barcode reading in asp.net i I -I in Software

Generator Code 128B in Software i I -I

i I -I
Reading Code 128 Code Set B 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 printer for Software Control to generate, create USS Code 128 image in Software applications.
s -plane
Code-128 Decoder In None
Using Barcode reader for Software Control to read, scan read, scan image in Software applications.
USS Code 128 Maker In C#.NET
Using Barcode creator for .NET Control to generate, create Code128 image in Visual Studio .NET applications.
SAMPLED-DATAcoNTRoLsYsTEMs
Drawing Code128 In Visual Studio .NET
Using Barcode generator for ASP.NET Control to generate, create Code 128 Code Set A image in ASP.NET applications.
USS Code 128 Printer In .NET Framework
Using Barcode encoder for .NET Control to generate, create Code128 image in Visual Studio .NET applications.
z-plane
Code128 Printer In Visual Basic .NET
Using Barcode generation for VS .NET Control to generate, create Code 128B image in VS .NET applications.
EAN 13 Generation In None
Using Barcode maker for Software Control to generate, create European Article Number 13 image in Software applications.
radius = 1
Code 3 Of 9 Drawer In None
Using Barcode generation for Software Control to generate, create Code 39 Extended image in Software applications.
Generating Barcode In None
Using Barcode drawer for Software Control to generate, create barcode image in Software applications.
FIGURE 24-2 Region of stability in the z-plane.
Barcode Printer In None
Using Barcode printer for Software Control to generate, create bar code image in Software applications.
Data Matrix Drawer In None
Using Barcode maker for Software Control to generate, create Data Matrix 2d barcode image in Software applications.
Routh Test
Printing Royal Mail Barcode In None
Using Barcode generation for Software Control to generate, create British Royal Mail 4-State Customer Barcode image in Software applications.
EAN / UCC - 13 Scanner In Visual Studio .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.
The Routh test, which is often used to examine the roots of the characteristic equation of a continuous system (see Chap. 14), may also be used to examine the roots of the characteristic equation of a sampled-data system. Recall that the Routh test detects the presence of roots in the right half plane. Since the criterion of stability of a sampled-data system requites that all roots fall within the unit circle of the z-plane, one must first apply a transformation that will map the inside of the unit circle of the z-plane into the left half of the w-plane. One can then apply the Routh test to discover roots in the right half of the w-plane, and if none are found, we know that the roots of the characteristic equation 1 + G(z) = 0 fall within the unit circle and that fhe sampled-data control system is stable. A transformation that will map the inside of the unit circle of the z-plane into the left half of the w-plane is w+ z=-l (24.4) w - l This transformation is called the bilinear transformation. The regions involving the transformation am shown in Fig. 24.3. An alternate transformation is 1+w z= l-w (24.5)
Create USS-128 In None
Using Barcode generation for Online Control to generate, create UCC.EAN - 128 image in Online applications.
Generate Barcode In Java
Using Barcode maker for Java Control to generate, create bar code image in Java applications.
The reader should check to see that the transformations given by Eqs. (24.4) and (24.5) do what is claimed. For example, if w = - 1 + j , a point in the left half of the w-plane, then Eq. (24.4) becomes z. = - l + j + l =A- l + j - 1 -2+j
EAN 13 Decoder In VB.NET
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET applications.
Generate Code 39 Full ASCII In Visual Studio .NET
Using Barcode creation for Reporting Service Control to generate, create ANSI/AIM Code 39 image in Reporting Service applications.
Multiplying numerator and denominator by -2 - j , the complex conjugate of -2 + j, gives - j
UCC - 12 Maker In None
Using Barcode creator for Microsoft Excel Control to generate, create EAN / UCC - 14 image in Microsoft Excel applications.
Decode Code 39 Full ASCII In Visual Studio .NET
Using Barcode reader for .NET Control to read, scan read, scan image in VS .NET applications.
=-2+j-2-j
- 2 - j c l-2j c 5
-1 5
a point inside the unit circle
STABILKY
FIGURE 24-3 Transformation from the z-plane to the w-plane.
A general proof that the transformation maps the inside of the unit circle into the left half plane is given here. Solving Eq. (24.4) for w gives
z+l w=-
z - l Let z = x + jy. Equation (24.6) becomes w= x+fY+l= (x+l)+jy x+jy-1 (x - 1) + jY or (x + 1) + jy (x - 1) - jy w = (x - 1) + jy (X - 1) - jy
(24.6)
(24.7)
(24.8)
Multiplying out the factors in the numerator and the denominator gives, after algebraic rearrangement x2 + y2 - 1 2Y w = (x - 1)2 + y2 - j (x - 1)2 + y2 We may now use the analytical expression for a unit circle, x 2 + y 2 = 1, to complete the proof. If a point is inside the unit circle of the z-plane, lzl<l a n d x2 + y2 < 1
Introducing this inequality into Eq. (24.9) leads to the result that the real part of w is negative; thus: Re{w} < 0 (24.10)
Since this is equivalent to stating that the values of w fall in the left half plane, we have completed the general proof.
SAMPLED-DATA
CONTROL
SYSTEMS
Root Locus
One may determine the stability of a sampled-data system by plotting the root locus diagram for the characteristic equation. In this case, there is no need to use a transformation, as is needed in applying the Routh test. In general, the open-loop transfer function for the sampled-data system can be placed in the form
G(z) = K (z - Vl>(Z - v2). . . (z - Pl>(Z - P2) * * *
(24.11)
where ~1, ~2,. . . are the zeros of the open-loop transfer function and p 1, ~2, . . . are the poles of the open-loop transfer function. To obtain the root locus plot for 1 + G(z) = 0, one places the open-loop zeros and poles on the complex plane and applies the angle criterion used in root locus construction. The stability boundary occurs when one of the branches of the root locus diagram crosses the unit circle. To find the gain K at the stability boundary, one applies the magnitude criterion of root locus construction. (See Chap. 15.) Example 24.1. The stability of proportional control of a first-order process will be
examined. This same problem was presented as Example 23.3. Both the Routh test and the root locus method will be used. The system is shown in Fig. 24.4. For this system, we have shown in Eq. (23.29) that
Copyright © OnBarcode.com . All rights reserved.