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barcode reader project in c#.net Eq. (9.3) becomes in Software
Eq. (9.3) becomes Recognizing Code 128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Creator In None Using Barcode drawer for Software Control to generate, create Code 128 Code Set A image in Software applications. Q + wC(T;  T ) = ,CVg (9.7) Scan USS Code 128 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code128 Generator In Visual C#.NET Using Barcode encoder for .NET Control to generate, create Code 128A image in Visual Studio .NET applications. Taking the Laplace transform of Eq. (9.7) gives Q(s) + wC[T, (s)  T (s)] = pCVsT (s) or
Generating Code 128 Code Set B In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create Code 128 Code Set C image in ASP.NET applications. Generating Code 128 Code Set C In .NET Using Barcode encoder for .NET Control to generate, create Code 128A image in VS .NET applications. =  + T;(s) Code 128 Code Set B Encoder In VB.NET Using Barcode generation for VS .NET Control to generate, create Code 128 Code Set B image in .NET applications. UPCA Supplement 5 Creation In None Using Barcode creator for Software Control to generate, create UPC Code image in Software applications. (9.8) Printing Barcode In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. Print Barcode In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. Q(s) Data Matrix ECC200 Creator In None Using Barcode generator for Software Control to generate, create Data Matrix 2d barcode image in Software applications. Code 128A Generator In None Using Barcode creation for Software Control to generate, create Code 128 Code Set C image in Software applications. (9.9) USD3 Creation In None Using Barcode drawer for Software Control to generate, create USS93 image in Software applications. DataMatrix Drawer In None Using Barcode generation for Font Control to generate, create ECC200 image in Font applications. *In this analysis, it is assumed that the flow rate of heat q is instantaneously available and independent of the temperature in the tank. In some stirredtank heaters, such as a jacketed kettle, q depends on both the temperature of the fluid in the jacket and the temperature of the fluid in the kettle. In this introductory chapter, systems (electrically heated tank or direct steamheated tank) are selected for which this complication can be ignored. In Chap. 21, the analysis of a steamjacketed kettle is given in which the effect of kettle temperature on q is taken into account. Generating UPC  13 In VS .NET Using Barcode creation for ASP.NET Control to generate, create GS1  13 image in ASP.NET applications. DataMatrix Decoder In C#.NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. LINEAR cwsEDLcmP sYwEM.5
Bar Code Recognizer In Visual C#.NET Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications. EAN 13 Creator In None Using Barcode printer for Office Excel Control to generate, create EAN / UCC  13 image in Microsoft Excel applications. This last expression can be written (9.10) where
GTIN  12 Generation In ObjectiveC Using Barcode creation for iPad Control to generate, create GS1  12 image in iPad applications. GTIN  12 Generator In None Using Barcode creation for Microsoft Word Control to generate, create UPC Code image in Microsoft Word applications. If there is a change in Q(t) only, then T, (t) = 0 and the transfer function relating T to Q is
T (s)= l/WC 7s + 1 Q(s) (9.11) If there is a change in T;(t) only, then Q(t) = 0 and the transfer function relating T to T/ is (9.12) I;: (s) Equation (9.10) is represented by the block diagram shown in Fig. 9.3~. This diagram is simply an alternate way to express Eq. (9.10) in terms of the transfer functions of Eqs. (9.11) and (9.12). Superposition makes this representation possible. Notice that, in Fig. 9.3, we have indicated summation of signals by the symbol shown in Fig. 9.4, which is called a summing junction. Subtraction can also be indicated with this symbol by placing a minus sign at the appropriate input. The summing junction was used previously as the symbol for the comparator of the controller (see Fig. 9.2). This symbol, which is standard in the control literature, may have several inputs but only one output. A block diagram that is equivalent to Fig. 9.3~ is shown in Fig. 9.3b. That this diagram is correct can be seen by rearranging Eq. (9.10); thus T (s) = [Q(s) + wCT;(s)]~ (9.13) _ T (s) 1 7s + 1
FIGURE 93 Block diagram for process.
THJ3
CONTROL SYSTEM
In Fig. 9.3b, the input variables Q(S) and wCT/(s) am summed before being operated on by the transfer function llwCl(~s + 1). The physical situation that exists for the control system (Fig. 9.1) if steam heating is used requires more careful analysis to show that Fig. 9.3 is an equivalent block diagram. Assume that a supply of steam at constant conditions is available for heating the tauk. One method for introducing heat to the system is to let the steam flow through a control valve and discharge directly into the water in the tank, where it will condense completely and become part of the stream leaving the tank (see Fig. 9.5). If the flow of steam, f (pounds/time), is small compared with the inlet flow w, the total outlet flow is approximately equal to w. When the system is at steady state, the heat balance may be written WC(Tj,  T,)  wC(T,  To) + f,(H,  HI,) = 0 where tering and leaving tank H, = specific enthalpy of the steam supplied, a constant HI, = specific enthalpy of the condensed steam flowing out at T,, as part (9.14) To = reference temperature used to evaluate enthalpy of all streams en of the total stream The term HI, may be written in terms of heat capacity and temperature; thus Hr, = C(Ts  To) (9.15) From this, we see that, if the steadystate temperature changes, HI, changes. In Eq. (9.14), f,(H,  HI,) is equivalent to the steadystate input qs used previously, as can be seen by comparing Eq. (9.2) with (9.14). Now consider an unsteadystate operation in whichfis much less than w and the temperature T of the bath does not deviate significantly from the steadystate WI Ti + L . ;. tI!F
Steam at constant conditions
w+fYw
FIGURE 95 Supplying heat by steam.
LJNEAR
CLOSEDLQOP
SYSTEMS
temperature T,. For these conditions, we may write the unsteadystate balance approximately; thus
wC(Tj  To)  wC(T  To) + f(Hg  HI,) = pCVs
(9.16) In a practical situation for steam, H, will be about 1000 Btu/lb,. If the temperature of the bath, T, never deviates from T, by more than loo, the error in using the term f(Hg  HI,) instead of f(Hg  HI) will be no more than 1 percent. Under these conditions, Eq. (9.16) represents the system closely, and by comparing Eq. (9.16) with Eq. (9. l), it is clear that q = fW, HI,) (9.17) Therefore, q is proportional to the flow of steam f, which may be varied by means of a control valve. It should be emphasized that the analysis presented here is only approximate. Both f and the deviation in T must be small. The smaller they become, the more closely Eq. (9.16) represents the actual physical system. An exact analysis of the problem leads to a differential equation with timevarying coefficients, and the transferfunction approach does not apply. The problem becomes considerably more difficult. A better approximation will be discussed in Chap. 21, where linearization techniques ate used.

