - CJG- lyofyR 0.35 mm/% 100% 0 At 10 gpm, the gain of the 15-gpm differential meter is GT = 2 (g)(z) = 8.9%/gpm Since the flow process itself has no dimensional gain, G, may be multiplied directly by GT to remove dimensions: G,GT = (0.35 gpm/ %) (8.9 %/gpm) = 3. I The proportional band required for s/4-amplitude damping is then 200 times the gain product of the dynamic and steady-state components of the loop : P = 200(0.33)(3.1) = 205% This is quite typical for a flow controller. Sotice by comparing Figs. 2.5 and 2.9 that the resistance of the piping is helpful in that it shapes the gain of the valve in a direction complementary to the flowmeter. Valve gain is higher at low flow, where the transmitter gain is lower, yielding a gain product that tends more toward uniformity than either of the multiplicands. Note also that an equalpercentage valve characteristic (Fig. 2.6) is of the opposite form, tending
Analysis of Some Common Loops 100
FIG 3 . 3 . Flow noise precludes the use of derivative.
40 20 0
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to augment the nonlinearity of the flowmeter except in cases of unusually severe line drop (Fig. 2.10). Increasing valve speed by means of a booster is helpful in reducing TV,, although the proportional band may not be affected. Mounting the controller at the valve helps even more by eliminating both transmission lines.
Flow Noise
In an equivalent electronic flow loop, absence of the transmission lines reduces the natural period to the vicinity of 2 sec. Noise, however, becomes more prominent. Noise means disturbances, either periodic or random, occurring at frequencies too high for control action. Figure 3.3 is a record of noise in an electronic flow loop. Turbulence in the stream and vibration from pumps are the chief sources of this noise. Even in pneumatic systems, flow noise is invariably present in sufficient magnitude to prevent the use of derivative. Phase lead is useful, but unfortunately the increase in high-frequency gain which accompanies it actually explodes the loop into instability.
Summary
The purpose of the analysis is not to show how an analysis should be made, but rather to explain why a flow loop behaves the way it does. Because many dynamic elements are present, a11 of the same order of magnitude, dynamic gain is high. The proportional band of a flow controller is rarely less than 100 percent, making reset mandatory. Where the valve and transmitter are in the same line, the period of oscillation will invariably fall within 1 to 10 sec. The presence of noise precludes the use of derivative. As long as these factors are appreciated, there is little reason to spend time analyzing flow loops.
PRESSURE REGULATION
The thermodynamic state of a system can be defined from its pressure, enthalpy, and volume. If a gas phase alone is present, pressure and
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