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Because the process is linear with respect to concentrate flow, a linear valve is chosen. Let the maximum flow of concentrate be 2 gpm. T h e n G, = 2 gpm/lOO% = 0.02 gpm/% To illustrate the close tolerances to which product quality is generally specified, the analyzer range will be chosen as 4.5 to 5.5 percent, with a normal set point of 5.0 percent. The span is 1.0 percent: GT = 100 %/I % = 100 The proportional band necessary for >i-amplitude damping is finally estimated as 200 t imes the gain product:
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P = 200(0.0737) (5 %/gpm) (0.02 gpm/ %) (100) = 147 %
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For a process that is really not very difficult, this is quite a wide proportional band. An extremely wide band may then be expected in a truly difficult application, indicating how sensitive composition loops are to changes in load. To summarize, composition loops are principally comprised of dead time plus a single capacity and are noted for high transmitter gain. A s a result, a wide proportional band is usually needed, leaving the controlled variable quite susceptible to load changes. CONCLUSIONS The purpose of this chapter has, been to acquaint the reader with the properties of common process control loops and the reasons for these properties. Analysis served as a useful tool to present the case, while TABLE 3.3 Properties of Common Loops Flow and liquid pressure Gas pressure Liquid level Temperature and vapor pressure Variable 3-6 Min - hrs Nonlinear l-2 None 10-100 % Composition
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Dead time. No Capacity. Multiple Period. l-10 set Linearity. Square G,GT.. 2-5 0.5-l Noise. Always _ _ _ _ _ Proportional 100-500 % 50-200 f!$, Reset. Essential Derivative No Valve. Linear
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No Single Zero Linear Integrating None O-5 % Unnecessary Unnecessary Eq. percent
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Single l-10 set Linear Integrating Always 5-50 70 Seldom No Linear
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Constant l-100 Min - hrs Either lo-1,000 Often ___-__ loo-l,OOO%
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Yes Essential Essential If possible Eq. percent Linear
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* Applies to liquid pressure.
Analysis of Some Common Loops
at the same time demonstrating how to identify the significant elements in a loop. Rarely will a flow or level loop need analysis, but when composition-control problems arise, this procedure can be of inestimable value. Much of what has been derived and weighed and discussed in the foregoing pages is summarized in Table 3.3. Nothing that has not been already covered is presented in the table, yet gathering all this information together discloses some interesting features. Notice, for example, the similarity between level and flow loops, with respect to both natural period and the presence of noise. Without any doubt, however, each of the five groups above is separate and distinct from the rest.
REFERENCES
Bradner, M.: Pneumatic Transmission Lag, ISA Paper No. 48-4-2. 2. Catheron, A. R.: Factors in Precise Control of Liquid Flow, ISA Paper No. 50-B-2. 3. Considine, D. M.: Process Instruments and Controls Handbook, chap. 2, McGraw-Hill Book Company, New York, 1957. 4. Esterson, G. L., and R. E. Hamilton: Dynamic Response of a Continuous Stirred Tank, presented at the Joint A u t o m a t i c C o n t r o l Conf., Palo Alto, Calif., June, 1964.
PROBLEMS
3.1 -1 volume booster installed at the inlet to the valve motor of Example 3.2 reduces its time constant to 0.5 sec. Predict the period of oscillation that Iv-ill result from the change, allowing- 45 phase lag in the proportional-plus-reset controller. Calculate the proportional band and reset time for jb-amplitude damping. 3.2 What would be the estimate of the natural period and proportional band in Prob. 3.1 if the dynamic elements were all assumed to be dead time rather than capacities Is this a valid approximation Why 3.3 Let pressure downst ream of the valve in Example 3.2 be controlled instead of flow. -kt no flow, there is a static head of 5 l)sig, while 10 gpm will raise the pressure to 13 psig; the range of the pressure transmitter is 0 to 25 psip. Estimate what the proportional band of the controller will be for ;/,-amplitude damping with the period and reset time used in the example. 3.4 A mercury manometer capable of reading f 15-in. differential pressure is used to indicate the flow in a gas stream. What is its natural period H O W would it affect the control of flow 3.5 T O verify the choice of an equal-percentage valve for Example 3.5, calculate the process gain and the product of process and valve gain for heat loads of 5000, 10000, and 15000 Btu/min; assume that. the difference between controlled reactor temperature and average coolant temperature varies linearl) with heat transfer rate.
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