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useful in a flo\v loop.
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Look at what a valve positioner
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Without n positioner, the
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The Cascade Flow Loop
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Cascade flow loops are used most often to provide consistent delivery of material to or froni the process in response to the demands of the
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primary controller. They overcome variable pressure drop, valve friction, and nonlinear valve characteristics. But if the measurement is in the differential form, its nonlinearity becomes part of the primary loop, because flow is being delivered to the process while flow squared is set by the primary controller. The nonlinearity of the differential meter was recognized earlier as a problem in a flow loop. But using a differential meter in the secondary loop of a difficult thermal or composition process is asking for trouble. Suppose the process is linear with respect to flow, as in Example 3.6. The output of the primary controller manipulates differential pressure, however, which varies as flow squared:
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Loop gain now varies inversely with flow (which is much worse than varying directly with flow, because it can approach infinity). And since many processes are started up or operated for extended periods at low flow, the problem is serious. If the primary controller is not placed in manual, the loop will limit-cycle around zero flow. The best solution is to insert a square-root extractor in the flow-measurement line to linearize the secondary loop. The problem of variable dead time was discussed in Chap. 2. This problem was resolved by using an equal-percentage control valve. If a flow loop were placed around the valve, however, its characteristic would be lost. Furthermore, if the flow loop were of the differential type, its nonlinearity would be in the wrong direction, making the primary-loop gain vary inversely as the square of flow. These factors deserve careful consideration before deciding on a cascade flow loop. Because flow loops resonate in the l- to lo-set range, they are safe to use in cascade with temperature or composition, but not ordinarily with liquid or gas pressure or other flow loops. Liquid level is only cascaded to flow in applications involving boiling liquids or condensing vapors, where the natural period of the primary loop is long compared to the flow loop.
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Temperature as the Inner Loop
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Perhaps the third most common cascade loop is that of temperature. Whereas a material balance can be enforced by flow controllers, temperature controllers are often used to manipulate a heat balance. Careful control of heat balance is most important in a chemical reaction. To ensure satisfactory performance, the reactor temperature controller generally positions the set point of the coolant temperature controller: a temperature-on-t emperature cascade loop. The rate of heat transfer to the coolant varies with the temperature difference between
1 6 0 1 Multiple-loop Systems
reactants and coolant, so the actual value of coolant temperature plays a vital role. Nonlinearities and lags in the coolant loop are, for the most part, removed from the primary loop. Since the proportional band of the secondary temperature controller is ordinarily 25 percent or less, reset may be omitted. A slight offset in coolant temperature is inconsequential, in that the outer loop will always have reset. Reset in the inner loop would only serve to slow it down. Reset is not used in the coolant temperature loop of a batch reactor. Again, whether a particular cascade configuration is workable is not so much a matter of what kind of measurements serve as the primary and secondary variables, but rather is a question of the natural periods of the loops differing by severalfold. If both loops have the same kind of measurement, their relationship is ordinarily linear, assuring a constant gain for the primary loop.
RATIO CONTROL SYSTEMS
In a ratio control system, the true controlled variable is the ratio K of two measured variables X and Y: K=; (6.3)
Control is usually effected by manipulating a valve influencing one of the variables, while the other is uncontrolled or wild. The obvious way to implement the ratio control function is by computing X/Y, as shown in Fig. 6.5. But this is not the best way. Figure 6.5 has a divider within the closed loop, regardless of which variable is affected by the output of the controller. If X is manipulated, loop gain changes with the wild variable Y: dk -=- 1 dx Y dK X K --=-dY= Y2 Y (6.4)
If Y is manipulated, the loop becomes nonlinear in that the gain changes with controller output. All these problems can be overcome by moving the calculation out of the closed loop. Ratio control is then brought about in the set-point x
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