Frequency domain specification

Since many closed-loop systems approximate to second-order systems, a few interesting observations can be made. For the case when the frequency domain specification has limited the value of Mp to 3 dB for a second-order system, then from equation (6.72)... 

The most useful frequency-domain specification is the maximum closedloop fog modulus. The phase margin and gain margin spedfications can sometimes give poor results when the shape of the frequency-response curve is unusual. 

Now we are ready to find the controller settings required to give various frequency-domain specifications with P, PI, and PID controllers. 

A PI controller has two adjustable parameters, and therefore we should, theoretically, be able to set two frequency-domain specifications and find the values of T/ and Kc that satisfy them. We cannot make this choice of specifications completely arbitrary. For example, we cannot achieve a 45 phase margin and a gain margin of 2 with a PI controller in this three-CSTR system. A PI controller cannot reshape the Nyquist plot to make it pass through both the ( — y/l, 5 Jl) point and the (-0.5,0) point because of the loss of phase angle at low frequencies. 

They can be expressed either as functions of frequency, called frequency domain specifications, or as functions of time, called time domain specifications. To develop the specifications the mathematical equations have to be solved. Modern computer software, such as MATLAB (e.g., Kuo 1995), has provided convenient tools for solving the equations. 

D-Tool an environment to facilitate the design/testing of conventional control strategies within MATLAB. It can handle single input single output processes and includes time domain and frequency domain specifications for control system design. 

A chart for vibration diagnosis is presented in Table 19-9. While this is a general criterion or rough guideline for diagnosis of mechanical problems, it can be developed into a very powerful diagnostic system when specific problems and their associated frequency domain vibration spectra are... 

A frequency-domain vibration signature is generally used for the analysis because it is comprised of discrete peaks, each representing a specific vibration source. 

The frequency-domain, or TFT, signature acquired at each measurement point is an actual representation of the individual machine-train component s motion at that point on the machine. Without knowing the specific location and orientation, it is difficult - if not impossible - to correctly identify incipient problems. In simple terms, the TFT signature is a photograph of the mechanical motion of a machine-train in a specific direction and at a specific point and time. 

In the time domain, a wavelet placed at a translation point, u, has a standard derivation, o- , around this point. Similarly, in the frequency domain a wavelet is centered at a given frequency, w (determined by the value of the dilation parameter) and has a standard deviation, cr, around the specific frequency. The values of a- and o- are given by... 

Yamaguchi, S. and Tahara, T. (2005) Interface-specific coherent raman spectroscopy in the frequency domain. 

There are many specific ways to generate equally spaced tags but they are all based on the same principle of manipulating the rf pulses to generate equally spaced bands of rf radiation in the frequency domain. It is well known that under ordinary conditions, meaning normal levels of nuclear spin excitation, the frequency spectrum of the rf excitation pulse(s) is approximately the Fourier transform of the pulses in the time domain. Thus, a single slice can be generated in the... 

Figure 20 Timing diagram of the suggested 2y,3y-HMBC experiment, including a LPJF3 for efficient 1JCH suppression. The sequence is virtually identical to the CIGAR-HMBC pulse sequence. The STAR operator is also a constant-time variable element. In this fashion, scalable F, modulation can be specifically introduced for 2JCH cross-peaks into the spectrum independently of the digitization employed in the second frequency domain.

There are two basic types of specifications that are commonly used in the frequency domain. The first type [phase margin and gain margin) specifies how near the openloop polar plot is to the critical (—1,0) point. The second... 

Another important insight gained from the frequency-domain analysis is the optimal shape of the modulation that reduces the decoherence rate. Given a specific coupling spectrum, one should choose a modulation so as to decrease the overlap between the modulation and coupling spectra [29]. This optimal... 

After processing in the time domain, Fourier transformation, phasing and basic processing (calibration, peak picking, integration) ahs been performed, additional processing steps to improve spectral quality are at your disposal. This includes operations common to both ID and 2D spectra e.g. baseline correction in the frequency domain, as well as operations specific to these different type.s of data sets. 

Fourier transformation of (10.13) and (10.14) to the frequency domain yields energy spectral densities, specifically... 

The preceding analysis views the problem of solving for the sine-wave amplitudes and phases in the frequency domain. Alternatively, the problem can be viewed in the time domain. It has been shown that [Quatieri and Danisewicz, 1990], for suitable window lengths, the vectors a andJ3 that satisfy Equation (9.75) also approximate the vectors that minimize the weighted mean square distance between the speech frame and the steady state sinusoidal model for summed vocalic speech with the sinusoidal frequency vector . Specifically, the following minimization is performed with respect to a andJ3... 

Stored waveform inverse Fourier transform (SWIFT) pulses [17] have been applied as a means of broadband ejection of matrix ions generated by Cs+ desorption [18]. These pulses are generated by taking the inverse Fourier transform of the desired frequency domain spectrum and applying the stored time domain waveform to the endcap electrodes via an arbitrary waveform generator. The magnitude of the SWIFT pulse determines the degree of excitation for ions of specific secular frequencies. 

The matter of sampling and limited representation of frequencies requires a second look at the representation of data in the time and frequency domains, as well as the transformation between those domains. Specifically, we need to consider the Fourier transformation of bandwidth-limited, finite sequences of data so that the S/N enhancement and signal distortion of physically significant data can be explored. We begin with an evaluation of the effect of sampling, and the sampling theorem, on the range of frequencies at our disposal for some set of time-domain data. 

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