Frequency response experimental data

Basic Principles for Treatment of Frequency Response Experimental Data. 242... 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

One of the most useful and practical methods for obtaining experimental dynamic data from many chemical engineering processes is pulse testing. It yields reasonably accurate frequency-response curves and requires only a fraction of the time that direct sine-wave testing takes. 

The numerator is the Fourier transformation of the time function The denominator is the Fourier transformation of the time function m, . Therefore the frequency response of the system G(j ) can be calculated from the experimental pulse test data x, and as shown in Fig. 14.3. 

H-n.m.r. [71], quasi-elastic neutron scattering [72], frequency response [73] and piezometric sorption uptake [34]. On the other hand, theself-consistency of data reported in [4,39,66,67] suggests further analysis of phenomena, probably interfered with bothithe samples and the experimental techniques used. 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

Summarizing, it is demonstrated that the developed model correctly reproduces the general trends in various experimentally measured responses, which include cuts of time- and frequency-gated spectra at particular frequencies, peak-shifts of the fluorescence spectra, and integral signals. Moreover, the relative shapes and intensities of the spectral cuts at different frequencies are correctly reproduced. For a more complete and quantitative description of the experimental data, the theoretical model has to be augmented by including additional system and/or solvation modes. 

No simple combination of resistors correctly models the phase angle and current response of Zf at all frequencies, but it can be modeled at any single frequency by a resistor and capacitor arranged either in series or in parallel. This effective impedance, now termed the Warburg impedance (Zw), is a function of frequency and can be extracted from experimental data either numerically or... 

The results show the transient effects due to a 15 kW step decrease to the generator (from 60 to 45 kW), which occurred at time zero. Figure 8.13 compares the dynamics of the shaft speed and shows that both models are in good agreement with the experimental data with regards to frequency. This is not surprising since the system volume will have the primary influence on the frequency response, and the mod-... 

A. Previous models of water (see 1-6 in Section V.A.l) and also the hat-curved model itself cannot describe properly the R-band arising in water and therefore cannot explain a small isotope shift of the center frequency vR. Indeed, in these models the R-band arises due to free rotors. Since the moment of inertia I of D20 molecule is about twice that of H20, the estimated center of the R-band for D20 would be placed at y/2 lower frequency than for H20. This result would contradict the recorded experimental data, since vR(D20) vR(H20) 200 cm-1. The first attempt to overcome this difficulty was made in GT, p. 549, where the cosine-squared (CS) potential model was formally (i.e., irrespective of a physical origin of such potential) applied for description of dielectric response of rotators moving above the CS well (in this work the librators were assumed to move in the rectangular well). The nonuniform CS potential yields a rather narrow absorption band this property agrees with the experimental data [17, 42, 54]. The absorption-peak position Vcs depends on the field parameter p of the model given by... 

Fig. 8.32. Bode plot showing experimental data and best and fit to the short circuit IMPS response of a dye sensitized cell. Dc photocurrent 6.3 mA. The upper solid line in each plot shows the fitted response in the absence of RC attenuation. Note the limiting high frequency phase shift is 45°, which is characteristic of diffusion control. The lower line illustrates the improved fit obtained by including the influence of r n. R = lOfl, C = 5 x 10 F.

When written with the help of the Tl matrix as in (19), from (20) the OR parameter and other linear response properties are seen to afford singularities where co = coj, just like in the SOS equation (2). Therefore, at and near resonances the solutions of the TDDFT response equations (and response equations derived for other quantum chemical methods) yield diverging results that cannot be compared directly to experimental data. In reality, the excited states are broadened, which may be incorporated in the formalism by introducing dephasing constants 1 such that o, —> ooj — iT j for the excitation frequencies. This would lead to a nonsingular behavior of (20) near the coj where the real and the imaginary part of the response function varies smoothly, as in the broadened scenario at the top of Fig. 1. 

We have performed optically heterodyne-detected optical Kerr effect measurement for transparent liquids with ultrashort light pulses. In addition, the depolarized low-frequency light scattering measurement has been performed by means of a double monochromator and a high-resolution Sandercock-type tandem Fabry-Perot interferometer. The frequency response functions obtained from the both data have been directly compared. They agree perfectly for a wide frequency range. This result is the first experimental evidence for the equivalence between the time- and frequency-domain measurements. 

In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and NMR lineshape analysis. 

The experimental data was fitted, as shown in Fig. 5.10, to a convolution of this response function with the instrument response function. As the result, the decay time T-2/2 was estimated to be 1.1 0.1 ps. Recently, the population lifetime Ti of G-phonons was measured by incoherent time-resolved anti-Stokes Raman scattering and the lifetime was found to be 1.1-1.2 ps in semiconducting SWNTs [57]. Therefore, one can reasonably assume ipu Ti at room temperature. This result is consistent with the conventional Raman line width of semiconducting SWNTs [58]. The observed short lifetime of the G-phonons implies anharmonic mode coupling between G-phonons and RBM-phonons [59]. In fact, a frequency modulation of the G mode by the RBM has been reported, suggesting the anharmonic coupling between these vibrations [56]. 

The reactive system shown in Table 16.1(b) may be considered to be an example of a class of systems for which, at the zero-frequency or dc limit, the resistcmce to passage of current is finite, and current can pass. Many electrochemical and electronic systems exhibit such nonblocking or reactive behavior. Even though the impedance response of the systems represented in this chapter is extremely simple as compared to that of t)q)ical electrochemical and electronic systems, the blocking and nonblocking systems comprise a broad cross-section of electrochemical and electronic systems. The concepts described can therefore be easily adapted to experimental data. 

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