Include a first-order time lag in the temperature measurement, using the [Pg.508]

In an ideal first-order system, only one capacity causes a time lag between the measured quantity and the measurement result. Typically, an unshielded thermometer sensor behaves as a first-order system. If this sensor is rapidly moved from one place having temperature Tj to another place of temperature T2, the change in the measured quantity is close to an ideal step. In such cases, the sensor temperature indicated by the instrument has a time histoty as shown in Fig. 12.13. [Pg.1133]

L(f(c)) = e-tDS Hence for a single first-order lag with time delay [Pg.85]

Figure 2.23. Fitting of measured response to a first-order lag plus time delay. |

Example 8.6. What are the Bode and Nyquist plots of a first order lag with dead time [Pg.152]

If C > 1, show that the system transfer function has two first-order lags with time constants r,i and. Express these time constants in terms of Tj, and . [Pg.332]

Higher-Order Lags If a process is described by a series of n first-order lags, the overall system response becomes proportionally slower with each lag added. The special case of a series of n first-order lags with equal time constants has a transfer function given by [Pg.723]

There are, however, other options for treating data from both first- and second-order kinetics. Collectively, they are known as time lag methods. These methods are primarily of historical interest, although the mathematical rearrangements provide insights into the nature of the functions involved. [Pg.26]

K and KH in (2-49a) are referred to as gains, but not the steady state gains. The process time constant is also called a first-order lag or linear lag. [Pg.33]

Experience has shown, that most chemical processes can often be modelled by a combination of several first-order lags in series and a time delay (Fig. 2.22). [Pg.85]

This particular type of transfer function is called a first-order lag. It tells us how the input affects the output C/, both dynamically and at steadystate. The form of the transfer function (polynomial of degree one in the denominator, i.e., one pole), and the numerical values of the parameters (steadystate gain and time constant) give a complete picture of the system in a very compact and usable form. The transfer function is property of the system only and is applicable for any input. [Pg.317]

For a better fit of the system response, the method of Oldenbourg and Sartorius, as described in Douglas (1972), using a combination of two first-order lags plus a time delay, can be used. The method is illustrated in Fig. 2.24. and applies for the case [Pg.86]

Thus as shown previously in Sec. 2.1.1.1, if the step response curve has the general shape of an exponential, the response can be fitted to the above first-order lag model by determining x at the 63% point. The response can now be used as part of a dynamical model, either in the time domain or in Laplace transfer form. [Pg.82]

The reflection of characteristic X-rays described in this note seems to be reasonably well explained by the assumption (mentioned in our first paper) that a primary X-ray excites secondary, characteristic X-rays in atoms, with a certain time lag, approximately the same for all atoms of one kind. It is not necessary to assume that the primary ray has wave-lengths, but only that it must have been produced by a voltage above certain critical values. If the secondary rays have wave-lengths they will interfere and produce beam s in the required directions. This point of view, however, does not appear to be compatible with the law of the conservation of energy-applied to the processes going on in individual atoms. [Pg.5]

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. [Pg.436]

The two most common temporal input profiles for dmg delivery are zero order (constant release), and half order, ie, release that decreases with the square root of time. These two profiles correspond to diffusion through a membrane and desorption from a matrix, respectively (1,2). In practice, membrane systems have a period of constant release, ie, steady-state permeation, preceded by a period of either an increasing (time lag) or decreasing (burst) flux. This initial period may affect the time of appearance of a dmg in plasma on the first dose, but may become insignificant upon multiple dosing. [Pg.224]

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. [Pg.372]

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