Frequency domain approach

However, a eontrol structure must be chosen, controllers must be tuned, and a series of disturbances must be specified. The closedloop system is then simulated, and the capacity factors are calculated for each design. Using dynamic simulation can require a lot of computer time. In Chapter 10 we describe how the procedure can be made much easier and quicker using a frequency-domain approach. 

Clearly, the final MDS diagram is partially dependent on the parameters of the noise imposed on the system. It is possible that frequency domain approaches to time series analysis [10] may help in a study of the role of frequency transfer functions in the control of chemical networks. We have assumed that all species involved in the mechanism may be identified and measured. For systems with many species this may be difficult. When there are missing species, CMC may still be performed on the measurable subset of species. The effects of the other species are subsumed into the correlations among the known species, and a consistent diagram can be constructed. The MDS diagram, then, may not be an obvious representation of the underlying mechanism. In fact, due... 

Besides the aforementioned time-domain approaches, many frequency-domain methods have also been developed and widely used. Examples are the complex curve fitting method [153], the maximum entropy method [4,263], the pole/zero assignment technique [271], the simultaneous frequency-domain approach [62], the rational fraction polynomial approach [219], the orthogonal polynomial approach [264], the polyreference frequency-domain approach [73], the multi-reference simultaneous frequency-domain approach [64] and the best-fit reciprocal vectors method [173]. 

In this chapter, the Bayesian spectral density approach, which is a frequency-domain approach, for modal/model updating using wide-band response data is presented. It utilizes the statistical properties of the spectral density estimator to obtain not only the optimal values of model parameters but also their associated uncertainty by means of the updated probability distribution of the uncertain parameters. Uncertainty quantification is important for many applications, such as damage detection and reliability analysis. 

S. Bittanti, G. Pronza, and G. Guardabassi. Periodic control A frequency domain approach. IEEE Trans. Auto. Cont., AC-18(l) 33-38, 1973. 

Two widely used approaches are used for lifetime measurements, the time-domain approach and the frequency-domain approach. In time-domain measurements, a pulsed source is employed and the time-dependent decay of fluorescence is measured. In the frequency-domain method, a sinusoidally modulated source is used to excite the sample. The phase shift and demodulation of the fluorescence emission relative to the excitation waveform provide the lifetime information. Commercial instrumentation is available to implement both techniques. "... 

In order to present briefly the frequency domain approach it should be observed that any linear time invariant control law can be written as... 

Karden, E., S. Buller, and R. W. De Doncker. 2002. A frequency domain approach to dynamical modeling of electrochemical power soiux es. Electrochimica Acta, 47, 2347-2356. 

In this paper the authors describe experiments which compare time domain and frequency domain approaches to the estimation of the four linearised damping coefficients associated with a squeeze-film vibration isolator. It is shown that while both algorithms satisfy a least-squares error criterion, the resulting coefficients can have quite different numerical values. Whilst the feasibility of both techniques has now been clearly established it is concluded that further work is required to ensure a more direct comparison. 

Discrepancies between numerical values of the estimated damping coefficients is shown in Table I. The frequency domain approach invariably produced an indication of strong cross-coupling terms which was not confirmed either by the time-domain results or by direct observation of the damper ring response. The authors believe that the squeeze-film was probably over-excited during the frequency domain tests and consequently driven out of the linear regime. The presence of significant nonlinear stiffness effects in the squeeze-film could account for the discrepancies which have been observed. 

The results presented in the paper extend previous work in that the feasibility of employing a frequency domain filter has been demonstrated. However further work (preferably using common data) is still required to provide a direct comparison between the time and frequency domain approaches. 

A gravity dam-reservoir system is selected for studying the interaction of structure-fluid systems under nonstationary random excitation. For an idealized random excitation with a zero start and a white power spectrxjun, the nonstationary power spectral density for the structural displacement is obtained by a frequency domain approach due to Shinozuka. The spectral density functions are then integrated to check the transient variance solution obtained previously by a time domain approach. Using this power spectral solution the random interaction effect is examined for the entire frequency range in detail. This interaction problem of the structure-fluid system is important because it simulates random and time dependent structural response to earthquake ground accelerations. 

The displacement response Y Ct) to the idealized nonstationary random excitation of ground acceleration Ug(t) with white spectral density Sq defined in Appendix B can be obtained in terms of the nonstationary power spectral density SY (t,a>) by the frequency domain approach originated by Shinozuka [2] and applied to simple structures by Yang [5], p. 244. For the simplified random excitation with Heaviside unit step time modulation function A(t,w) - 1 for t - >0, A(t,w) 0 for t < 0, the simple input-output relation in the frequency domain is... 

Nonstationary power spectral density functions for the displacement response of a dam reservoir system subjected to a simple but nonstationary random acceleration excitation are obtained by a frequency domain approach due to Shinozuka. These spectral response solutions are new and are checked satisfactorily in the limiting stationary case and against the corresponding solution obtained previously by a time domain approach. For the range of frequency ratio Oj- representing dam reservoir interaction effect, it is found that the displacement spectral peak value increases with increasing dam flexibility. The location of the spectral peak is at a nearly constant value of f2Qj- (w/o) ) (c x/ s) 0.6, which means that the peak spectral response is at... 

In principle, the technique can also be extended to the fitting of pulsed EPR spectra using the frequency domain approach [62]. Each peak in the ESEEM spectrum is given by one or more frequencies, a complex intensity, and a linewidth. Derivatives of the ESEEM frequencies with respect to each of the spin Hamiltonian parameters can be calculated and utilized in an identical fashion to that used for CW spectra simulations. 

Hu, R., Kazimi, M.S., 2012. Boihng water reactor stabdity analysis by TRACE/PARCS modeling effects and case study of time versus frequency domain approach. Nuclear Technology 177, 8—28. 

In theory, ambient modal identificadmi can be performed in either the time domain or the frequency domain. In practice, however, a frequency domain approach is preferable because it allows a natural partitioning of information in the data for identifying the modes of interest It sigifificantly simplifies the identification model because it only needs to model the modes in the selected band. For well-separated modes, one can select the band to cover one mode only, so that it can be identified independently of other modes. In general, the number of modes in the identification model only needs to be equal to the number of closely spaced modes, which rarely exceeds three. In the Bayesian formulation, this does not require any band-pass filtering because it can be done by simply omitting the FFT data of the excluded bands from the likelihood function. 

Pintelon, R. Schoukens, J. (2001). System Identification - A Frequency Domain Approach, IEEE Press. 

In any case, taking into account both time-domain and frequency-domain techniques, there are basically four methods to measure the lifetime of an excited state, as described in detail in the next Sect. 7.2. The first three methods use the time-domain approach to rebuild the intensity-time curve the fourth one uses the frequency-domain approach and is based on the phase shift between excitation and emission. 

Although the coolant flow in the Super LWR is single-phase, the coolant enthalpy and therefore the density change substantially in the core because the coolant flow rate per thermal power in the Super LWR core is less than one eighth of LWR cores. Thus, the Super LWR can be susceptible to flow oscillations as the BWRs are. In Sect. 5.4, thermal hydraulic stability of the Super LWR is analyzed with the frequency domain approach. The analysis includes both supercritical and subcritical pressure conditions. 

There are two types of approaches used in stability analyses a time domain approach and a frequency domain approach. 

In the time domain approach, the purpose is to simulate the transient behavior of the reactor plant system. The governing equations, which describe the physical phenomena of the reactor dynamics system, are integrated in the time domain. This approach permits the considerations of detailed physical mechanisms, including nonlinear features. It does not need simplified assumptions and can provide information on the behavior of the reactor system beyond the stability threshold. However, a much longer time is necessary to calculate the extensive number of time steps than the frequency domain approach. 

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