Apparent deadtime

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 filter adds lag and, because it increases the order of the system, also increases the apparent deadtime. Adding a filter after a controller has been tuned is therefore inadvisable. Either the plant test should be repeated to identify the new dynamics or, if the model identification package permits it, the original test data may be used with the filter simulated in the package. 

When T is varied the echo envelope is modulated only by the two basic frequencies CDa and (Up, the sum and difference frequencies do not appear, in contrast to the two-pulse ESEEM experiment. This is usually advantageous, as it simplifies spectra, but it may also be a disadvantage for disordered systems where the sum-combination line is often the only narrow feature in the ESEEM spectrum. Another important difference is the dependence of the three-pulse ESEEM amplitudes on r, as is apparent from Eq. (17) by the factors 1 - cos(copr) and 1 - cos(cOcir). Due to this suppression effect, individual peaks in the spectrum can disappear completely. These blind spots occur for the a(P) peak when r = 2n /(Up(a) (k = 1, 2,. ..). In principle they can be avoided by using r < Inlco, where (Umax is the maximum nuclear frequency however, this is usually precluded by the spectrometer deadtime. Consequently, the three-pulse ESEEM experiment has to be performed at several r values to avoid misinterpretation of the spectra due to blind-spot artifacts. 

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