 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode reader integration with asp.net f ( s ) = /omf(t)el dt Let in Software
f ( s ) = /omf(t)el dt Let Code 128 Code Set C Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Generating Code 128 Code Set B In None Using Barcode maker for Software Control to generate, create Code128 image in Software applications. u = eS
Decode Code 128 Code Set C In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Code 128C Creation In Visual C# Using Barcode encoder for .NET Control to generate, create Code128 image in Visual Studio .NET applications. dv = f(t)dt
Code 128 Code Set C Creator In VS .NET Using Barcode maker for ASP.NET Control to generate, create Code 128A image in ASP.NET applications. Code128 Maker In Visual Studio .NET Using Barcode printer for .NET Control to generate, create Code128 image in VS .NET applications. Then
Making Code 128 Code Set A In Visual Basic .NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128A image in .NET applications. Paint UPCA Supplement 5 In None Using Barcode encoder for Software Control to generate, create UPC Code image in Software applications. d u = sems dt v = f(t)dt I0
Bar Code Printer In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. Draw Data Matrix ECC200 In None Using Barcode creator for Software Control to generate, create DataMatrix image in Software applications. Hence, UCC128 Maker In None Using Barcode drawer for Software Control to generate, create EAN 128 image in Software applications. Code 3/9 Generation In None Using Barcode generator for Software Control to generate, create Code39 image in Software applications. f ( s ) = eCS ~otf(t)dt~~+sjoX[jo~f(t)dt]estdt
Standard 2 Of 5 Drawer In None Using Barcode generator for Software Control to generate, create 2/5 Standard image in Software applications. UPC Symbol Maker In ObjectiveC Using Barcode maker for iPad Control to generate, create GS1  12 image in iPad applications. Since f(t) must satisfy the requirements for possession of a transform, it can be shown that the first term on the right, when evaluated at the upper limit of 03, vanishes because of the factor eesr. Furthermore, the lower limit clearly vanishes, and hence, there is no contribution from the first term. The second term may be recognized as sL{&, f (t)dt}, and the theorem follows immediately. UCC128 Generation In None Using Barcode encoder for Office Word Control to generate, create GTIN  128 image in Word applications. Bar Code Generator In None Using Barcode generation for Font Control to generate, create bar code image in Font applications. THE LAPLACE
Encode Code 39 Full ASCII In ObjectiveC Using Barcode encoder for iPad Control to generate, create Code39 image in iPad applications. Encode UPCA Supplement 2 In None Using Barcode drawer for Office Word Control to generate, create UPCA Supplement 5 image in Microsoft Word applications. TRANSFORM
GTIN  13 Printer In Java Using Barcode maker for Java Control to generate, create EAN13 Supplement 5 image in Java applications. Encode Bar Code In .NET Framework Using Barcode maker for .NET Control to generate, create barcode image in .NET framework applications. Example
4.6. Solve the following equation for x(t): x(t)dt  I
Taking the Laplace theorem
transform of both sides, and making use of the previous sx(s)  3 = q  L s2
Solving for x(s), x(s) = 3s2  1 39  1 s(s2  1) = s(s I l)(s  1) This may be expanded into partial fractions according to the usual procedure to give 1 1 x(s) = A + +s s+1 s  l Hence, x (t) = 1 + ej + 62 The reader should verify that this function satisfies the original equation. PROBLEMS
4.1. If a forcing function f(t) has the Laplace transform
f(s) = ; + es i2e
graph the function f(t). 4.2. Solve the following equation for y(t):  e3s
G(t) I0 y(M7 = dt
Y(O) = 1 4.3. Express the function given in Fig. P4.3 in the tdomain and the sdomain.
FIGURE P43 FURTHER
PROPERTIES
TRANSFORMS
4.4. Sketch the following functions: f(t) = u(t)  2u(t  1) + u(t  3) f(t) = 3tu(t)  3u(t  1)  u(t  2) 4.5. The function f(t) has the Laplace transform f(s) = (1  2eAS + ee2 j/s2 Obtain the function f(t) and graph f(t). 4.6. Determine f(t) at t = 1.5 and at t = 3 for the following function: f(t) = OSu(t)  OSu(t  1) + (r  3)u(r  2) THELAPLACETRANSFORM
Example 4.6. Solve the following equation for x(t): x(t)dt  t
x(0) = 3 Taking the Laplace theorem transform of both sides, and making use of the previous SX(S)  3 = +)  L s2 Solving for x(s), x(s) = 39  1 3s2  1 s(s2  1) = s(s + I)(s  1) This may be expanded into partial fractions according to the usual procedure to give 1 1 x(s) = f + +s+l Sl Hence, i(t) = 1 + eet + et The reader should verify that this function satisfies the original equation. PROBLEMS
4.1. If a forcing function f(t) has the Laplace transform
f(s) = f + ems ;2ep2s em3
graph the function f(t). 4.2. Solve the following equation for y(t): y(T)dT = 5 y(0) = 1 4.3. Express the function given in Fig. P4.3 in the tdomain and the sdomain.
FIGURE P43 FURTHER PROPERTIES OF TRANSFORMS
Sketch
following
functions: f ( t ) = u(t)  2u(t  1) + u(t  3) f(t) = 3tu(t)  3u(t  1)  u(t  2) 4.5. The function f(t) has the Laplace transform f(s) = (1  2emS + e2s)/s2 Obtain the function f(t) and graph f(t). 4.6. Determine f(t) at t = 1.5 and at t = 3 for the following function: f(t) = 054(t)  OSu(t  1) + (t  3)u(t  2) PART
LINEAR OPENLOOP SYSTEMS
CHAPTER 5 RESPONSEOF FIRSTORDER SYSTEMS
Before discussing a complete control system, it is necessary to become familiar with the responses of some of the simple, basic systems that often are the building blocks of a control system. This chapter and the three that follow describe in detail the behavior of several basic systems and show that a great variety of physical systems can be represented by a combination of these basic systems. Some of the terms and conventions that have become well established in the field of automatic control will also be introduced. By the end of this part of the book, systems for which a transient must be calculated will be of highorder and require calculations that are timeconsuming if done by hand. The reader should start now using Chap. 34 to see how the digital computer can be used to simulate the dynamics of control systems. TRANSFER
FUNCTION
MERCURY THERMOMETER. We shall develop the transfer function for a Jirst order system by considering the unsteadystate behavior of an ordinary mercury inglass thermometer. A crosssectional view of the bulb is shown in Fig. 5 !l . Consider the thermometer to be located in a flowing stream of fluid for which the temperature x varies with time. Our problem is to calculate the response or the time variation of the thermometer reading y for a particular change in x.* *In order that the result of the analysis of the thermometer be general and therefore applicable to other firstorder systems, the symbols x and y have been selected to represent surrounding temperature and thermometer reading, respectively.

