Determination of optimal feedback terminal controllers for general boundary conditions using generating functions

Given a nonlinear system and a performance index to be minimized, we present a general approach to expressing the finite time optimal feedback control law applicable to different types of boundary conditions. Starting from the necessary conditions for optimality represented by a Hamiltonian system, we solve the Hamilton-Jacobi equation for a generating function for a specific canonical transformation. This enables us to obtain the optimal feedback control for fundamentally different sets of boundary conditions only using a series of algebraic manipulations and partial differentiations. Furthermore, the proposed approach reveals an insight that the optimal cost functions for a given dynamical system can be decomposed into a single generating function that is only a function of the dynamics plus a term representing the boundary conditions. This result is formalized as a theorem. The whole procedure provides an advantage over methods rooted in dynamic programming, which require one to solve the Hamilton-Jacobi-Bellman equation repetitively for each type of boundary condition. The cost of this favorable versatility is doubling the dimension of the partial differential equation to be solved.     

Anodic oxidation of mecoprop herbicide at lead dioxide

The electrochemical oxidation of an aqueous solution containing mecoprop (2-(2-methyl-4-chlorophenoxy)propionic acid) has been studied at PbO₂ anodes by cyclic voltammetry and bulk electrolysis. The influence of current density, hydrodynamic conditions, temperature and pH on the degradation rate and current efficiency is reported. The results obtained show that the use of PbO₂ leads to total mineralization of mecoprop due to the production of oxidant hydroxyl radical electrogenerated from water discharge. The current efficiency for the electro-oxidation of mecoprop is enhanced by low current density, high recycle flow-rates and high temperature. In contrast, the pH effect was not significant. It has also been observed that mecoprop decay kinetics follows a pseudo-first-order reaction and the rate constant increases with rising current density.     

Development of calibration models for quality control in the production of ethylene/propylene copolymers by FTIR spectroscopy,multivariate statistical tools,and artificial neural networks

Principal component regression (PCR), partial least squares (PLS), StepWise ordinary least squares regression (OLS), and back‐propagation artificial neural network (BP‐ANN) are applied here for the determination of the propylene concentration of a set of 83 production samples of ethylene–propylene copolymers from their infrared spectra. The set of available samples was split into (a) a training set, for models calculation; (b) a test set, for selecting the correct number of latent variables in PCR and PLS and the end point of the training phase of BP‐ANN; (c) a production set, for evaluating the predictive ability of the models. The predictive ability of the models is thus evaluated by genuine predictions. The model obtained by StepWise OLS turned out to be the best one, both in fitting and prediction. The study of the breakdown number of samples to be included in the training set showed that at least 52 experiments are necessary to build a reliable and predictive calibration model. It can be concluded that FTIR spectroscopy and OLS can be properly employed for monitoring the synthesis or the final product of ethylene–propylene copolymers, by predicting the concentration of propylene directly along the process line. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Synthesis and applications of heterobifunctional poly(ethylene oxide) oligomers

Poly(ethylene oxide) (PEO) oligomers are employed extensively in pharmaceutical and biomedical arenas mainly due to their excellent physical and biological properties, including solubility in water and organic solvents, lack of toxicity, and absence of immunogenicity. PEO can be chemically modified and reacted with, or adsorbed onto, other molecules and surfaces. Sophisticated applications for PEO have increased the demand for PEO oligomers with tailored functionalities, and heterobifunctional PEOs are often needed. This review discusses the synthesis and applications of heterobifunctional PEO oligomers possessing amine, carboxylate, thiol, and maleimide functional groups.     

Plasma power can make better powders

It may be a truism to say that round powders pack better, but spheroidisation of powder particles is one of the successful commercial applications of induction plasma technology and can play a key role in substantial improvement of powder quality and fluidity…     

Parametric circles and spheres

Formulations for parametric circles and spheres in terms of rational Gaussian (RaG) curves and surfaces are introduced. With the proposed formulations, a full circle is generated by interpolating a closed RaG curve to the vertices of an equilateral triangle, and a full sphere is generated by interpolating a closed RaG surface to the vertices of an octahedron with equilateral triangular faces. Generation of circles and spheres in this manner is very intuitive and easy to remember as the weights are all 1 and the nodes are all unique and uniformly spaced.