Applied Engineering Letters Vol. 1, No 3, 67-71 (2016) e-ISSN: 2466-4847
CONTACT: Djordje Dihovicni, ddihovicni@gmail.com
POLE ASSIGNMENT FOR GLASS CAPILLARY TUBE DRAWING PROCESS BY
USING MATLAB AND MAPLE LANGUAGE
Djordje Dihovicni
1
1
Technical College, Bulevar Zorana Djindjica 152a, Belgrade, Republic of Serbia, Tel.:+381-11-2600-131,
e-mail: ddihovicni@.gmail.com
Abstract:
The question of pole placement for glass capillary tube drawing process
is considered. It is used a frequency domain approach to an arbitrary
finite spectrum assignment for multivariable time delay systems in
order to control glass capillary tube drawing process. The Padé
approximation is used for the system of third order and time delay is
eliminated from the transfer function of the process. The responses are
shown as well the transfer function of the closed loop after applying
finite spectrum method. By choosing state variables it is obtained non
degenerative transfer function of process model. The time delays in
open loop remained the same as in the closed loop. The all poles are
located in the left half plane and system is stable. Appropriate program
support for this type of problems is developed in Maple language.
ARTICLE HISTORY
Received 15 August 2016
Accepted 18 September 2016
Available online 30 September 2016
KEYWORDS
Glass capillary, pole placement, time
delay, stability, finite spectrum,
mathematical model, frequency
domain, Pade approximation.
1. INTRODUCTION
Hower despite the fact that the drawing of glass
capillary tubes is well known technological process,
and that the process of drawing of optical fibers is
good described in the literature, there is yet not
many references relating to this specific field, and
as well detailed analyze and synthesis in the
frequency domain of this phenomena [3-5]. In
brief, the glass capillary tube is produced by
heating an end of the hollow cylindrical glass
preform and then by drawing out melted part
thereof which contracts first quickly and then
slowly during cooling process [6-7].
The glass capillary tube takes part at the
relatively low temperatures in contrast with
drawing process of optical fibre [11]. At low
temperatures the viscous stresses are dominant,
and thickness of a wall of the capillary tybe should
be controlled [12].
The studies of Geyling (1976), Clermont (1984),
Mayers (1989) and Papamichael and Miaulis (1990)
were extremely important and by them was given
the significant contribution to explaining and
describing whole process [15]. Taking into account
that a very rapid change of the viscosity is very
complex problem, the best way is to describe the
drawing process qualitatively.
There are various processes of drawning glass
tubes from a source of molten glass such as Vello,
Danner and Down, and the shape of the glass tube
is characterized by the diameter of cross sectional
area of the tube and the thickness of the wall.
The geometry of the tube may be circular,
rectangular or square, and there are different
geometry techniques for obtaining required results.
Sometimes it is used inversion problem such as
in manufacturing of non-axisymmetric capillary
tubing where the necessity for determination the
diametar of the shape is required to achieve the
final shape.
Mathematical models of the process are usually
complex and described by nonlinear partial
different equations of higher order [1].
In order to present valid mathematical method
time delay which is presented in the system should
not be neglected [2]. In time delay systems, delay
might occur in state, control and as well in state
and in control, when arises the principal difficulty
in the control loop, such as increased phase lag