how to use barcode scanner in asp.net c# FIG 2.1. Noninteracting (above) compared to interacting (below) capacities. in .NET

Printer Quick Response Code in .NET FIG 2.1. Noninteracting (above) compared to interacting (below) capacities.

FIG 2.1. Noninteracting (above) compared to interacting (below) capacities.
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Characteristics of Real Processes
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In the upper left, the two tank levels do not interact, because the flow from the first to the second is independent of the level in the second. The lower picture, however, illustrates the case where both. inflow and outflow are a function of tank level. The levels interact, because any change in t he downstream level will affect the upstream level. An electrical analog of each process appears on the right. The amplifier in the upper figure isolates the two lags by preventing the voltage on the second from affecting that on the first. The lower right figure, without the amplifier, is a two-stage ladder network. A mult istage ladder is often used to simulate a transmission line. The significance of int,eraction is that. it changes the effective time const ants of the individual capacities. The magnitude of the change is striking. The solution of the equation for determining the effective time constants is irrat ional and unfortunately somewhat unclear. But for the special case where two equal capacities with equal time const ants 7 interact, their combined response is that of two noninteracting lags with t he following values:
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T1 2 = 3 k & 2 r 71 = 2.6187 and
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i-2 = 0.382~
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The following general rules apply to the principle of interaction: 1. The degree of interaction is proportional to the ratio of the smaller to the larger capacity (not time constant). Where this ratio is low (<O.l), the capacities may be assumed not to interact . 2. Interaction always works toward increasing the larger time constant and decreasing the smaller one. 3. Specifically with regard to the behavior of systems wit)11 equal t,imc constants 7, of equal capacity, the effect. is a combination of one large and the rest small time constants whose normalized sum is
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i=n. i=7l C~=Ci=nT!
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i=l i=l
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( 2 . 1 )
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where i = each time constant n = number of capacities and whose normalized product is
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n ; = 1.0
(2.2)
A cast in point is the two-capacity process cit,cd above:
71 + 72
= 2.618 + 0.882 = 3
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Since 72 = 2,
n2 + n zz-= 3 4+2 2 2
3: = (2.618)(0.382)
= 1.00
With three capacities of time constant 7,
Tl - = 7 72 5.0503
- = 0.6403 i73. - = 0.3090 7 G.0000 and (5.0505) (0.6405) (0.3090) = 1.00. The reasons for interaction can be visualized to some extent. For example, in the interacting tanks of Fig. 2.1, the flow entering the first tauk must ultinmtely fill both tanks, whereas that euteriug the second fills the second. The sum of the time constants theu becomes three. An important point to grasp is that interaction ninkes control easier. I<ecall that the proportional band required to regulate a two-capacity process varies with 7 /7,,n-lth t h e m o s t difficwlt ~nse b e i n g 72 = 71. . Where capacities interact, ho\wver, it is impossible to make 7 = TV. The ratio of two equal iutcmctiug time constants is 0.382 :2.618 = 0.146. By this stnudnrd the nonintcwc~ting proress is nearly seven times more difficult to control! At this poiiit it is worthwhile to review the esaniples of two-capacity prowsses that hnvc already been presented, from the aspect of interaction. The process shown in ITig. 1.20 is definitely interacting, bemuse chlgcs in c*hnnlbcr level (*a11 cause changes in tallI; ltvcl. Hut the capacity of 4, the chamber i s s o mudi le..: than that of the tank, t h a t t h e cffwt is virtually nil. 1 0~ prac+iwl p u r p o s e s , thcu, the two wpacities rn:~y b e considered Iloninternc,tillg. I t would cvcn bc possible t o t h r o t t l e the valves to the c~han~bcr cwough to m:~I;e its t imc constant cqu:~l or exceed that of the tank. This i)ropcrty ia n o t rcprcsrntntivc of intcrwting
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