Abstract: Controlling the flow of fluids is a challenging problem
that arises in many fields. Burgers’ equation is a fundamental
equation for several flow phenomena such as traffic, shock waves,
and turbulence. The optimal feedback control method, so-called
model predictive control, has been proposed for Burgers’ equation.
However, the model predictive control method is inapplicable to
systems whose all state variables are not exactly known. In practical
point of view, it is unusual that all the state variables of systems are
exactly known, because the state variables of systems are measured
through output sensors and limited parts of them can be only
available. In fact, it is usual that flow velocities of fluid systems
cannot be measured for all spatial domains. Hence, any practical
feedback controller for fluid systems must incorporate some type of
state estimator. To apply the model predictive control to the fluid
systems described by Burgers’ equation, it is needed to establish
a state estimation method for Burgers’ equation with limited
measurable state variables. To this purpose, we apply unscented
Kalman filter for estimating the state variables of fluid systems
described by Burgers’ equation. The objective of this study is to
establish a state estimation method based on unscented Kalman filter
for Burgers’ equation. The effectiveness of the proposed method is
verified by numerical simulations.
Abstract: Recently, crystal growth technologies have made
progress by the requirement for the high quality of crystal materials.
To control the crystal growth dynamics actively by external forces
is useuful for reducing composition non-uniformity. In this study,
a control method based on model predictive control using thermal
inputs is proposed for crystal growth dynamics of semiconductor
materials. The control system of crystal growth dynamics considered
here is governed by the continuity, momentum, energy, and mass
transport equations. To establish the control method for such thermal
fluid systems, we adopt model predictive control known as a kind
of optimal feedback control in which the control performance over
a finite future is optimized with a performance index that has a
moving initial time and terminal time. The objective of this study
is to establish a model predictive control method for crystal growth
dynamics of semiconductor materials.
Abstract: The aim of the present study was to investigate the dissolution kinetics of ulexite in sodium dihydrogen phosphate in a mechanical agitation system and also to declare an alternative reactant to produce the boric acid. Reaction temperature, concentration of sodium dihydrogen phosphate, stirring speed, solid-liquid ratio, and ulexite particle size were selected as parameters. The experimental results were successfully correlated by using linear regression and a statistical program. Dissolution curves were evaluated in order to test the shrinking core models for solid-fluid systems. It was observed that increase in the reaction temperature and decrease in the solid/liquid ratio causes an increase in the dissolution rate of ulexite. The activation energy was found to be 36.4 kJ/mol. The leaching of ulexite was controlled by diffusion through the ash (or product) layer.
Abstract: Ulexite (Na2O.2CaO.5B2O3.16H2O) is boron mineral
that is found in large quantities in the Turkey and world. In this
study, the dissolution of this mineral in the disodium hydrogen
phosphate solutions has been studied. Temperature, concentration,
stirring speed, solid liquid ratio and particle size were selected as
parameters. The experimental results were successfully correlated by
linear regression using Statistica program. Dissolution curves were
evaluated shrinking core models for solid-fluid systems. It was
observed that increase in the reaction temperature and decrease in the
solid/liquid ratio causes an increase the dissolution rate of ulexite.
The activation energy was found to be 63.4 kJ/mol. The leaching of
ulexite was controlled by chemical reaction.