Ud erstanding Feedback Control n in .NET framework

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1 Ud erstanding Feedback Control n
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3.6 Two fluids are blended in a pipeline 20 ft upstream of where the mixture is sampled. The pipe contains 0.4 gal/ft of length, and the flow rate of the blend varies from 10 to 80 gpm. Dead time in the sample line to the analyzer is 15 sec. A circulating pump is installed to maintain 100 gpm flow through that 20-ft section of pipe without affecting the throughput. Compare the natural period for integral control with and without the pump in operation. What else does the pump provide 3.7 In the same process, the flow of additive is manipulated through a linear valve whose maximum flow is 1.2 gpm. The range of the analyzer is 0 to 1 percent, additive concentration. Estimate the proportional band required for at least ~-amplitude damping if the reset time is set for 60 phase lag with the pump operating.
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o w that the characteristics of typical processes have been thoroughly presented, it is possible to look more closely into various means for controlling them. The range of process difficult y has been seen t o vary from zero to several hundred, as measured by the proportional band needed for damping. The very existence of such-a range of control problems suggests the possibility of a variety of means for their control. The first distinction to be made is between linear and nonlinear control methods. A linear device is one whose output is directly proportional to its input(s) and any dynamic function thereof. This definition includes not only proportional !:ontrollers, but those with reset, derivative, lag, dead tinrePin short, any time function of a linear variable. To be sure, a device is only linear over a specified range. A pneumatic controller, for example, ceases to operate linearly when its output falls to zero or reaches full supply pressure. All linear devices are similarly limited, and their proper use demands an appreciation of these limitations.
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1 Selecting the Feedback Controller
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In the earlier chapters certain nonlinear characteristics were dealt with, both in processes and in the measuring devices and valves. A n attempt was made in every case to compensate for process nonlinearities so as to obtain constant loop gain. This assures uniformity of performance under all conditions of operation. In general, compensation is effected external to the controller, leaving the controller as a linear device. But within the domain of linear controllers, a variety of dynamic elements exists. Each dynamic element, such as reset or derivative, has certain undesirable properties along with those which are beneficial. A thorough understanding of the assets and liabilities of each control mode is prerequisite to their intelligent selection.
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If selection between various control configurations is to be made, some basis must be established for their comparison. For example, a given process may be controlled in a number of ways. One way will be better than the others from the standpoint of performance, i.e., how it responds to a set-point or load change. The three load-response curves in Fig. 1.13 show the performance of three different controllers in the same process. The shape of the load-response curve depends to a considerable degree on the type of control action used and the settings of the parameters involved. Furthermore, the penalty ascribed to a typical response curve is determined by the specifications of the process. Several means of weighing the response curve suggest themselves: 1. Integrated error: Since the error (T - c) can be either positive or negative, an integrated error of zero could be obtained in a continuously oscillating loop. Integrated error is therefore not, of itself, a measure of stability. 2. Error magnitude: This criteria allows the possibility of offset (a small permanent error), which is generally undesirable in any loop. 3. Integrated absolute error (ME) : This is a measure of the total area under the response curve on both sides of zero error. It is one of the generally accepted performance criteria. Since the error following a load change eventually disappears, the IAE approaches a finite value for any stable loop. 4. Integrated square error (ISE): The instantaneous error is first squared and then summed (integrated). Squaring prevents a negative error from canceling a positive one (as does absolute value) and also weighs large errors more heavily than small ones. 5. Root mean square (rms) error: This index is the standard deviation of t,he error. If the error reduces to zero with time, so does the rms
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