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barcode reader project in c#.net Overall lhnsfer hnction for SingleLoop Systems in Software
Overall lhnsfer hnction for SingleLoop Systems Decode Code128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code 128B Generation In None Using Barcode creation for Software Control to generate, create Code 128 Code Set C image in Software applications. Once a control system has been described by a block diagram, such as the one shown in Fig. 12.1, the next step is to determine the transfer function relating C to R or C to U. We shall refer to these transfer functions as overall transfer functions because they apply to the entire system. These overall transfer functions are used to obtain considerable information about the control system, as will be demonstrated in the succeeding chapters. For the present it is sufficient to note that they are useful in determining the response of C to any change in R and U. Decoding Code128 In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Printing Code 128C In C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128 Code Set B image in .NET applications. FIGURE 122 Code 128 Code Set C Generator In VS .NET Using Barcode creation for ASP.NET Control to generate, create USS Code 128 image in ASP.NET applications. Encode USS Code 128 In VS .NET Using Barcode creator for VS .NET Control to generate, create Code 128 image in .NET framework applications. Block diagram for a multiloop, multiload system.
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GTIN  128 Printer In ObjectiveC Using Barcode creation for iPhone Control to generate, create GTIN  128 image in iPhone applications. Universal Product Code Version A Recognizer In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. The response to a change in set point R, obtained by setting U = 0, represents the solution to the servo problem. The response to a change in load variable U, obtained by setting R = 0, is the solution to the regulator problem. A systematic approach for obtaining the overall transfer function for setpoint change and load change will now be presented. Decoding Data Matrix In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Scan Bar Code In .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. Overall Ikansfer Function in Set Ebint
for Change
For this case, U = 0 and Fig. 12.1 may be simplified or reduced as shown in Fig. 12.3. In this reduction, we have made use of a simple rule of blockdiagram reduction which states that a block diagram consisting of several transfer functions in series can be simplified to a single block containing a transfer function that is the product of the individual transfer functions. This rule can be proved by considering two noninteracting blocks in series as shown in Fig. 12.4. This block diagram is equivalent to the equations Y = GA X Multiplying these equations gives YZ   = GAGB XY which simplifies to Z  = GAGB X Thus, the intermediate variable Y has been eliminated, and we have shown the overall transfer function Z/X to be the product of the transfer functions GAGS. This proof for two blocks can be easily extended to any number of blocks to give the rule for the general case. This rule was developed in Chap. 7 for the specific case of several nonintemcting, firstorder systems in series. Z  = GB Y x@++z
FIGURE 124 ltvo aoaiateractiag blocks ia series.
LINEAR
cLosEDL.ooP SYSTEMS
With this simplification the following equations can be written directly from Fig. 12.3b. C = GE B = HC E=RB (12.1) (12.2) (12.3) Since there are four variables and three equations, we can solve the equations simultaneously for C in terms of R as follows: C = G(R  B) C = G(RHC) C = GRGHC or finally C G = l+GH
(12.4) This is the overall transfer function relating C to R and may be represented by an equivalent block diagram as shown in Fig. 12.3~. Overall Transfer Fbnction for Change in Load
In this case R = 0, and Fig. 12.1 is drawn as shown in Fig. 12.52. From the diagram we can write the following equations: C = M= B = E = G2(U+M) G,Gle HC B (12.5) (12.6) (12.7) (12.8) Again the number of variables (C, U, M, B, E) exceeds by one the number of equations, and we can solve for C in terms of U as follows: C = G2(U + G,Gle) C = G2[U + G,GI(HC)] FIGURE 125 Block diagram for change in load.
CLOSEDLOOP
TRANSFER FUNCI IONS
or finally (12.9) where G = GcGiG2. Notice that the transfer functions for load change or setpoint change have denominators that are identical, 1 + GH. The following simple rule serves to generalize these results for the singleloop feedback system shown in Fig. 12.1: the transfer function relating any pair of variables X, Y is obtained by the relationship Y Tf =negative feedback X 1 + lr[ where rrf = product of transfer functions in the path between the locations of the signals X and Y 7~1 = product of all transfer functions in the loop (i.e., in Fig. 12.1, al = G,G1G2H) If this rule is applied to finding C/R in Fig. 12.1, we obtain C G GcGG = R .l + G,GIG2H = l+GH which is the same as before. For positive feedback, the reader should show that the following result is obtained: Y f =positive feedback (12.11) X 1  TT[ Example 12.1. Determine the nansfer functions C/R, C/Ul, and B/U2 for the system show in Fig. 12.6. Also determine an expression for C in terms of R and Ur for the situation when both setpoint change and load change occur simultaneously. Using the rule given by Eq. (12.10), we obtain by inspection the results (12.12) (12.13) (12.14)

