barcode reader integration with asp.net The parameter T is called the time constant of the system and has the units of time. in Software

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The parameter T is called the time constant of the system and has the units of time.
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The expression on the right side of Eq. (5.7) is called the transferfunction of the system. It is the ratio of the Laplace transform of the deviation in thermometer reading to the Laplace transform of the deviation in the surrounding temperature. In examining other physical systems, we shall usually attempt to obtain a transfer function. Any physical system for which the relation between Laplace transforms of input and output deviation variables is of the form given by Eq. (5.7) is called a jfirst-order system. Synonyms for first-order system are first-order lag and single exponential stage. The naming of all these terms is motivated by the fact that Eq. (5.7) results from a first-order, linear differential equation, Eq. (5.5). In Chap. 6 is a discussion of a number of other physical systems which are first-order. By reviewing the steps leading to Eq. (5.7), one can discover that the introduction of deviation variables prior to taking the Laplace transform of the differential equation results in a transfer function that is free of initial conditions because the initial values of X and Y are zero. In control system engineering, we are primarily concerned with the deviations of system variables from their steady-state values. The use of deviation variables is, therefore, natural as well as convenient. PROPERTIES OF TRANSFER FUNCTIONS. In general, a transfer function relates two variables in a physical process; one of these is the cause (forcing function or input variable) and the other is the effect (response or output variable). In terms of the example of the mercury thermometer, the surrounding temperature is the cause or input, whereas the thermometer reading is the effect or output. We may write Y(s) Transfer function = G(s) = X(s) where G(s) = symbol for transfer function X(s) = transform of forcing function or input, in deviation form Y(s) = transform of response or output, in deviation form The transfer function completely describes the dynamic characteristics of the system. If we select a particular input variation X(t) for which the transform is X(s), the response of the system is simply Y(s) = G(s)X(s)
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By taking the inverse of Y(s), we get Y(t), the response of the system. The transfer function results from a linear differential equation; therefore, the principle of superposition is applicable. This means that the transformed response of a system with transfer function G(s) to a forcing function X(s) = UlXl(S) + a2X2(s) where Xi and X2 are particular forcing functions and a i and u2 are constants, is Y(s) = G(s)X(s)
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= = alG(s)Xl(s) alYl(s> + + a2W)X,(s> a2Y2(s)
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Yi(s) and Y,(s) are the responses to X1 and X2 alone, respectively. For example, the response of the mercury thermometer to a sudden change in surrounding temperature of 10 F is simply twice the response to a sudden change of 5 F in surrounding temperature. The functional relationship contained in a transfer function is often expressed by a block-diagram representation, as shown in Fig. 5.2. The arrow entering the box is the forcing function or input variable, and the arrow leaving the box is the response or output variable. Inside the box is placed the transfer function. We state that the transfer function G(s) in the box operates on the input function X(S) to produce an output function Y(S). The usefulness of the block diagram will be appreciated in Chap. 9, when a complete control system containing several blocks is analyzed.
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TRANSIENT
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Now that the transfer function of a first-order system has been established, we can easily obtain its transient response to any forcing function. Since this type of system occurs so frequently in practice, it is worthwhile to study its response to several common forcing functions: step, impulse, and sinusoidal. These forcing functions have been found to be very useful in theoretical and experimental aspects of process control. They will be used extensively in our studies and hence, each one is explored before studying the transient response of the first-order system to these forcing functions.
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