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barcode reader project in c#.net TRANSPORTATION in Software
TRANSPORTATION Recognizing Code 128C In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Creating Code 128A In None Using Barcode creation for Software Control to generate, create Code 128 Code Set C image in Software applications. A phenomenon that is often present in flow systems is the transportation Zag. Synonyms for this term are dead time and distance velocity lag. As an example, consider the system shown in Fig. 8.6, in which a liquid flows through an insulated tube of uniform crosssectional area A and length L at a constant volumetric flow rate q. The density p and the heat capacity C are constant. The tube wall has negligible heat capacity, and the velocity profile is flat (plug flow). The temperature x of the entering fluid varies with time, and it is desired to find the response of the outlet temperature y(t) in terms of a transfer function. As usual, it is assumed that the system is initially at steady state; for this system, it is obvious that the inlet temperature equals the outlet temperature; i.e., xs = Ys (8.41) Code 128 Recognizer In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Code 128B Drawer In C# Using Barcode drawer for VS .NET Control to generate, create Code128 image in VS .NET applications. If a step change were made in x(t) at t = 0, the change would not be detected at the end of the tube until r set later, where T is the time required for the entering fluid to pass through the tube. This simple step response is shown in Fig. 8.7~. If the variation in x(t) were some arbitrary function, as shown in Fig. 8.7b, the response y(t) at the end of the pipe would be identical with x(t) but again delayed by r units of time. The transportation lag parameter r is simply the time needed for a particle of fluid to flow from the entrance of the pipe to the exit, and it can be calculated from the expression 7= Generate Code128 In .NET Using Barcode maker for ASP.NET Control to generate, create Code 128C image in ASP.NET applications. Painting Code 128 Code Set A In VS .NET Using Barcode maker for Visual Studio .NET Control to generate, create Code 128 Code Set B image in .NET applications. qz A L  Generating Code 128 Code Set B In Visual Basic .NET Using Barcode generation for VS .NET Control to generate, create Code 128A image in .NET applications. Painting Bar Code In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. volume of pipe volumetric flow rate
Paint UPC A In None Using Barcode encoder for Software Control to generate, create GS1  12 image in Software applications. Print Bar Code In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. (8.42) DataMatrix Creator In None Using Barcode creator for Software Control to generate, create ECC200 image in Software applications. EAN128 Generation In None Using Barcode creator for Software Control to generate, create GS1 128 image in Software applications. x(t) USPS POSTNET Barcode Creator In None Using Barcode drawer for Software Control to generate, create Postnet image in Software applications. Barcode Generation In None Using Barcode creation for Online Control to generate, create bar code image in Online applications. It can be seen from Fig. 8.7 that the relationship between y(t) and y(t) = x(t  7) EAN13 Supplement 5 Creation In None Using Barcode creation for Online Control to generate, create EAN13 image in Online applications. Code 39 Generator In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create Code 3 of 9 image in ASP.NET applications. (8.43) Encode Bar Code In ObjectiveC Using Barcode drawer for iPhone Control to generate, create barcode image in iPhone applications. Data Matrix 2d Barcode Reader In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. FIGURE 86 System with transportation lag.
Scan Code39 In C# Using Barcode decoder for .NET Control to read, scan read, scan image in .NET applications. EAN13 Creation In ObjectiveC Using Barcode printer for iPad Control to generate, create EAN13 image in iPad applications. LINEAR
OPENLOOP
SYSTEMS
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FIGURE 87 Response of transportation lag to various inputs.
Subtracting Eq. (8.41) from (8.43) and introducing the deviation variables X = x  x, and Y = y  ys give Y(r) = X(t  7) (8.44) If the Laplace transform of X(t) is X(s), the Laplace transform of X(t  7) is e X(s). This result follows from the theorem on translation of a function, which was discussed in Chap. 4. Equation (8.44) becomes Y(s) = e X(s) or Y(s) s7 X(s)=e (8.45) Therefore, the transfer function of a transportation lag is e s7. The transportation lag is quite common in the chemical process industries where a fluid is transported through a pipe. We shall see in a later chapter that the presence of a transportation lag in a control system can make it much more difficult to control. In general, such lags should be avoided if possible by placing equipment close together. They can seldom be entirely eliminated. APPROXIMATION OF TRANSPORT LAG. The transport lag is quite different
from the other transfer functions (firstorder, secondorder, etc.) that we have discussed in that it is not a rational function (i.e., a ratio of polynomials.) As shown in Chap. 14, a system containing a transport lag cannot be analyzed for stability by the Routh test. The transport lag is also difficult to simulate by computer as explained in Chap. 34. For these reasons, several approximations of transport lag that are useful in control calculations are presented here. One approach to approximating the transport lag is to write e  as l/e and to express the denominator as a Taylor series; the result is 1 e rs= eTs 1 1 + rs + r*s*/2 + r3s3/3! + . .. 1 e TS g1 + 7s Keeping only the first two terms in the denominator gives
(8.46) HIGHERORDER SYSTEMS: SECONDORDER AND TRANSPORTATION LAG
This approximation, which is simply a firstorder lag, is a crude approximation of a transport lag. An improvement can be made by expressing the transport lag as e 7s = ed2 

