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The wide use of digital computers in control makes the inclusion of a section on sampled-data control imperative. Sampled-data control was actually established over 25 years ago by electrical engineers before the digital computer was widely used to control chemical processes. A sampled-data system is one in which the flow of signals in the control system is interrupted at one or more points. In this book, the interruption or sampling will occur every T units of time. Such sampling is called uniform sampling and is the usual type in practical applications. To understand the nature of a sampled-data system, consider a typical, singleloop continuous control system, shown in Fig. 22.1~. The system is referred to as continuous because the signal flow between blocks is continuous or without interruption; i.e., at any instant of time and at any location in the loop, one can observe a changing value of the signal during a transient. For example, the response from the measuring element varies in a continuous manner from moment to moment. A typical temperature transmitter would provide such a continuous signal. In chemical processes, some measurements cannot be made continuously. Chemical composition is a measurement that may not be continuous. For example, a sample of a process stream may have to be subjected to a chemical analysis that takes some finite period of time. An example would be an automatic chromatograph that must process a sample of fluid in a packed column for a fixed time T. For this example the measured value of composition is known only at the end of the processing time T. If a new sample of fluid is taken successively every T units of time and the result of the chemical analysis is held constant between
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sampling instants, one can represent the control system as shown in Fig 22.M. In this case, the measured signal B is held constant between sampling instants and delayed by an amount T. The delay occurs because of the time needed to process the sample of fluid in the chromatograph. Note that for simplicity, the chromatograph processing time and the sampling time have been taken to be the same value T. In Fig. 22. lb this disruption in the flow of signal B is represented by a sampling switch and the holding of the value of the signal is obtained by the block labeled hold. The natme of the signals from the measuring element B and the sampled signal B, are shown in Fig. 22.1 b. The output from the hold is a stair-step response, which approximates the continuous signal B mote accurately as the sampling period T decreases. Another reason for studying sampled-data control is to be able to describe the operation of a digital computer as a controller. The output of a continuous electronic or pneumatic controller changes in a continuous manner. When a digital computer is used to implement a control law, a calculation must be performed to calculate the new value of the controller output every T units of time. The calculation, which is based on a numerical expression of the control law, will be developed in detail later. At each sampling instant, the computation of the controller output is made and then held at a constant value until the next sampling
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,Sampling 2
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FIGURE 22-1 Comparison of (a) continuous control and (b) sampled-data control.
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FIGURE 22-2 Computer control system.
instant occurs, at which time a new controller output is computed and held. This computation and holding is repeated every T units of time, Figure 22.2 shows a diagram that represents a digital control system. In this figure, the typical elements of the system (valve, process, and measuring element) are continuous and behave the same as those in a continuous control system. The usual continuous controller is replaced by a digital computer, which is programmed to implement a control law, such as PI control. Since the digital computer works with digital information, an analog-to-digital converter (A/D) is needed to convert the continuous (analog) signal to a digital signal that can be used by the computer. Since the output from the calculation is a digital signal, a digital-to-analog converter (D/A) is needed on the output of the computer so that a continuous (analog) signal is available to operate the valve. Typical analog signals associated with the A/D and D/A converters range from 4-20 ma or 1-5 V. The sampling switches am shown to indicate the sampled nature of the signals. These switches are purely symbolic; there are no mechanical switches in the hardware used to implement a controller. The hold block, which is shown in the figure, holds the value of the controller output constant between sampling instants. The output of the hold is a stair-step function.
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