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barcode reader project in c#.net SUMMARY AND GUIDE FOR FURTHER STUDY in Software
SUMMARY AND GUIDE FOR FURTHER STUDY Recognize Code 128C In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code 128 Creator In None Using Barcode maker for Software Control to generate, create Code128 image in Software applications. A definition of stability for a control system has been presented and discussed. This definition was translated into a simple mathematical criterion relating stability to the location of roots of the characteristic equation. Briefly, it was found that a control system is stable if all the roots of its characteristic equation lie in tbe left half of the complex plane. The Routh criterion, a simple algebraic test for detecting roots of a polynomial lying in the right half of the complex plane, was presented and applied to control system stability analysis. This criterion suffers from two limitations: (1) It is applicable only to systems with polynomial characteristic equations, and (2) it gives no information about the actual location of the roots and, in particular, their proximity to the imaginary axis. This latter point is quite important, as can be seen from Fig. 14.2 and the results of Example 14.3. The Routb criterion tells us only that for K, < 10 the system is stable. However, from Fig. 14.2 it is clear that the value K, = 9 Code 128C Decoder In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Code 128A Drawer In C#.NET Using Barcode drawer for .NET Control to generate, create Code 128C image in .NET framework applications. LINEAR CUXEDLOOP S Y S T E M S
Creating Code 128B In .NET Using Barcode creation for ASP.NET Control to generate, create Code 128B image in ASP.NET applications. Make Code 128B In Visual Studio .NET Using Barcode creator for Visual Studio .NET Control to generate, create Code 128A image in .NET framework applications. produces a response that is undesirable because it has a response time that is too long. In other words, the controlled variable oscillates too long before returning to steady state. It will be shown later that this happens because for K, = 9 there is a pair of roots close to the imaginary axis. In the next chapter tools will be developed for obtaining more information about the actual location of the roots of the characteristic equation. This will enable us to predict the form of the curves of Fig. 14.2 for various values of K,. The advantage of these tools is that they are graphical and are easy to apply compared with standard algebraic solution of the characteristic equation. There are two distinct approaches to this problem: rootlocus methods and frequencyresponse methods. The former ate discussed in Chap. 15 and the latter in Chaps. 16 and 17. These groups of chapters am written in parallel, and the reader may study one or both groups in either order. As a guide to making this decision, here am some general comments concerning the two approaches. Rootlocus methods allow rapid determination of the location of the roots of the characteristic equation as functions of parameters such as K, of Fig. 14.1. However, they ate difficult to apply to systems containing transportation lags. Also, they require a reasonably accurate knowledge of the. theoretical process transfer function. Frequencyresponse methods are an indirect solution to the location of the roots. They utilize the sinusoidal response of the openloop transfer function to determine values of parameters such as K, that keep these toots a safe distance from the right half plane. The actual transient response for a given value of K, can be only crudely approximated. However, frequencyresponse methods are easily applied to systems containing transportation lags and may be used with only experimental knowledge of the unsteadystate process behavior. A mastery of control theory requires knowledge of both methods because they ate complementary. However, the reader may choose to study only frequency response and still be adequately prepared for most of the material in the remainder of this book. The choice of studying only root locus will be more restrictive in terms of preparation for subsequent chapters. In addition, much of the literature on process dynamics relies heavily on frequencyresponse methods. Paint Code 128B In VB.NET Using Barcode encoder for .NET Control to generate, create Code 128 Code Set B image in .NET framework applications. Painting GS1  13 In None Using Barcode creation for Software Control to generate, create EAN 13 image in Software applications. PROBLEMS
Data Matrix 2d Barcode Printer In None Using Barcode printer for Software Control to generate, create DataMatrix image in Software applications. Bar Code Printer In None Using Barcode creation for Software Control to generate, create barcode image in Software applications. 14.1. Write the characteristic equation and construct the Routh array for the control
USS Code 39 Creation In None Using Barcode drawer for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. Generate Barcode In None Using Barcode generator for Software Control to generate, create barcode image in Software applications. system shown in Fig. P14.1. Is the system stable for (a) Kc = 9.5, (b) Kc = 11, (c) K, = 12 USPS POSTNET Barcode Maker In None Using Barcode generator for Software Control to generate, create Postnet image in Software applications. EAN 128 Generator In .NET Using Barcode maker for VS .NET Control to generate, create EAN 128 image in Visual Studio .NET applications. FIGURE P141 Barcode Drawer In Java Using Barcode maker for Java Control to generate, create bar code image in Java applications. Code128 Maker In None Using Barcode printer for Excel Control to generate, create Code 128 Code Set C image in Office Excel applications. STAB Data Matrix Creation In .NET Framework Using Barcode encoder for ASP.NET Control to generate, create Data Matrix image in ASP.NET applications. 1D Barcode Creation In .NET Framework Using Barcode creator for ASP.NET Control to generate, create 1D Barcode image in ASP.NET applications. 1 7 5 UCC  12 Creator In Java Using Barcode drawer for Java Control to generate, create UPCA Supplement 2 image in Java applications. EAN 128 Creator In Java Using Barcode generator for Java Control to generate, create GTIN  128 image in Java applications. FIGURE Pl42 4.2 By means of the Routh test, determine the stability of the system shown in Fig. P14.2 when K, = 2. 4. In the control system of Prob. 13.6, determine the value of gain (psi/ F) that just 9 causes the system to be unstable if (a) 70 = 0.25 min, (b) 70 = 0.5 min. 14.4. Prove that, if one or mom of the coefficients (ao, a 1, . . . , an) of the characteristic equation [Eq. (14.9)] is negative or zero, then there is necessarily an unstable root. Hint: First show that allao is minus the sum of all the rqots, u2/uo is plus the sum of all possible products of two roots, u/uo is ( 1) times the sum of all possible products of j roots, etc. 14.5. Prove that the converse statement of Prob. 14.4, i.e., that an unstable root implies that one or mom of the coefficients will be negative or zero, is untrue for all n > 2. Hint: To prove that a statement is untrue, it is only necessary to demonstrate a single counterexample. 14.6. Deduce an extension of the Routh criterion that will detect the presence of roots with real parts greater than (+ for any specified cr > 0. 14.7. Show that any complex number s satisfying 1s 1 1 yields a value of < 1+s z== that satisfies Re(z) > 0

