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Output to valve,p,
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Arm attached to stem to sense valve position
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FIGURE 20-8 Control valve with positioner (Compare with Fig. 20.1).
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into the design of the positioner and cannot be adjusted. The valve positioner is especially important for speeding up the valve motion, and eliminating hysteresis and valve stem friction. SUMMARY The control valve is a component of a control system often overlooked in a course on process control. In this chapter, the description, selection, and sizing of pneumatic control valves were presented. Valves may be of the pressure-to-close or the pressure-to-open type; the selection of the type is often related to safety considerations. If the air pressure fails, the valve should return to a position which ensures safe operating conditions for a process. The flow capacity of a valve is based on an equation relating flow to the square root of the pressure drop across the valve; the proportionality constant C, in this equation is a measure of the valve s capacity for flow. The larger Cv, then the larger the flow. Valves are classified according to their inherent flow characteristics such as linear or equal percentage. A linear valve produces a flow (for constant pressure drop across the valve) that is proportional to the valve stem position, which in turn is proportional to the valve-top pressure. The presence of a long, small-diameter line supplying a valve causes the pressure drop across the valve to decrease with the increase of flow, for a fixed, overall pressure drop across the system. If the pressure drop in the line is excessive, the characteristic of the linear valve will become nonlinear and in terms of control theory, the steady-state gain K, of the valve decreases with flow. As a result of the change in valve gain, the controller in the loop must be readjusted for different flow rates in order to maintain the same degree of stability. To overcome this limitation of the linear valve, an equal percentage (or logarithmic) valve is available for which the gain of the valve increases with flow rate. Such a valve compensates
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for the line loss and produces an effective charateristic that approaches a linear relation. The basis for the name equal percentage (or logarithmic) is related to one form of the mathematical expression that describes the valve. In this form, an equal percentage change in flow occurs for a specified change in stem position, regardless of the stem position. In order to eliminate hysteresis, which can produce cycling and cause wear of the valve plug and seat, a valve positioner may be attached to a control valve. The positioner also speeds up the motion of the valve in response to a signal from the controller.
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20.1. A linear control valve having a CV of 0.1 is connected to a source of water. If the pressure drop across the valve is 400 psi and if the pneumatic pressure to the valve top is 12 psig, what is the flow rate through the valve The valve goes from completely shut to completely open as the valve-top pressure varies from 3 to 15 psig. 20.2. (a) Under what conditions would an equal percentage valve be used instead of a linear valve (b) What am some reasons to use a valve positioner
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CHAPTER
THEORETICAL ANALYSIS OFCOMPLEX PROCESSES
In order to investigate theoretically the control of a process, it is necessary first to know the dynamic character of the process that is being controlled. In the previous chapters, the processes have been very simple for the purpose of illustrating control theory. Many physical processes are extremely complicated, and it requires considerable effort to construct a mathematical model that will adequately simulate the dynamics of the actual system. In this chapter, we shall analyze several complex systems to indicate some of the types of problems that can be encountered. In these examples, the technique of linearization, first presented in Chap. 6, will be applied to a function of several variables. One example will lead to a multiloop control system. In the last section, distributed-parameter systems will be discussed.
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