Frequency response technique

A frequency response technique was tried first and some results were received. The useful frequency domain was less than one order of magnitude, while in electrical problems five orders of magnitude can be scanned. The single pulse technique was more revealing, but evaluation by moments had the usual accumulation of errors. Fourier transform of the pulse test results was the final method. 

The role of the support on hydrogen chemisorption on supported rhodium catalysts was studied using static and frequency response techniques. In all Instances, several klnetlcally distinct H2 cheml-sorptlve sites were observed. On the basis of the kinetics, at least one site appears to sorb H2 molecularly at temperatures below 150°C, regardless of the support. At higher temperatures, a dissociative mechanism may become dominant. Inducement of the SMSI state In Rh/T102 does not significantly alter Its equilibrium H2 chemisorption. 

Process design modifications usually have a bigger impact on operability (dynamic resilience). Dynamic resilience depends on controller structure, choice of measurements, and manipulated variables. Multivariable frequency-response techniques have been used to determine resilience properties. A primary result is that closed-loop control quality is limited by system invertability (nonmin-imum phase elements). Additionally, it has been shown that steady-state optimal designs are not necessarily optimal in dynamic operation. 

As an alternative approach to conventional uptake measurements, in the frequency response technique [44-48] one follows the response of the sample to a regular periodic perturbation, e.g. a sinusoidal variation of the system volume. Using complex notation, one may write for the time dependence of the system volume,... 

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. 

Fig. 18. Self-diffusion coefficients of benzene in NaX at 458 K PFG NMR, O (97) and (92) (JENS, A (13) deduced from NMR lineshape analysis, (10). Comparison with nonequilibrium measurements T, sorption uptake with piezometric control (93) , zero-length column method (96) o, frequency-response and single-step frequency-response technique (98). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

Characterisation of acid sites in decationated zeolites Study of NH3 sorption by frequency-response technique and FTIR spectroscopy... 

Careful determinations of the axial Peclet number using a frequency response technique will be found in ... 

Since World War II, frequency response techniques have been applied to an increasing variety of control problems, and although the bulk of progress prior to the war came from treating servomechanisms, there has been heightened effort in process control problems since the war. The works of Rutherford (R3), Aikman (Al), and Young (Yl) in Great Britain have been notable in this respect. 

Fortunately, frequency response techniques are applicable with... 

R.R. Hudgins in "Catalytic Dehydration of Ethanol using a Frequency Response Technique". Thesis, Princelon Univ, N.J., June, 1964. 

The frequency response technique for studying catalytic adsorption phenomena is an important experimental method. There is every indication from the existing literature that its importance will increase in the future. 

In order to illustrate why the sinusoidal input or frequency response technique is the most applicable in a gas-catalyst system with wide distributions in adsorption rates, a review of the tools of process dynamics and their application to adsorption studies is in order. 

We have examined the frequency response technique for its utility in the area of distinguishing different adsorption sites. This sinusoidal forcing technique has yielded surprisingly interesting results. There is... 

Equations (A-22) and (A-23) contain a remarkable discovery, namely, that free volume measurements are unnecessary for obtaining meaningful information by the frequency response technique. Heretofore, when... 

Design of Feedback 18 Control Systems Using Frequency Response Techniques... 

We can use frequency response techniques (see Chapter 17) to identify experimentally a poorly known process. Do you have any ideas on how you could do it To help you in your thoughts, consider the Bode diagrams of various systems that were examined in Chapter 17. Notice the information provided by characteristics such as the corner frequency (determines the unknown time constant), the level of low-frequency asymptotes (determines the value of static process gains), the slope of high-frequency asymptotes (determines the order of a system), and the behavior of phase lag (keeps increasing for systems with dead time). Note For further details, consult Ref. 11.)... 

Economics in process control, 3, 10-11, 15, 26, 532-34 Environmental regulations, 3 Equal-percentage valve, 254, 255 Equations of state, 57 Equilibria, 56, 78 chemical, 56 phase, 56-57, 71, 75, 78 Error criteria (see Time integral criteria) Euler s identities, 131-32, 149 Experimental modeling, 45, 656 frequency response techniques, 668 process identification, 657-62 time constant determination, 228, 232 Exponential function, 130 approximations, 215-16 Laplace transform, 130 z-transform, 592... 

In a recent development of the frequency response technique Bourdin et al. applied the frequency response approach to their IR temperature measurement system [35-37]. In this experiment the volume of the system is perturbed sinusoidally and both the pressure and temperature responses are measured. It was found that the phase differences between the pressure and temperature were more reliable and reproducible than the phase differences between the pressure and the volume. The explanation seems to be that since the quantity of adsorbent is quite small, a small amount of superficial adsorp-... 

The frequency response technique is a quasi-steady state relaxation technique in which a system in equilibrium is perturbed slightly by a rapid, periodic change in a property of the system which disturbs the equihbrium. The adjustment of the system to the new equihbrium is followed and characterised by one or more relaxation times. The response of a parameter characteristic... 

Accessories necessary for DRIFT measurements are described in the literature and in part are commercially available [174-176]). However, reflectance equipment maybe also conveniently made in the laboratory using commercial lenses and mirrors [177]. An interesting new combination of DRIFT spectroscopy with the frequency response technique was recently developed and tested by Harkness et al. [178]. This enables one to measure simultaneously the dynamic responses of both the gas and adsorbate, which should be of great potential for the study of heterogeneous catalysis. A cell for fast response DRIFT spectroscopy is described in Ref. [178]. 

More recently, essentially the same technique as proposed by Hermann et al. [944,945], viz. FTIR microscopy (Fourier transform micro-IR spectroscopy on single crystals), and by Mirth and Lercher [815], was successfully employed by Zhobolenko and Dwyer [949], who determined the transport diffusivities of a number of hydrocarbons (benzene, toluene, p-xylene, cyclohexane) in sili-calite-1 in different crystallographic directions. No significant differences of the diffusivities in the straight and sinusoidal channels of the structure were found (cf. Fig. 54), at remarkable variance to results reported by Rees et al., who used the frequency response technique [950] and found significant differences for the diffusion coefficients in both types of channels, viz. one order of magnitude smaller ones for the sinusoidal than for the straight channels. 

In the frequency response technique the volume is periodically increased and decreased in square waves, and the response of the pressure measured and analysed in terms of Fick s laws under equilibrium conditions. It has the twin advantages of being applicable over a wide frequency range and being able to distinguish between independent kinetic processes. As a result, it appears to show close agreement with microscopic processes, because it can resolve the effects on different length scales. 

Vardar, E, and Lilly, M.D. (1982), The measurement of oxygen-transfer coefficients in fermenters by frequency response techniques, Biotechnology and Bioengineering, 24(7) 1711-1719. 

Yasuda, Y. and Sugasawa, G., A frequency response technique to study zeolitic diffusion of gases, J. Catal. 88, 530-534, 1984. 

White C, Whittingham B, Li HC, Herszberg I, Mouritz AP. Comp. Struct.. 2009, 87, 175-181. Damage detection in repairs using frequency response techniques. 

Because the second-order process in this example overdamped ( = 1.19), we expect that sinusoidal perti -bations in the reactor temperature always will be atten ated (reduced in amplitude) in the measurement syste regardless of the frequency of the perturbation. Furth discussion of sinusoidal forcing is contained in Chapter on frequency response techniques. 

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