Deadtime, problems

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

As it is clear from the above discussion, the deadtime problem is independent from the phase shift problem in their origins. They become related only when we attempt to eliminate the deadtime problem by adjusting the FID time origin so that tQ=0. This adjustment introduces a frequency dependent... 

Although FT NMR can become a major tool for wide line NMR spectroscopy, cw spectrometers will still be necessary to record spectra which are so broad that the deadtime is comparable to or greater than T2 from samples which do not give rise to echoes. In the frequency domain, this means that the (sinx)/x wiggles shown in the last figure will have frequencies and amplitudes comparable or greater than the peak itself, thus obscuring the desired spectrum. See IV. B. 3. and VI.D.4. for other pulse techniques to overcome the deadtime problem. 

Unfortunately, the solid echoes do not have nice physical explanations as does the Hahn echo. They are extremely useful, nevertheless, because they can overcome the deadtime problem and, in addition, can yield information which is otherwise difficult or impossible to obtain. The following discussion describes the properties and uses of echoes without detailed explanations. Original references (Lowe, 1957 Powles and Mansfield, 1962 Powles and Strange, 1963 Mansfield, 1965 Warren and Norberg, 1967), reviews (Boden, 1971), and applications (Boden, et al., 1975 a, b Moskvich, et al., 1975) should be consulted. 

Because the solid echo can reduce the deadtime problem, it can be used in conjunction with other pulse sequences to detect signals which are otherwise difficult to see. In particular, the solid echo sequence can be used in place of the monitoring pulse in any of the T sequences mentioned in Section III.D.2. 

Another problem in many NMR spectrometers is that the start of the FID is corrupted due to various instrumental deadtimes that lead to intensity problems in the spectrum. The spectrometer deadtime is made up of a number of sources that can be apportioned to either the probe or the electronics. The loss of the initial part of the FID is manifest in a spectrum as a rolling baseline and the preferential loss of broad components of... 

For a first order function with deadtime, the proportional gain, integral and derivative time constants of an ideal PID controller. Can handle dead-time easily and rigorously. The Nyquist criterion allows the use of open-loop functions in Nyquist or Bode plots to analyze the closed-loop problem. The stability criteria have no use for simple first and second order systems with no positive open-loop zeros. 

However, there are two practical problems with this ideal choice of the feedback controller C, y. First, it assumes that the model is perfect More importantly it assumes that the inverse of the plant model Cmo) physically realizable. This is almost never true since most plants have deadtime and/or numerator polynomials that are of lower order than denominator polynomials. 

A process has an openloop transfer function that is approximately a pure deadtime of D minutes. A proportional-derivative controller is to be used with a value of a equal to 0.1. What is the optimum value of the derivative lime constant Note that part of this problem involves defining what you mean by optimum. 

Fig. 21. The new five-pulse sequence for recording static 2H exchange spectra.51 The experiment differs from the simple three pulse sequence in Fig. 19 in the addition of r-90°-r (or A — 90° - A) echo sequences before the t and h periods to avoid spectral distortions caused by receiver deadtime and finite pulse width problems. The broader pulses are 90° pulses the narrower ones 54.7° pulses.

We want tight control of these important quantities for economic and operational reasons. Hence we should select manipulated variables such that the dynamic relationships between the controlled and manipulated variables feature small time constants and deadtimes and large steady-state gains. The former gives small closed-loop time constants and the latter prevents problems with the rangeability of the manipulated variable (control valve saturation t... 

Distributed Control Systems often sample the transmitted signal at a one-second interval, sometimes faster or slower depending on the characteristics of the process response. One concern related to sample data measurement is aliasing of the signal, which can shift the observed frequency. However, at a one-second sample interval, this has seldom been a problem for all but the fastest process responses. A general rule for good performance is to make the period between scans less than one-tenth of the deadtime, or one-twentieth of the lag in the process response. 

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... 

Experimental strategies for overcoming the common problems of sensitivity, probe deadtime and ringing, and broad resonance lines are discussed in Chapter 3. 

The performance of PID controllers suffers from several limitations disturbances, analyzer deadtime, process nonlinearity, constraints, windup, abrupt startup of a loop, and flow control over a wide operating range. This section addresses approaches that have been developed to improve the performance of PID controllers with respect to this set of control problems. 

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