November 1991
lastrumentotion Optimalizing control is an interesting new development which can be applied to several input variables
bg W p h E. M u w h first step in instrumentation was learning to measure quantitatively those features of our environment which interested us, using instruments instead of making qualitative observations by means of the human senses. To do this, we had to learn how to convert variables which we could not measure directly, such as temperature, into linear or angular displacement, or changes in pressure, voltage, resistance, or some other variable which could be measured. Not long after moderately dependable means for measuring became available, the idea that measuring instruments could be made t o control waa conceived. The initial efforts in this direction mere crude but useful. Level control by means of a float mechanically linked to a valve in such a way that, as the level rose, the float closed the valve, was an early example. Control devices became more and more sophisticated, when it was found that on-off and proportional response controllers were not suitable for all control applications. T o solve these more difficult problems, various combinations of proportional, reset, and rate responses, as well as cascaded controls, are used. Usually, the variables which we measure and control are not those we actually wish to control, but secondary variables related to the ones we wish t o control liy some simple fixed law. For example, a catalytic vapor-phase oxidation process might be controlled by controlling the rate of feed of material to be Oxidized, the ratio of air to material to be oxidized, and the catalyst temperature. With these variables controlled a t proper values, a good yield will he main-
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November 1951
tained as long as the characteristics of the catalyst remain constant. If the catalyst changes, the maximum yield will no longer result from the same set of conditions. We will be unable to tell that the yield is no longer optimum by measuring the values of any of the variables specified because the law relating these variables to yield is not constant. Control to obtain maximum yield would then become much more difficult. The first requisite would be a direct method of mewuriiig the yield. Since the
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Characteristic Curves of Two Processes
suitnbla for degulatory oontrol suitable for aptimalizing control
maximum yield which could be obtained would not be a constant, such an instrument could not be used in the ordinary way to control the process. An operator could use it by changing each variable in turn over a range great enough to cause the yield to pass through a maximum, remembering what values of the variables gave the maximum yields, then returning each of the variables to those settings. Thus, we have a situation which cannot be taken care of by controls of the kind we are familiar with. Y. T. Li has named this type of co?trol “optimalizing control.” In a paper entitled [‘Optimalizing System for Process Control,” presented at the Texas A & M Symposium on Instrumentation held in conjunction with the Sixth National Instrument Conference and Exhibit of the Instrument Society of America, in Houston, September 10-14, 1951, he describes the theory of such control systems. As is stated above, the advantage of optimalizing control is that the laws relating the input variables to the output need not be known or constant. The only assumption is that some optimum performance condition exists. An important distinction between systems suitable for control by ordinary regulators and those where optimalizing control is needed is the following: For regulatory control, it is necessary that a given output can be produced by only one value of the input for a given (Continued on page 108 A )
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
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set of conditions. An example is a t>emperature control system where a greater supply of heating medium always produces a higher temperature, other conditions being constant. Figure 1A shows the characteristic curve for such n process. On the other hand, for optimalizing control, there must be a maximum in the curve relating input to output. This implies that two different values of input, which will produce the same output, such as C and D (Figure lB), can in general be found. Figure 1B illustrates tahecharacteristic curve which might be found for the catalytic process considered above.
to the input changes as a function of the input. As can be seen, the rate has a high positive value for values of the input much below that required to produce maximum output. It decreases as the input is brought nearer to the optimum value, passes through zero at the optimum value, and becomes increasingly more negative as the input passes beyond the optimum value. S o w if a sinusoidal component of suitable constant amplitude is superimposed on the input, the resulting sinusoidal component in the output will decrease in amplitude as the input is increased toward the value a t which maximum output is obtained. It will become zero a t that value of the input for which the output is a maximum, change phase, and increase in amplitude as the input increases beyond that required for maximum output. Such a signal can be used to control the input to give maximum output. In the peak-holding type optimalizing control system, the input correction signal is generated by taking the difference between the indicated maximum output signal and the output signal. The indicated optimum output signal is equal to the output signa1 as long as this signal is increasing; it remains constant a t the highest level reached when the output signal decreases. As soon as the' output signal starts to decrease, the difference between the indicated maximum output signal and the output signal is used to generate a suitable input correction signal. Optimalizing control can be applied to several input variables. Li has controlled both the air supply and the ignition timing for an internal combustion engine, using the control system to optimalize these two variables alternately. Thus, we see that control systems can be designed to take over another type job which formerly could only be done by human intelligence.
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Figure 2. Characteristic Curve and Corresponding Sensitivity Curve for an Optimalizing Control System
There are two classes of optimalining controllers: The first of these are the input-output sensitivity operated controllers; the second are t,he peak-holding controllers. Consideration of Figure 2 will reveal the fundamental operating principle of the input-output sensitivity controllers. In Figure 2 the upper cyirve shows the relationship between output and input a t some particular time. The lower curve shows how the sensitivity or rate a t which the output changes with respect (Continued on page 110 A ) 108 A
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