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barcode reader project in c#.net 4s n>(s P~)(s p3) + K(s  zd = 0 in Software
4s n>(s P~)(s p3) + K(s  zd = 0 Decode ANSI/AIM Code 128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Painting Code128 In None Using Barcode creation for Software Control to generate, create USS Code 128 image in Software applications. Us z d = o
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Universal Product Code Version A Generator In .NET Using Barcode encoder for Reporting Service Control to generate, create UPC Symbol image in Reporting Service applications. Barcode Generator In Java Using Barcode encoder for Java Control to generate, create barcode image in Java applications. adding integral action has been to destablize the system in terms of the amount of proportional action that can be used before instability occurs. A method for quickly sketching the rootlocus diagram was developed by Evans (1954, 1948) and has been presented in many textbooks on control theory. In the next section, this method will be presented. PLOTTING THE ROOTLOCUS DIAGRAM
Having introduced the concept of root locus by two examples, here are some rules that were first introduced by Evans (1954, 1948) for plotting rootlocus diagrams of characteristic equations of any order. Without these rules, the time and effort needed to plot rootlocus diagrams would be too great to render them useful in engineering computations. The first step in applying the rootlocus technique to determine the ro ts % of the characteristic equation of the closedloop control system is to write t e openloop transfer function (G = GiGzH) in the standard form G=K; where K = constant
D = ts  PI)(S  ~2). . .(s  PA
The term zi is called a zero of the openloop transfer function. The term pi is called a pole of the openloop transfer function. This term was defined earlier in this chapter. A zero of G(s) is any value of s for which G(s) equals zero. The factored terms (S  zi) and (S pi) in N/D arise naturally in the openloop transfer function. For example, in the control system considered at the beginning of this chapter, Eq. (15.2) was written in the standard form with KC K=7172 73 D = (8  PINS  pz)(s
N = l The second example for PI control considered earlier [Eq. (15.6)] illustrates a situation where a term (z  zi) appears in N. Using the form of G given by Eq. (15.9), the characteristic equation 1 + G = 0 may be written in the alternate form or , D+KN =0
(15.10) ROOTLOCUS
It is assumed in the remainder of this chapter that n L m, which is true for all physical systems. This being the case, the characteristic equation will be of nth order and have n roots, r 1, t2, . . . , rn . To develop the graphical method for determining the root locus, the characteristic equation is rewritten as (15.11) In terms of the poles and zeros of the openloop transfer function, Eq. (15.11) becomes K(s  zm  ZZ) (S  tm) = 1 (15.12) (s  Pl)(S  P2) * * *(s  Pn) Since the lefthand member is in general complek, we may write Eq. (15.12) in the equivalent form involving magnitude and phase angle; thus 4(s  Zl) +
4(s  z2) +
... + 40  zd
 [4(s
 Pl) + .**

