Nonlinear system instrumentation

Nonlinearity In addition, it is well known that the process kinetics shows a highly nonlinear behavior. This a serious drawback in instrumentation and automatic control because, in contrast to linear systems where the observability can be established independently of the process inputs, the nonlinear systems must accomplish with the detectability condition depending on the available on-line measurements, including process inputs in the case of non autonomous systems [23]. 

Chemical and physical nonlinearities are caused by interactions among the components of a system. They include such effects as peak shifting and broadening as a function of the concentration of one or more components in the sample. Instrumental nonlinearities are caused by imperfections and/or nonideal behavior in the instrument. For example, some detectors show a... 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

A note of caution should be sounded here. Whilst the curves shown in Figure 6.5 are characteristic of many charged dispersions it should be recalled that once we apply a sinusoid to a non-linear system the response need not be a sinusoid. As the strain is increased into the nonlinear region, the waveform passing through the sample becomes progressively distorted. The instrumental analysis in this case involves... 

Photographic plates used in early instruments have now been abandoned because they are slow, non-reproducible and their response is nonlinear with ion intensity (low dynamic range). However, the principle of simultaneous detection is very attractive. Spark source Mattauch-Herzog spectrographs have long used this detection system. 

The probe has been long and successfully commercialised (see http //www.aber-instruments.co.uk) and since we have reviewed this approach on a number of occasions (e.g. Kell et al. 1990, Davey 1993a,b, Davey et al. 1993 a, b) we will not do so here, save to point out (in the spirit of this review) the trend to the exploitation of multi-frequency excitation for acquiring more (and more robust) information on the underlying spectra. [124, 125]. Most recently, we have also devised a number of novel routines for correcting for the electrode polarisation that can occur under certain circumstances [126, 127], and have turned our attention to the nonlinear dielectric spectra of biological systems. 

Mattson also found that the 1375-cm 1 peak had the largest analytical error of those peaks measured. Part of the reason is that the peak is so strong that its absorbance approaches 1 in a 0.05-mm cell and 2 in a 0.1-mm cell. According to Hannah (36), thick cells in optical null instruments give nonlinear absorbance. They are linear only up to absorbances of 0.8 to 1.0. Ratio recording systems, such as that used by Mattson, are... 

Measuring systems such as sensor arrays of nonselective sensors or sensors with nonlinear cross-sensitivities require different feedback calibration strategies and the choice of different calibration gases. This need not be discussed here, because detailed calibration instructions come with the measuring instrument. 

A comprehensive overview of frequency-domain DOT techniques is given in [88]. Particular instraments are described in [166, 347, 410]. It is commonly believed that modulation techniques are less expensive and achieve shorter acquisition times, whereas TCSPC delivers a better absolute accuracy of optical tissue properties. It must be doubted that this general statement is correct for any particular instrument. Certainly, relatively inexpensive frequency-domain instruments can be built by using sine-wave-modulated LEDs, standard avalanche photodiodes, and radio or cellphone receiver chips. Instruments of this type usually have a considerable amplitude-phase crosstalk". Amplitude-phase crosstalk is a dependence of the measured phase on the amplitude of the signal. It results from nonlinearity in the detectors, amplifiers, and mixers, and from synchronous signal pickup [6]. This makes it difficult to obtain absolute optical tissue properties. A carefully designed system [382] reached a systematic phase error of 0.5° at 100 MHz. A system that compensates the amplitude-phase crosstalk via a reference channel reached an RMS phase error of 0.2° at 100 MHz [370]. These phase errors correspond to a time shift of 14 ps and 5.5 ps RMS, respectively. 

Instrumental Factors. Unsatisfactory performance of an instrument may be caused by fluctuations in the power-supply voltage, an unstable light-source, or a nonlinear response of the detector-amplifier system. A double-beam system helps to minimize deviations due to these factors. In addition, the following instrumental sources of possible deviations should be understood ... 

---