how to use barcode scanner in asp.net c# Ud erstanding Feedback Control n in .NET

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1 Ud erstanding Feedback Control n
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FIG 1.5. A loop gain of 0.5 will provide Mamplitude damping.
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trolled by proportional only, adjusted to fi-amplitude damping, the natural period is fixed at 2 min, and the proportional band must be 200 percent. The nature of the process determines the results.
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Proportional Offset
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The prime function of a controller is that of regulation. The controller is intended to change its output as often and as much as necessary to keep the controIled variable at the set point. Every process is subject to variations in load. In a well-regulated loop, the manipulated variable will be driven to balance the load. Consequently, the load is often measured in terms of the corresponding value of controller output. In the equation describing the proportional controller, the bias b equals the output when the error is zero. This bias may be fixed at the normal value of output, usually 50 percent, or it may be adjusted by hand to match the current load. This adjustment is called manual reset. But because of the proportional relationship between input and output, a change in output by any amount cannot be gained without a corresponding change in error. Should the output of the proportional con-
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troller have to change to meet a new load condition, a deviation will appear: e= P(m - b) 100 (1.5)
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The deviation in this case is known as offset, and it increases with proportional band. With a 200 percent band, which was necessary for >i-amplitude damping in the previous example, a 10 percent change in load would produce a 20 percent offset-an int,olerable amount. The characteristics of a dead-time process under proportional control may be observed in a simple algebraic simulat.ion. Let the present output of the controller equal the measurement one dead time later:
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cn = m,-l
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where n = t/rd. dead time is Ed.
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This represents a process whose gain is unity and whose When the controller is introduced to close the loop,
m n = 7 (r - c,)
mnfl = $j (r - c~+~) = F (T - mn>
With initial conditions of co = 0, b = 0, r. = 0, and P = 200 percent, let the hp be upset by a set-paint change to 5Q peycent. Subsequent udxes of c at inkx-&s of &a& %irne ale as fo\\~s.
1 0 = 1 1 = 50
co= 0% cl= 0 c2 = 2 5 c3 = 12.5 c4 = 18.75 c5 = 15.625 C 2 = 16.667
mo = 0 70 7121 = 0.5(50 - 0 ) mz = 0.5(50 - 25) 1123 = 0.5(50 - 12.5) 1n4 = 0.5(50 - 18.75) 172, = 16.667
= = = =
25 12.5 18.75 15.625
Notice that c exhibits a damped oscillation whose period is two calculations (two dead times). Sotice also that the amplitude of successive crests is diminished by one-quarter. Finally, there is an offset. The controller output comes to rest at 16.667 percent above the bias. The offset is r - c = 33.333% which equals
go ( m - b) = 2(16.667%)
Ud erstanding Feedback Control n
FIG 1.6. Proportional control of pure dead time can oscillate in a square wave.
n = t/q
The tabulated course of the controlled variable plots as a damped square wave. This is entirely possible when a process of pure dead time is excited by a step. The loop responds to higher harmonics as well as to fundamental, since the process does not attenuate waves of any period. Odd harmonics shift the phase in increments of 360 , so as to permit oscillation at these periods also, and square waves are made of odd harmonics. Although a square-wave response is possible, it is not likely to occur in processes, because ordinarily energy cannot be delivered fast enough to make the controlled variable rise steeply. The kind of response more likely to occur is a load change, requiring a different value of controller output. What could happen to a dead-time process under proportional control in the event of a gradual load change is plotted in Fig. 1.7.
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