Sensitivity function S

Calibration function Normal equations Sensitivity function S(x)... 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

The comparison of open and closed-loop responses (12.37) and (12.38) reveals that the sensitivity function S gives the reduction of sensitivity to disturbances, achieved by feedback control. It is evident that S =0 and T = 1 are desirable. In this way, the output follows perfectly the setpoint, and the process is not affected by disturbances. Both can be achieved by large controller gain, that is oo. However, large controller gain leads to instability, which sets limits on the achievable closed-loop performance. 

Loosely speaking, bandwidth may be defined as the frequency range [a>i, Wi] over which control is effective. In most cases we require tight control at steady state. Since coi=0 we call co the bandwidth. The word effective may be interpreted in different ways, giving rise to different definitions of bandwidth. The interpretation we use is that control is effective if we obtain some benefit in terms of performance. For example, considering the interpretation of the sensitivity function S, we arrive at the following definition ... 

The basis for all these sensitivity functions is the differential sensitivity function S (r, , SI). In the following subsections we present examples of differential and other sensitivity functions for several integral parameters pertaining to variations in different input parameters. 

Stein and Doyle [35] developed an expression to calculate ft for the Robust Performance Problem in the case where the plant is minimum phase and is controlled by an inverse-based decoupling controller. The modeled uncertainty is described by a complex unstructured input block with weighting function w, and performance requirement Wj measured by the closed-loop sensitivity function S. The decoupling controller K is based on the inverse of G in the form. (s) = G (s) (s), where k(s) is a scalar transfer function which makes K s) proper and gives a stable closed-loop system. Note that G s) is a linear stable system with stable inverse (i. e. G is minimum-phase).This compensator produces diagonal sensitivity and complementary sensitivity functions with identical diagonal elements, namely... 

Very briefly, this rather large subject in the general area of chemical kinetics [43-45] was carried into electrochemistry in the studies by Bieniasz et al. [46-48]. It asks the question, when fitting some parameter to a proposed mechanism by means of simulation using some simulation output (concentrations or current or some other result), how sensitive to the changes in the output is the value of the fitted parameter. This is expressed in the form of a sensitivity function s. If the simulation yields, for example, an array of concentrations c x,t,p), where x are positions in space, t the time (which may enter the problem) and the parameter(s) p, then the function is defined [46] as 5 = dc/dp, which is an expression of the sensitivity to changes in concentration. This can be useful in estimating the reliability of fitted parameters by a series of simulations. This subject will not be persued further here. 

A which is not observed in individual solutions of the two enones at the same concentrations and may thus be indicative of a complex formation. However, the ratio of isomeric cyclobutane products resulting from such photocycloadditions is generally seen to be a quite sensitive function of steric effects and of the properties of the reaction solvent, of the excited state(s) involved (in some cases two different excited triplet states of the same enone have been found to lead to different adducts) and of the substituents of the excited enone and substrate. No fully satisfactory theory has yet been put forth to draw together all the observations reported thus far. 

Addition of a proton occurs to give the more-substituted carbocation, so addition is regioselective and in accord with Markovnikov s rule. A more detailed discussion of the reaction mechanism is given in Section 6.2 of Part A. Owing to the strongly acidic and rather vigorous conditions required to effect hydration of most alkenes, these conditions are applicable only to molecules that have no acid-sensitive functional groups. The reaction is occasionally applied to the synthesis of tertiary alcohols. 

Indicate one or more satisfactory oxidants for effecting the following transformations. Each molecule poses issues of selectivity or the need to preserve a sensitive functional group. Select oxidants that can avoid the installation of protecting groups. In most cases, a one-pot reaction is possible, and in no case is a sequence of more than three steps required. Explain the reason for your choice of reagent(s). 

A possible alternative is the microvillous part of the chemosensory epithelium in the Organ of Rodolfo-Masera (Septal Organ), which is VN-like (Taniguchi etal., 1993). This mixed receptor population requires much further study since it could prove to have intermediate odourant sensitivities (Giannetti et al., 1995). Its distribution and function(s) are still incompletely known however it is sufficiently widespread, from Opossums to Rodents, to warrant an intensive survey (Rodolfo-Masera, 1943 Kratzing, 1978 Giannetti et al., 1992 and 1995). 

Whereas the tensile strength was not a sensitive function of the monomer structure, the tensile modulus (Young s Modulus) was clearly related to the monomer structure. This is expected since the tensile modulus is a measure of the polymer s resistance to deformation and is related to the "stiffness" of a polymeric material. The highest tensile modulus (22,000 kg/cm2,2.2 GPa) was measured for poly(BPA iminocarbonate). Replacement of BPA by Dat-Tyr-Hex reduced the tensile modulus significantly. This observation can possibly be attributed to the presence of the long hexyl ester pendent chain in Dat-Tyr-Hex. Generally, the polyiminocarbonates were somewhat "stiffer" than the corresponding polycarbonates. Thus, the tensile moduli of poly(Dat-Tyr-Hex iminocarbonate) and poly(Dat-Tyr-Hex carbonate) were 16,300 kg/cm2 (1.6 GPa) and 13,900 kg/cm2 (1.3 GPa) respectively. 

For the purpose of comparisons, the sensitivity of the centre of the calibration curve S(x) having the character of an average sensitivity can be used. Sensitivity functions corresponding to diverse calibration functions are given in Table 6.2. 

The simplest method of determining the function S, in the visible region of the spectrum is to take photomultiplier readings when the entrance slit of the monochromator is illuminated by a tungsten lamp giving light of known spectral distribution. If RSL represents the values so obtained, the spectral sensitivity is then calculated from... 

Spectral sensitizing dyes are considered functional dyes to distinguish them from conventional colorants. The absorption of radiation by a functional dye causes some additional function(s) to occur, and in many... 

It is important to note that under the slightly basic conditions (pH 8.6-9.8) employed under the standard Anelli s protocol, many base-sensitive functional groups remain unaffected, including the ubiquitous ester groups.44 On the other hand, it may be advisable to limit the reaction time in order to minimize the hydrolysis of acetates.16... 

Equation 7.2-22 indicates that the separating force is proportional to the local shear stress (fiy) in the liquid, it is a sensitive function of the Euler angles of orientation, and is proportional to the projection of the cross-sectional are (S = nc2). The angular velocities of rotation of the freely suspended spheroid particle were given by Zia, Cox, and Mason (46)... 

By more completely suppressing the M-channel, the true spectral peak of the L-channel receptors can be determined. The long-dash overlay is for such a condition. The relative amplitudes for this overlay are Figure 5.5.10-10 Wald s figure 2 with overlays. The ksi ik O O 1000 with the same half-amplitudes as upper overlay (dashed line) shows the overall spectral above. Under this more complete adaptation, the peak in sensitivity function of this work. The lower the long wavelength receptor channel is seen to occur at overlay(dashed line) shows the overall spectral sensitivity 625 nm function of this work for a chromatically adapted subject. 

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