Identification second order parameters

Under suitable simplifying assumptions, a kinetic mechanism based on 13 components and 89 second-order reactions is developed. The relevant kinetic parameters (preexponential factors, activation energies, and heats of reaction) are computed on the basis of literature information. In the subsequent chapters, this kinetic model is used to test the techniques for identification, thermal stability analysis, control, and diagnosis of faults presented. 

Vibrational spectroscopy (ATR-FTIR, IRRAS, Raman) Identification of interfacial molecules orientational order (second-rank order parameter S )), and conformational order. ATR-FTIR restricted to the ATR-crystal/fluid interface. 

Saturation of controllers, 247, 257, 637 Scheduling computer control, 33 Secondary loop, cascade control, 395, 397, 398-99, 400-2 Secondary measurements, 16, 16-18 Second-order system, 186-87 Bode diagrams, 328-30 with dead time, 215, 216 discrete-time model, 585-86 dynamic characteristics, 187-93 experimental parameter identification, 233,668... 

To tackle the difficulty of the identification of the FR spectra, Do and co-workers have developed non-linear frequency response models for both isothermal and nonisothermal systems by using the concept of higher-order FRFs [23,31-33]. By applying the second order FRFs, these theoretical models are able to give unique FR spectra for the multi-kinetic mechanisms occurring in microporous material systems [33]. More parameters have to be measured experimentally, however, which needs a more complex apparatus, and there are no experimental data available yet to test the proposed models. 

The easiest way for identification is the comparison of the spectra to a database by computer. However, since only a small part of the compounds relevant to the CWC are compiled in databases, the identification of chemicals in most cases depends on the experience of an NMR expert. The spectral parameters used for comparison are the chemical shifts, the coupling patters and the signal integrals. For H-1 spectra, it has to be kept in mind, that coupling patterns can vary with the static magnetic field, due to second order effects. Direct comparison is therefore only possible at the same magnetic field. For complicated spectra, two dimensional (2D) correlated spectroscopy allows to find the connection between spectra of different nuclei. 

If a linear discrete-time model is desired, one approach is to fit a continuous-time model to experimental data (cf. Section 7.2) and then to convert it to discrete-time form using the above approach. A more attractive approach is to estimate parameters in a discrete-time model directly from input-output data based on linear regression. This approach is an example of system identification (Ljung, 1999). As a specific example, consider the second-order difference equation in (7-36). It can be used to predict y k) from data available at times, k - l)At and (k - 2)At. In developing a discrete-time model, model parameters a, U2, b, and 62 are considered to be unknown. They are estimated by applying linear regression to minimize the error criterion in Eq. 7-8 after defining... 

The second group involves polymers with three-dimensional ordering of side branches (e.g., those forming Mj-phaseXTable 5). On X-ray patterns of these polymers 3-4 narrow reflexes at wide angles are observed. As a rule, the authors define this type of structure as crystalline, or ascribe a smectic type of structure, characteristic for ordered smectics in SE or SH phases. The heats of transition from anisotropic state to isotropic melt are usually small and do not exceed the heats of transition smectic liquid crystal — isotropic melt . The similarity of structural parameters of three-dimensionally ordered smectics and that of crystalline polymers of the type here considered, make their correct identification quite a difficult task. 

In chapter 3, the model was evaluated and examined, which was proposed in chapter 2. Firstly, parameter identification method was proposed based on mechanism. We can identify adsorption parameter and dissociation parameter by observing the deformation response of the beam-shaped gel in uniform electric field. The tip position and orientation of beam-shaped gel is a function of internal state of the whole gel. Therefore, we can identify parameters through observation of the tip. Secondly, the method was extended to calibrate the parameters. Adsorption parameter mainly affects the deformation speed of the material, which also scatters. Two methods were considered in order to calibrate reaction parameter. One is to estimate it by the deformation response of the gel for a given period of time. Another is to do it by the time required to deform into the particular shape of the gel. Thirdly, the resolution was changed to digitize spatial and temporal variables. The convention deformable objects must be modeled with minute elements was broken down. It was made clear that beam-shaped gel whose length is 16 mm could be approximated into multi-link mechanism whose links are 1 mm in length. 

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