A Supervisor for Control of Mode-switch Process

Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, and adaptive controller could be used. When the operation point changes often, a large number of parameters would have to be adapted over and over again. This makes application of conventional adaptive control unattractive, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are co-ordinated by a ¿supervisor¿. This concept is referred to as a supervisor for control of mode-switch processes. It leads to an adaptive control structure which quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on experimental set-ups of a flexible beam and of a flexible two-link robot arm, but it is directly applicable to other processes, for instance, in the (petro) chemical industry

Sylvester's question and the Random Acceleration Process

Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).Comment: 29 pages, 4 figures; references added and minor change

The distribution of ATP within tomato (Lycopersicon esculentum Mill.) embryos correlates with germination whee as total ATP concentration does not

The distribution of ATP in tomato seeds was visualized by monitoring the luminescence of frozen sections on top of a gel containing all the components of the luciferase reaction, but excluding ATP. ATP was imaged in germinating tomato seeds at intervals of 3, 6, 17, 24 and 48 h and in seeds with primary or secondary dormancy. ATP was present mainly in the embryo and concentrated in the radicle tip towards the completion of germination. In contrast to germinating seeds, ATP was distributed more evenly in dormant seeds. For germination, the ratio of ATP concentration in the radicle tip versus cotyledons was decisive, rather than the absolute concentration

Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results

We achieve a detailed understanding of the $n$-sided planar Poisson-Voronoi cell in the limit of large $n$. Let ${p}\_n$ be the probability for a cell to have $n$ sides. We construct the asymptotic expansion of $\log {p}\_n$ up to terms that vanish as $n\to\infty$. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as $n\to\infty$, and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in $1/n$ they have nontrivial long range correlations whose expressions we provide. The $n$-sided cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where $\lambda$ is the cell density; hence Lewis' law for the average area $A\_n$ of the $n$-sided cell behaves as $A\_n \simeq cn/\lambda$ with $c=1/4$. For $n\to\infty$ the cell perimeter, expressed as a function $R(\phi)$ of the polar angle $\phi$, satisfies $d^2 R/d\phi^2 = F(\phi)$, where $F$ is known Gaussian noise; we deduce from it the probability law for the perimeter's long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure

Seed vigor, aging, and osmopriming affect anion and sugar leakage during imbition of maize (Zea mays L.) caryopses

Conductivity was significantly increased by aging and decreased by osmopriming of maize (Zea mays L.) caryopses. Chloride, phosphate, and sulfate were the main anions that leaked out of maize seeds; their leakage was closely related to conductivity, increased by aging, and decreased by osmopriming. The anion leakage of isolated embryos correlated closely to seed vigor and was more sensitive to aging and priming than that of the whole seed. Anion leakage may be a more sensitive measure for seed vigor than bulk conductivity readings. Aging did not increase the sugar leakage of whole seeds but significantly increased the sugar leakage of isolated embryos. Sugar leakage was not closely related to total soluble sugar content of seeds. While priming decreased seed conductivity, the decreased anion and sugar leakage of the primed seeds was mainly caused by the washing effect during priming. The total anions or sugars left in the polyethylene glycol (PEG) solution after priming and in the conductivity solution of the primed seeds was almost the same as in the conductivity solution of the unprimed seeds alone

Supervisory Control of Mode-switch Processes; Application to a flexible beam

Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, an adaptive controller could be used. Then, if the operation point changes often, a large number of parameters would have to be adapted over and over again. This prohibits application of conventional adaptive control, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are coordinated by a “supervisor”. This concept is referred to as supervisory control. It leads to an adaptive control structure which, after a learning phase, quickly adjusts the controller parameters based on retrieval of old information, without the need to fully releam each time. This approach has been tested on an experimental set-up of a flexible beam, but it is directly applicable to processes in e.g. the (petro)chemical industry as well