Selecting the Feedback Controller in .NET framework

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1 Selecting the Feedback Controller
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The proportional action produces an instantaneous change in output, which is removed when the error returns to zero. Some overshoot does occur, but it disappears before the next sample. Only one combination of proportional and reset will provide this critical damping:
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P = 1OOK g p Td R = rd (4.17)
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If 7d > At, critical damping cannot be achieved. As with complementary feedback, reducing P by one-half produces zero damping, by one-fourth gives >i-amphtude damping. Response curves for sampled loops are made of steps. The rate of rise of even a small step is extremely high; therefore derivative control action on a sampled signal produces pulsing of the manipulated variable. T h i s pulsing cannot contribute much to the closed-loop response, because sampling prevents the effect of such action from being seen-consequently the manipulated variable is driven severely without cause. Derivative is therefore of lit,tle value in the sampled loop.
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A Sampling Controller
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Why operat,e on old informat ion There is really no value in continuing to drive the controller output when it can have no immediately observable effect. A sampling controller is suggested as being more compatible with the sampled process. Here is the control strategy. At the start of the sample interval, when the controller sees new information, it is enabled to operate for a very short time. This will be called t,he control interval At,. Then the error signal is removed, preventing further integration until the next intervalthe action of the controller is similar in effect to a sample and hold circuit. By means of this sampling controher, critica damping may be achieved on a sampled dead-time process with integral action alone. Figure 4.23 shows the sequence of events.
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FIG 4.22. The proper combination of proportional and reset adjustments can produce critical damping. 0
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2 3 n=t/At 4 5 6
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Linear Controllers
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FIG 4 . 2 3 .
Performance i s improved
by operating the controller for only a fraction of the sampling interval.
2 I
2 n=t/At 3 4
Since the controller only operates during the short control interval, the reset time needed for critical damping is determined only by this interval and the process gain:
R = K, At,
(4.18)
Again, half this value leaves the loop undamped. Critical damping was obtained with a conventional proportional-plus-reset controller whose settings were related to both dead time and sample interval. But with the sampling controller, reset alone is required, and dead time can have any value less than At - At,, without affecting the closed loop. Critical damping cannot be realized if the dead time is longer than At - At,. So if this situation arises, a circuit should be arranged which would activate the controller only every kth sample, having selected
k > rd + At,
Odd as it may seem, it is actually better, if the process consists of pure dead time, to reject information occurring in intervals less than the dead time. A sampling integral controller is capable of critically damping a process dominated by dead time, while a continuous controller is not. This line of reasoning parallels that of complementary feedback, i.e., sampling is similar in nature to dead time whereas automatic reset is not. When the process contains some capacity, proportional action can be used to advantage. A proportional jump in output held during the control interval serves to hasten the response of the process lag. At the
FIG 4.24. A sampling two-mode controller can be very effective on a continuous process dominated by dead time.
2 s z n
Time
1 Selecting the Feedback Controller
Measurement
Set-point regulator
FIG 4.25. Outside of the control interval, the set-point signal goes to both inputs of the con troller.
end of the control interval, the error is removed and the proportional component of output disappears. Figure 4.24 shows the effect a sampling two-mode controller can have OIL a process dominated by dead time but with some capacity. As long as the proportional band is sufficiently wide to avoid overshoot of itself, reset time is the key adjustment. For critical damping,
fi = PKP At,
100 The proportional band can then be gradually reduced, increasing the speed of the loop, until overshoot begins. A conventional controller whose set, point and measurement are both accessible as electrical or pneumatic signals can be readily connected for sampling servicck5 One timer is necessary to set t,hc control interval, and another to set t,he samplin g interval, if no sampling analyzer is used. Figure 4.25 shows how a pneumatic controller would be connected.
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