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2.3 The process in Prob. 2.2 has a linear valve whose capacity is 50 gpm. A change in flow of 1 gpm causes 0.5 percent change in product quality, analyzed over a span of 10 percent. Estimate the proportional band required for >Samplitude damping. 2.4 If a differential Aow controller is adjusted for s/4-amplitude damping at 30 percent flow, at what flow is it likely to be undamped 2.5 What value of CR in relation to the C, of a linear valve will provide reasonable compensation for the nonlinear characteristic of a differential flowmeter If the value of CR existing in a pipeline is too high, how can it be adjusted What is the effect of Cn on valve size requirements. 2.6 9 process exhibits a dead time of 23 sec. At 50 percent flow, proportional control with a 20 percent band causes undamped oscillations of 1.5-min period. At 25 percent flow, however, its natural period increases to 2.9 min. Draw some conclusions about the process and make suitable recommendations.
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lassification of processes into broad areas with certain common characteristics is both desirable and informative. We know, for example, that a temperature-control loop behaves very differep.tly from a level-control loop. Why it does so is the essence of the classlficatjion. The first control loop to be considered is flow. It has the distinction that the manipulated variable and the controlled variable are the same. They may not have the same range or the same linearity, nevertheless they are the same variable. For this reason the flow loop is the easiest to understand, as far as steady-state characteristics are concerned. We will now analyze the control of variables that are the integral of flow. Liquid level is the integral of liquid flow, whereas the integral of gas flow in a constant-volume system is pressure. These loops have certain features not common to other classifications. For example they can be non-self-regulating. This is never true of flow and rarely true of other variables. Second, the rate of change of measurement is a function of the difference between inflow and outflow; either inflow or
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outflow will be load-dependent, while the other is manipulated. Furthermore these processes are dominated by capacity; dead time will rarely be found, because pressure waves travel through the process at the velocity of sound. The third group includes energy and mass transfer processes, where control is exercised primarily over temperature and composition. The controlled variable here is always a property of the flowing stream, as opposed to being the flowing stream or its integral. These processes ordinarily have a steady state in which the controlled variable is a function of the ratio of the manipulated flow to the load. (Kate the abscissa of Fig. 2.12, expressed in terms of this ratio.) Because the controlled property travels with the fluid, it must be transported to the measuring element. Transportation involves dead time. Hence loops in this category are usually dominated by dead time, which makes control difficult and response slow. In this chapter, five typical control loops will be analyzed: flow, level, pressure, temperature, and composition. The principal dynamic elements of each process Iv-ill be deri.ved and will be related to the closed-loop response, Constraints and nonlinearities will be included, as well as means for coping with them. A few additional comments will serve to dist inguish those control problems which are not typical or which appear to cross into other areas.
FLOW CONTROL
Flow is the manipulated variable as well as the controlled variable, so it seems as though the process is unity. But this is not the case. Opening a valve does admit flow, but t he response is not quite instantaneous. If the fluid is gaseous, it is subject to expansion upon a change in pressure; therefore the contents of a pipe vary somewhat with pressure drop, hence with flow. In a liquid stream, inertia is significant-flow cannot be started or stopped without accelerating or decelerating. To demonstrate the dynamic character of inertia, the time constant of a column of liquid in a pipe will be derived.
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