# barcode reader using c#.net LINEAR in Software Creator Code 128 Code Set B in Software LINEAR

LINEAR
Recognize Code128 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 creator for Software Control to generate, create Code-128 image in Software applications.
CLOSED-LOOP
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
Code 128 Code Set C Maker In Visual C#
Using Barcode maker for VS .NET Control to generate, create Code 128C image in Visual Studio .NET applications.
SYSTEMS
Code 128 Code Set B Creation In .NET Framework
Using Barcode maker for ASP.NET Control to generate, create ANSI/AIM Code 128 image in ASP.NET applications.
Code 128 Code Set B Maker In VS .NET
Using Barcode generator for .NET framework Control to generate, create Code 128A image in .NET applications.
4. (Rule 4) Since n - m = 3, we have three asymptotes and the center of gravity is y = (-3 - 2 - 1)/3 = -2. Angles which the asymptotes make with the real axis are 7r/3, 31rl3, and 51~13. These asymptotes are shown in Fig. 15.5a. With these few steps completed, a rough sketch of the root-locus diagram can be made as follows: Since the real axis to the left of -3 is an asymptote and one branch emerges from the pole at -3, it should be clear that one entire branch is the real axis to the left of the -3. Furthermore, from the fact that two loci must emerge from the poles - 1 and -2 and that the real axis between these poles is part of the locus, we see that two loci move toward each other along the real axis between - 1 and -2 and eventually meet at some common point. Since the location of the asymptotes is known, it is therefore necessary that the two loci that meet on the real axis must break away and eventually follow the asymptotes. From these observations, we could sketch a root-locus diagram that closely resembles that of Fig. 15.5~. If the breakaway point and the crossings of the imaginary axis were known, the sketch could be made with considerable accuracy. We now continue the example by applying Rule 5 to find the breakaway point and the Routh test to find the crossings of the imaginary axis. 5. Breakaway point. (Rule 5) The roots emerging from - 1 and - 2 move toward each other until they meet, at which point the loci leave the real axis at angles of + 7r/2. The breakaway point is found from Eq. (15.16) as follows 1 1 1 o = -+ -+s -p3 s -Pl s-p:!
Code 128 Code Set C Printer In Visual Basic .NET
Using Barcode creation for .NET Control to generate, create Code128 image in Visual Studio .NET applications.
UCC.EAN - 128 Printer In None
Using Barcode generator for Software Control to generate, create EAN / UCC - 13 image in Software applications.
01 rJ=L-+
Painting Barcode In None
Using Barcode generator for Software Control to generate, create bar code image in Software applications.
Bar Code Encoder In None
Using Barcode encoder for Software Control to generate, create barcode image in Software applications.
1 s+l
Encoding UPC Symbol In None
Using Barcode drawer for Software Control to generate, create UPC-A image in Software applications.
ECC200 Creator In None
Using Barcode drawer for Software Control to generate, create DataMatrix image in Software applications.
1 1 -+s+2 s+3
ISBN - 13 Encoder In None
Using Barcode maker for Software Control to generate, create ISBN image in Software applications.
Create Bar Code In .NET Framework
Using Barcode encoder for Reporting Service Control to generate, create bar code image in Reporting Service applications.
Solving this by trial and error gives s = -1.42 6. To find the points at which the loci cross the imaginary axis, the Routh test (theorem 3) of Chap. 14 may be used. Writing the characteristic equation D + KN = 0 in polynomial form gives
Generating Data Matrix ECC200 In Java
Using Barcode printer for Java Control to generate, create Data Matrix image in Java applications.
EAN13 Creation In Java
Using Barcode creator for Java Control to generate, create GTIN - 13 image in Java applications.
D + KN = (s + l)(s + 2)(s -t 3)+ K = 0
Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications.
Bar Code Maker In None
Using Barcode drawer for Excel Control to generate, create barcode image in Office Excel applications.
s2 +6s2 + 11s + K +6 = 0
GTIN - 128 Printer In Visual Basic .NET
Using Barcode creator for .NET framework Control to generate, create GTIN - 128 image in VS .NET applications.
Drawing Matrix Barcode In Java
Using Barcode printer for Java Control to generate, create Matrix 2D Barcode image in Java applications.
from which we can write the Routh array:
--I-bl
2 3 6
K-k6
ROOT LOCUS
The theorem states that, if one pair of roots are on the imaginary axis and all others in the left half plane, all the elements of the nth row must be zero. From this we obtain for the element bl
b, =
(6)Ul)
Solving for K, K = 60
A root on the imaginary axis is expressed as simply ju. Substituting s = j a and K = 60 into the polynomial gives -ju3 - 6a2 + llaj + 66 = 0 (66 - 6a*) + (11~ - u3)j = 0 Equating the real part or the imaginary part to zero gives a = r fi = 23.32 Therefore the ioci intersect the imaginary axis at + j fi and - j fi. 7. Having found these general features of the root-locus plot, we can sketch the root locus. If it is desirable to have a more accurate plot of the loci, the construction is continued by the trial-and-error method described earlier in this chapter. + To illustrate the method of finding roots, suppose the trial point, si = -0.75 + 1.5 j of Fig. 15.5b, is selected. This point is checked by the angle criterion [Eq. (15.14), which for this example may be written
&(s + 1) + i\$(s + 2) + &(s + 3) = (2i + 1)Tr or
I31 + I32 + 03 = (2i + l) r From Fig. 15.5b, these angles are found to be 19~ = 81 and we have 81 + 51 + 34 = 166 + (2i + 1)7r e* = 51 03 = 34O
+Several computer software packages are now available for plotting the root-locus diagram. For example, the program CC is especially useful for root-locus plotting. Details on CC and other software packages are given in Appendix 34A (of Chap. 34). Evans (1954, 1948), who developed the root-locus method, produced an instrument for plotting root-locus diagrams called the Spirule. The Sprirule was essentially a drawing instrument that was used to add angles by rotating an arm with respect to a disk. The Sprirule, which is no longer available, is now obsolete as a result of the availability of computer programs for plotting root-locus diagrams.