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Control system for a stirred-tank heater.
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Components of a Control System
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The system shown in Fig. 9.1 may be divided into the following components: 1. 2. 3. 4. Process (stirred-tank heater). Measuring element (thermometer). Controller. Final control element (variable transformer or control valve).
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Each of these components can be readily identified as a separate physical item in the process. In general, these four components will constitute most of the control systems that we shall consider in this text; however, the reader should realize that more complex control systems exist in which more components are used. For example, there are some processes which require a cascade control system in which two controllers and two measuring elements are used. A cascade system is discussed in Chap. 18.
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For computational purposes, it is convenient to represent the control system of Fig. 9.1 by means of the block diagram shown in Fig. 9.2. Such a diagram makes it much easier to visualize the relationships among the various signals. New terms, which appear in Fig. 9.2, are set point and loud. The set point is a synonym for the desired value of the controlled variable. The load refers to a change in any variable that may cause the controlled variable of the process to change. In this example, the inlet temperature Z i is a load variable. Other possible loads for this system are changes in flow rate and heat loss from the tank. (These loads are not shown on the diagram.) The control system shown in Fig. 9.2 is called a closed-loop system or a feedback system because the measured value of the controlled variable is returned or fed back to a device called the comparator. In the comparator, the controlled variable is compared with the desired value or set point. If there is any difference
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FIGURE 9-2 Block diagram of a simple control system.
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between the measured variable and the set point, an error is generated. This error enters a controller, which in turn adjusts the final control element in order to return the controlled variable to the set point.
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Negative Bedback versus pbsitive
Feedback
Several terms have been used that may need further clarification. The feedback principle, which is illustrated by Fig. 9.2, involves the use of the controlled variable T to maintain itself at a desired value TR. The arrangement of the apparatus of Fig. 9.2 is often described as negative feedback to contrast with another arrangement called positive feedback. Negative feedback ensures that the difference between TR and T, is used to adjust the control element so that the tendency is to reduce the error. For example, assume that the system is at steady state and that T = T,,, = TR. If the load Ti should increase, T and T,,, would start to increase, which would cause the error E to become negative. With proportional control, the decrease in error would cause the controller and final control element to decrease the flow of heat to the system with the result that the flow of heat would eventually be reduced to a value such that T approaches TR. A verbal description of the operation of a feedback control system, such as the one just given, is admittedly inadequate, for this description necessarily is given as a sequence of events. Actually all the components operate simultaneously, and the only adequate description of what is occurring is a set of simultaneous differential equations. This more accurate description is the primary subject matter of the present and succeeding chapters. If the signal to the comparator were obtained by adding TR and T,, we would have a positive feedback system, which is inherently unstable. To see that this is true, again assume that the system is at steady state and that T = T,,, = TR. If Ti were to increase, T and T,,, would increase, which would cause the signal the comparator (E in Fig. 9.2) to increase, with the result that the heat to the system would increase. However, this action, which is just the opposite of that needed, would cause T to increase further. It should be clear that this situation
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