Geometric feedback

In regard dynamics and control scopes, the contributions address analysis of open and closed-loop systems, fault detection and the dynamical behavior of controlled processes. Concerning control design, the contributors have exploited fuzzy and neuro-fuzzy techniques for control design and fault detection. Moreover, robust approaches to dynamical output feedback from geometric control are also included. In addition, the contributors have also enclosed results concerning the dynamics of controlled processes, such as the study of homoclinic orbits in controlled CSTR and the experimental evidence of how feedback interconnection in a recycling bioreactor can induce unpredictable (possibly chaotic) oscillations. 

Fig. 5. Optimized temperature sets for the two-dimensional Ising ferromagnet. The initial temperature set with 20 temperature points is determined by a geometric progression for the temperature interval [0.1,10]. After feedback of the local diffusivity the temperature points accumulate near the critical temperature Tc = 2.269 of the phase transition dashed line). Similar to the ensemble optimization in energy space the feedback of the local diffusivity relocates resources towards the bottleneck of the simulation...

An optimized temperature set for the parallel tempering simulation of HP-36 in the ECEPP/2 force field can then be found by feeding back the local diffusivity appl3ung the algorithm outlined above. Results for a temperature set with 20 temperature points are illustrated in Fig. 8 for an initial temperature set which similar to a geometric progression concentrates temperature points at low temperatures [27]. After the feedback temperature points concentrate around the bottleneck of the simulation, primarily around the helix-coil transition at T 500 K and in the temperature regime 350 K < T < 490 K below the transition where a shoulder in the local diffusivity was found. 

Fig. 8. Optimized temperature sets with 20 temperature points for the parallel tempering simnlation of the 36-residue protein HP-36. The initial temperatnre set covers a temperatnre range 250 K < T < 1000 K and concentrates temperatnre points at low temperatures similar to a geometric progression. After the feedback of the local diffusivity temperature points accumulate around the hehx-coil transition at T fs 500 K where the strong suppression of the local diffusivity points to a severe bottleneck...

Fig. 9.4(b) shows the spiral tip trajectory obtained experimentally under this feedback control. After a short transient the spiral core center drifts in parallel to the line detector. The asymptotic drift trajectory reminds the resonance attractor observed under one-channel control, because a small variation of the initial location of the spiral wave does not change the final distance between the detector and the drift line. To construct the drift velocity field for this control algorithm an Archimedean spiral approximation is used again. Assume the detector line is given as a = 0 and an Archimedean spiral described by Eq. (9.5) is located at a site x,y) with a > 0. A pure geometrical consideration shows that the spiral front touches the detector each time ti satisfying the following equation ... 

The shape of an etched feature depends on a plethora of geometric, material, and plasma parameters. The shape evolution problem is coupled to the plasma reactor through the sheath (Fig. 23, top). Feedback from the feature to the reactor occurs through the flux of product species coming out of the feature and the varying surface area available for reaction as the feature shape evolves. The former affects the plasma gas composition and in turn the flux and energy distribution of species incident on... 

However, it is not easy to calculate the exact relation between the probe current and the probe-sample distance in the feedback mode due to the geometric complexity in the experimental system. For quantitative analyses, digital simulation has been used in the feedback mode SECM both for conductor and insulator substrates [ 18]. Digital simulation is a powerful technique for analysis of relatively complicated electrochemical systems such as SECM. In the simulation, the space between the probe and the substrate are divided into small volimie elements. Mass transfer based on diffusion for each volume element is calculated. If one chooses suitable initial and boundary conditions, the experimental situation including the mass transfer and various chemical reactions can be simulated. Erom the simulation, one can determine the heterogeneous rate... 

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