Effect of Deadtime

Deadtime in a sampled-data system is very easily handled, particularly if the deadtime D is an integer multiple of the sampling period T,. Let us assume that 

Consider an arbitrary functionThe original function), ) before the time delay is assumed to be zero for time less than zero. Running the delayed function through an impulse sampler and z-transforming give 

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Remember that in a continuous system, the presence of deadtime made the phase angle go to — c as to went to oo. So the effect of deadtime on the Nyquist plots of sampled-data systems is difTerent than its effect in continuous systems. 

The effect of deadtime on the random error leads to the question of whether there is a counting rate that provides the best precision in estimating the true counting rate at the detector. The relative precision in the calculated true counting rate arising from the random error is given by Eqs. (4.137) and (4.138) and is plotted in Fig. (4.55). 

Dynamic fundamentals The importance of designing processes and establishing loop pairing to minimize undesirable dynamics in a feedback loop is obvious to an engineer who xmderstands the effects of deadtime, multiple lags and inverse response on the stability and performance of a closedloop system. 

Figure 13.20 shows the closedloop servo transfer function Bode plots for P and PI controllers with the ZN settings for a deadtime of 0.5 min. The effect of... 

In Chap. 15 we reviewed a tittle matrix mathematics and notation. Now that the tools are available, we will apply them in this chapter to the analysis of multivariable processes. Our primary concern is with closedloop systems. Given a process with its matrix of openloop transfer functions, we want to be able to see the effects of using various feedback controllers. Therefore we must be able to find out if the entire closedloop multivariable system is stable. And if it is stable, we want to know how stable it is. The last question considers the robustness of the controller, i.e., the tolerance of the controller to changes in parameters. If the system becomes unstable for small changes in process gains, time constants, or deadtimes, the controller is not robust. 

If the process contains a significant amount of deadtime, your intuition might tell you that a sampled-data controller might possibly give better control than a continuous controller because it might make sense to wait a little after the manipulated variable has been moved to see what its effect has been. In this section we will explore this interesting idea. 

Fourier transforming this gives the FT of the FID (i.e. the expected spectrum) convoluted with sinc((rt-o)o)tdead, the latter manifested as a rolling of the baseline. An example is shown in Figure 3.9A. The effect of this deadtime-induced baseline roll is not a significant problem if the spectral lines are narrow compared to the frequency of the... 

Since deadtimes in this type of spectrometer are quite long ( 60 fis), the system must normally operate with deadtime losses in the 10 to 60% range. Consequently, most multichannel analyzers are equipped with an electronic means of deadtime correction, such that the observed spectrum represents the true number of photons arriving at the detector during the period of data accumulation. In addition to the ability to display the spectrum on a cathode-ray tube or television monitor, the analyzer can usually drive an X-Y plotter to produce a permanent copy. Alternatively, the contents of the analyzer memory can be printed as the number of counts in each channel, listed by channel number. Most quantitative fluorescence spectrometers include a personal computer with approximately 2-6 megabytes of memory plus some form of mass storage. In such a system the computer may control specimen presentation, the excitation conditions, and data accumulation in the multichannel analyzer. At the end of data acquisition for each specimen the computer analyzes the spectrum in the multichannel analyzer, computes the raw element intensities, corrects for interelement effects, and computes the concentration of each element. 

Product concentration can be controlled by measuring a number of physical properties. On-stream composition analyzers are often used. Commonly used physical properties include density, boiling point rise, temperature/pressure combinations, temperature difference, conductivity, differential pressure, refractive index, buoyancy float, and viscosity. Each method has certain advantages as well as limitations. In all cases, however, a representative measurement location must be carefully selected to eliminate entrained air bubbles or excessive vibration, and the instrument must be mounted in an accessible location for cleaning and calibration. The location of the product quality transmitter with respect to the final effect should be considered also. Long piping runs between the product and the instrument increase deadtime, which in turn reduces the effectiveness of the control loop. 

The window shown on the left-hand side of Figure 4.44 opens and a value of the deadtime is entered. We will look at the effect of deadlime by using values of 2 and 5 min. 

We can omit the lag term when characterising the process dynamics of an integrating process. Although the process is just as likely to include a lag, this manifests itself as deadtime. Figure 2.19 illustrates the effect of adding lag to the PV. In this case a lag of 3 minutes has caused the apparent deadtime to increase by about the same amount. After the initial response the PV trend is still a hnear ramp. We can thus characterise the response using only Kp and 6. 

The residence time was determined for our neutron counter by measuring the time intervals between beta start signals and neutron stop signals. With a residence half-time of 11 ms and a coincidence resolving time of 40 ms. 92 of the true coincidence events were included. The fraction of true events not detected does not influence the present results because we normalize the Pn measurements to a known Pn value measured under identical conditions. The coincidence rate was measured by a simple overlap coincidence module where the beta pulse Input was stretched to 40 ms by a gate and delay generator. To measure the accidental coincidence rate, the same beta pulse was sent to a second coincidence module and overlapped with neutron pulses which had been delayed 45 ms. After correcting each coincidence rate for deadtime effects, the difference was the true coincidence rate. 

The second difference is the dynamic response to disturbances or changes in manipulated variables. In a perfectly mixed CSTR, a change in an input variable has an immediate effect on variables in the reactor. In a tubular reactor it takes time for the disturbance to work its way through the reactor to the exit. Therefore there are very significant dynamic lags and deadtimes between changes made at the inlet of the reactor and... 

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