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has less and less effect as D approaches At. For this reason At should be short where derivative is used. On the other hand, if At is too short, the cont rolled variable may not change enough between samples to escape truncation. Again, the choice of At will have already been dictated by other requirements-reset range, programming, etc. Derivative limited by a lag about ${o of its time constant produces a maximum phase lead of about 4.5 . Therefore, if derivative is t o be effect ive, D should exceed 10 At. In loops with a sampling interval of 10 set, derivative time of less than 1.8 min will be limited in effectiveness. Where At = 30 set, derivative time ought to exceed 5 min. Some advantage is gained, however, by the absence of interaction between the digital control modes. This certainly offsets, in part at least, t,he other limitations encountered by the derivative mode.
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Perhaps the most outstanding feature of a digital computer is its versatility. With analog components, the system designer is constrained on many sides by physical limitations, accuracy, cost, and availability of devices. But a digital machine can be readily programmed to perform all sorts of unusual control functions: complementary feedback, nonlinear modes, logic, adaptation, feedforward-almost without limit. But at this writing, DDC is so new, in actual application at least, that few of these innovations have been thoroughly explored. In the chapters that follow, many unconventional control schemes will be presented. They have all been tried using analog devices. SureIy these and more can be implemented as well or better with a digital computer. The important point is the ease with which these things can be done once a computer is available. DDC may never pay for itself as an exact substitute for analog control. But the improvement in performz&e that is possible by employing novel control modes, with minimum additional expense, could easily justify the investment.
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REFERENCES 1. Clarridge, R. E.: An Improved Pneumatic Control System, Trans. ASME, April, 1951. 2. Giloi, W.: Optimized Feedback Control of Dead-time Plants hy Complementary Feedback, Tmns. IEh E, May, 1964. 3. Smith, 0. J. M.: A Controller to Overcome Dead Time, ISA Journal, February, 1959. 4. Kleiss, L. D.: Better Controller Memory Improves Control of Difficult Processes, Control Eng., March, 1958.
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5. Hausner, M. J.: Get the Benefits of Sampled Data Control from Modified Process Controllers, Control Eng., March, 1961. 6. Bernard, J. W., and J. F. Cashen: Direct Digital Control-Questions That Must Be Answered, Proc. 19th flnnual ISA Conf., New York, October, 1964.
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4.1 Find the optimum combination of proportional and reset for a dead-time process from the information given in Table 1.1. Why is it different from the situation described for the two-mode controller in Table 4.2 4.2 Given a process controlled with a two-mode controller whose proportional band is 200 percent and whose reset time is 10 min, estimate the maximum error developed by a step load change of 5 percent. What would the error be if the same load change were made gradually over an interval of 30 min What would the error be if the load change entered as a sine wave of 5 percent amplitude and 2-hr period 4.3 Referring to Table 4.1, what other settings of proportional, reset, and derivative could produce effective values identical to those in the second row of the table What is the maximum ratio of effective derivative time to effective reset time 4.4 Calculate PR/lOO for values of R = 0.90rd and II = 0.45~~ set into an interacting controller, following the example given in Table 4.2. What conclusion can you draw from the result 4.5 Find the optimum settings for two-mode control of a process consisting of a 30-min lag, a 2-min dead time and an analyzer with a 5-min sampling interval. Leave the proportional band in terms of K,. 4.6 This chapter describes three different methods for controlling a process dominated by dead time. , c 1ect t,hc best method, calculate the optimum values i of all the parameters, and estimate the integrated area per unit load change, for a dead time of 2 min and a process gain of 2.5.
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