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barcode reader project in c#.net LlNEAR in Software
LlNEAR Code128 Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encode USS Code 128 In None Using Barcode drawer for Software Control to generate, create Code128 image in Software applications. OPENLOOP SYSTEMS
USS Code 128 Decoder In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. ANSI/AIM Code 128 Creator In C# Using Barcode printer for Visual Studio .NET Control to generate, create Code 128 Code Set A image in Visual Studio .NET applications. FIGURE 74 Step response of noninteracting firstorder systems.
ANSI/AIM Code 128 Printer In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create Code128 image in ASP.NET applications. Code 128 Generation In VS .NET Using Barcode printer for .NET Control to generate, create Code 128 Code Set A image in Visual Studio .NET applications. 2 am the same as before and are given by Eqs. (7.1) and (7.2). However, the flowhead relationship for tank 1 is now Generating Code 128 Code Set A In VB.NET Using Barcode creation for .NET Control to generate, create Code 128 image in .NET framework applications. ANSI/AIM Code 39 Printer In None Using Barcode creator for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. 4 1 = &l  h 2 ) GS1  12 Drawer In None Using Barcode encoder for Software Control to generate, create UPCA Supplement 2 image in Software applications. Barcode Creation In None Using Barcode drawer for Software Control to generate, create barcode image in Software applications. The flowhead relationship for R2 is the same as before and is expressed by Eq. (7.4). A simple way to combine Eqs. (7.1), (7.2), (7.4), and (7.13) is to first express them in terms of deviation variables, transform the resulting equations, and then combine the transformed equations to eliminate the unwanted variables. At steady state, Eqs. (7.1) and (7.2) can be written Draw GTIN  13 In None Using Barcode creation for Software Control to generate, create EAN13 image in Software applications. Code 128B Creator In None Using Barcode generation for Software Control to generate, create Code 128 Code Set C image in Software applications. 4 s 4 1 ,  4 1 ,  q2, = 0 = 0 2 Of 5 Industrial Generator In None Using Barcode encoder for Software Control to generate, create 2/5 Standard image in Software applications. 1D Printer In .NET Framework Using Barcode creation for ASP.NET Control to generate, create Linear 1D Barcode image in ASP.NET applications. (7.14) (7.15) Paint Barcode In ObjectiveC Using Barcode drawer for iPhone Control to generate, create barcode image in iPhone applications. Scan Barcode In .NET Framework Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. Subtracting Eq. (7.14) from Eq. (7.1) and Eq. (7.15) from Eq. (7.2) and introducing deviation variables give Q  Ql = AL% Ql  Q2 Barcode Creator In .NET Framework Using Barcode drawer for .NET framework Control to generate, create bar code image in .NET applications. Bar Code Creator In ObjectiveC Using Barcode printer for iPad Control to generate, create bar code image in iPad applications. = AZ% Drawing Barcode In Java Using Barcode creation for Android Control to generate, create barcode image in Android applications. Encoding EAN13 In None Using Barcode printer for Online Control to generate, create GS1  13 image in Online applications. (7.16) (7.17) Expressing Eqs. (7.13) and (7.4) in terms of deviation variables gives
Ql =
HI H2 Rl
(7.18) RESPONSE
FIRSTORDER
SYSTEMS
SERIES
Transforming Eqs. (7.16) through (7.19) gives
Q(s)  Ql<s> = AlsHl(s) Ql(s>  Qz(s) = A2sH2(~) RlQl(s) = HI(S)  H2(s) (7.20) (7.21) (7.22) (7.23) R2Q20) = H20) The analysis has produced four algebraic equations containing five unknowns: (Q, Q 1, Q2, HI, and Hz). These equations may be combined to eliminate Q 1, Q 2, and Ht and arrive at the desired transfer function: H2(S) _ Q(s) 71~2s2
+ (q + r2 + AIR2)s + 1
(7.24) Notice that the product of the transfer functions for the tanks operating separately, Eqs. (7.5) and (7.6), does not produce the correct result for the interacting system. The difference between the transfer function for the noninteracting system, Eq. (7.7), and the interacting system, Eq. (7.24), is the presence of the term AlR2 in the coefficient of s. The term interacting is often referred to as loading. The second tank of Fig. 7.lb is said to Eoad the first tank. To understand the effect of interaction on the transient response of a system, consider a twotank system for which the time constants are equal (rt = 72 = 7). If the tanks are noninteracting, the transfer function relating inlet flow to outlet flow is (7.25) The unitstep response for this transfer function can be obtained by the usual procedure to give Q2(t) = 1  et/r  $t/T 7
If the tanks sre interacting, the overall transfer function, according to Eq. (7.24), is (assuming further that Al = A9 Q2(s) E  Q(s) 1 2252 + 37s + 1
(7.27) By application of the quadratic formula, the denominator of this transfer function can be written as 1 Q2(s)  = (0.387s + 1)(2.62~s + 1) Q(s) (7.28) LINEAROPENLOOPSYSTEMS
For this example, we see that the effect of interaction has been to change the effective time constants of the interacting system. One time constant has become considerably larger and the other smaller than the time constant T of either tank in the noninteracting system. The response of Qa(t) to a unitstep change in Q(t) for the interacting case [Es. (7.28)] is Q2(t) = 1 + 0.17~~~~.~*  1.17em.62T (7.29) In Fig. 7.5, the unitstep responses [Eqs. (7.26) and (7.29)] for the two cases ate plotted to show the effect of interaction. From this figure, it can be seen that interaction slows up the response. This result can be understood on physical grounds in the following way: if the same size step change is introduced into the two systems of Fig. 7.1, the flow from tank 1 (41) for the noninteracting case will not be reduced by the increase in level in tank 2. However, for the interacting case, the flow q1 will be reduced by the buildup of level in tank 2. At any time tr following the introduction of the step input, q1 for the interacting case will be less than for the noninteracting case with the result that h2 (or q2) will increase at a slower rate. In general, the effect of interaction on a system containing two firstorder lags is to change the ratio of effective time constants in the interacting system. In terms of the transient response, this means that the interacting system is mom sluggish than the noninteracting system. This chapter concludes our specific discussion of firstorder systems. We shall make continued use of the material developed here in the succeeding chap

