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19.1. Use the semi-log graphical method to determine the process model for the following unit-step response data:
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One of the basic components of any control system is the final control element, which comes in a variety of forms depending on the specific control application. The most common type of final control element in chemical processing is the pneumatic control valve, which regulates the flow of fluids. Some other types include the variable speed pump and the power controller (used in electrical heating). Since the pneumatic control valve is so widely used in chemical processing, this chapter will be devoted to the description, selection, and sizing of control valves.
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The control valve is essentially a variable resistance to the flow of a fluid, in which the resistance and therefore the flow, can be changed by a signal from a process controller. As shown in Fig. 20.1, the control valve consists of an actuator and a valve. The valve itself is divided into the body and the trim. The body consists of a housing for mounting the actuator and connections for attachment of the valve to a supply line and a delivery line. The trim, which is enclosed within the body, consists of a plug, a valve seat, and a valve stem. The actuator moves the valve stem as the pressure on a spring-loaded diaphragm changes. The stem moves a plug in a valve seat in order to change the resistance to flow through the valve. When a valve is supplied by the manufacturer, the actuator and the valve are attached to each other to form one unit.
304 PROCESS APPLICATIONS
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FlGURE 20-1 Pressure-to-close valve with single seating.
For most actuators, the motion of the stem is proportional to the pressure applied on the diaphragm. In general, this type of actuator can be used for functions other than moving a valve stem. For example, it can be used-to adjust dampers, variable speed drives, rheostats, and other devices. As the pressure to the valve varies over its normal range of operation (3 to 15 psig) the range of motion of the stem varies from a fraction of an inch to several inches depending on the size of the actuator. Manufacturers provide a range of actuators for various valve sizes. The valves available vary over a wide range of sizes. The size is usually referred to by the size of the end connectors. For example, a one-inch valve would have connectors (threaded or flanged) to fit into a one-inch pipe line. In general, the larger the valve size the larger the flow capacity of the valve. For the control valve shown in Fig. 20.1, an increase in signal pressure above the diaphragm exerts a force on the diaphragm and back plate, which causes the stem to move down; this causes the cross-sectional area for flow between the plug and the seat to decrease, thereby reducing or throttling the flow. Such valve action as shown in Fig. 20.1 is called pressure-to-close action. The reverse action, pressure-to-open, can be accomplished by designing the actuator so that pressure is applied to the under side of the diaphragm, for which case an increase in pressure to the valve raises the stem. An alternate method to reverse the valve action is to leave the actuator as shown in Fig. 20.1 and to invert the plug on the stem and place it under the valve seat. The valve shown in Fig. 20.1 is single-seated, meaning the valve contains one plug with one seating surface. For a single-seated valve, the plug must open against the full pressure drop across the valve. If the pressure drop is large, this means that a larger, more expensive actuator will be needed. To overcome this problem, valves are also constructed with double seating as shown in Fig. 20.2. In this type valve, two plugs are attached to the valve stem and each one has a seat. The flow pattern through the valve is designed so that the pressure drop across the seat at A tends to open the plug and the pressure drop across the seat at B tends to close the plug. This counterbalancing of forces on the plugs reduces
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