Overshooting problem

The calculation can be made for an arbitrary number of points provided their abscissa lie inside the range of x values. Figure 3.7 shows the characteristic features of spline interpolation, a very smooth aspect although with some overshooting problems, i.e., extrema located between the data points. Alternative interpolation schemes are discussed by Wiggins (1976). o... 

The classic Richardson overshoot problem has no mean flow. Hence there is no constant contribution in the pressure-gradient term,... 

In Newton s method, various approaches have been suggested to adjust the step length to alleviate the overshoot problem. These adjustments do not guarantee convergence of the Newton s method in early iterations. 

The structure(Zn,Ph)-property(a,/ ,7,) relationship has been investigated in this work by semiempirical PM3 and PM6 methods. The ZnTPP-(C)4-[60] dyad was found to exhibit large values of second hyperpolarizability. We found almost linear correlation between the size of the conjugated polyalkynyl linkage and the optical properties of the whole fullerene-porphyrin dyad. As a part of the present study, we have found that the nonlinear optical properties of model donor-substimted [60]fullerene derivatives are poorly described by the BLYP functional. The long-range corrected LC-BLYP functional, on the other hand, successfully cures the overshoot problem both for / and 7. The calculations for A-methylfulleropyrrolidine shows that the linear absorption spectra is reproduced quite well by conventional PBEO and B3LYP functionals. 

Control problem For a speeifie hull, the eontrol problem is to determine the autopilot setting K ) to provide a satisfaetory transient response. In this ease, this will be when the damping ratio has a value of 0.5. Also to be determined are the rise time, settling time and pereentage overshoot. 

The sign of the rate of change in the error could be opposite that of the proportional or integral terms. Thus adding derivative action to PI control may counteract the overcompensation of the integrating action. PD control may improve system response while reducing oscillations and overshoot. (Formal analysis later will show that the problem is more complex than this simple statement.)... 

If we assume that an oscillatory system response can be fitted to a second order underdamped function. With Eq. (3-29), we can calculate that with a decay ratio of 0.25, the damping ratio f is 0.215, and the maximum percent overshoot is 50%, which is not insignificant. (These values came from Revew Problem 4 back in Chapter 5.)... 

Example 4.7B Let us revisit the two CSTR-in-series problem in Example 4.7 (p. 4-5). Use the inlet concentration as the input variable and check that the system is controllable and observable. Find the state feedback gain such that the reactor system is very slightly underdamped with a damping ratio of 0.8, which is equivalent to about a 1.5% overshoot. 

I hope I explained this well enough to be understood. Basically Problem 2 is easily defined and solved, whereas Problem 1 is not. As I have mentioned, I have not been able to reproduce this overshoot on the boards I have. The best I can do about this now is to have... 

Figure 1.3 sketches the problem. The question is which curves (1 or 2) represent the actual paths that F and h will follow. Curves 1 show gradual increases in h and F to their new steadystate values. However, the paths could follow curves 2 where the liquid height rises above its final steadystate value. This is called overshoot. Clearly, if the peak of the overshoot in fc is above the top of the tank, we would be in trouble. 

Problem 6.11 gives some very useful relationships between these parameters (damping coefTicient and time constant) and the shape of the response curve. There is a simple relationship between the peak overshoot ratio and the damping coefficient. Then the time constant can be calculated from the rise time and the damping coefficient. Refer to Prob. 6.11 for the definitions of these terms. 

This problem can be solved analytically, but it is complicated to do so. In any case, an interesting attribute of result is called the Richardson annular overshoot. The numerical solution is shown in Fig. 4.11. In this illustration, fi — I and the frequency is [Pg.176]

This average root-mean-square velocity has a peak value away from the centerline (i.e., the overshoot). The magnitude of the velocities depend on fi and w. The root-mean-square profile has a relatively weak dependence on [Pg.176]

One further problem is the large overshoot in ABA production in wilted leaves. With applied ABA a doubling of the ABA content of the leaf is usually adequate for stomatal closure, while increases up to 40-fold have been reported in wilted leaves. However, extractions of whole leaves do not take into account the location of ABA within the leaf. Perhaps much of the hormone is sequestered in a compartment that has no access to the guard cells. Thus, it would be of much importance to determine the distribution of ABA at the tissue level as well as its intracellular location. Since ABA is a small water-soluble molecule, conventional fractionation techniques may not be suitable to determine its distribution in various organelles. A highly specific immunological method for detection of ABA has recently been developed (38, 39). It is conceivable that this technique could be further developed for determining the cellular localization of ABA as has already been done for the photoreceptor phytochrome (77, 78). 

The most commonly advocated solution to this problem is the introduction of the Yates correction. However, the use of this correction is somewhat problematic as it is rather drastic and tends to overshoot, sometimes converting a liberal situation (too willing to declare significance) into a conservative one (too reluctant). We need a policy that never produces a markedly misleading result and is not so complex or obscure as to arouse suspicions that some sort of statistical fiddle is afoot. A simple and commonly used rule is that we should apply Yates correction only where there are just two categories. With more than two categories, the effect of discontinuity is so small, we are better off not trying to compensate for it. 

As mentioned above, it is far more difficult to measure extensional viscosity than shear viscosity, in particular of mobile liquids. The problem is not only to achieve a constant stretch rate, but also to maintain it for a sufficient time. As shown before, in many cases Hencky strains, e = qet, of at least 7 are needed to reach the equilibrium values of the extensional viscosity and even that is questionable, because it seems that a stress overshoot is reached at those high Hencky strains. Moreover, if one realises that that for a Hencky strain of 7 the length of the original sample has increased 1100 times, whereas the diameter of the sample of 1 mm has decreased at the same time to 33 pm, then it will be clear that the forces involved with those high Hencky strains become extremely small during the experiment. 

At first glance, it may appear that draining the jacket of coolant when the controller is asking for steam might result in controller overshoot. This turns out not to be a problem for two reasons First, the time it takes to drain the jacket, compared with the speed of most reactor temperature loops, is usually insignificant. Second, depending on the jacket volume, draining the jacket can... 

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