Department of Mechanical Engineering
Carbon Steel Ball Mold for Casting,

Iterative Learning Control
Minoru YAMADA
Professor, Dr. Eng.
Email : myamada@gifu-nct.ac.jp
Research Fields
Keywords

casting, control theory
mold, iterative learning control system● Research Outline
Carbon Steel Ball Mold for Casting

Iterative Learning Control

The carbon steel boll mold that has merit of the metal
mold and the sand mold was produced. Steel balls were
heated and joined to produce the carbon steel ball mold.

Iterative control is a method to track the output of adynamic system to the desired trajectory by modifyingthe input based on the trial error. For example, iterative
learning control systems (ILCS) and linear multipass
processes (LMP) are known as iterative control.

The steel ball mold is expected to reduce theoccurrences of chill because thermal conductivity issmaller than the metal mold due to the existence of the
air gap between steel balls. Furthermore, the mold canbe used repeatedly if its strength is strong more than asand mold. The mold is taken apart by adjusting joining
strength between steel balls like a sand mold and it ispossible to reuse used steel balls. From these features,
this steel boll mold is suitable for the casting of a small
quantity, or the production of the prototype.
It is assumed that the mechanism of joining due toheating the steel ball molds as follows. Steel balls after
the heating are covered with the thin oxide film,
furthermore, steel balls have joined through the oxidefilm. When steel balls are heated in the hightemperature in the air, it oxidizes steel balls and theoxide film are formed to the surface of steel balls.
Oxidization doesn't happen easily in the point of contact
at the early stages of heating, because there is no supplyof oxygen. But when oxidization progresses in thesurface except for the contact point, oxygen aresupplied from the oxide in the neighbourhood of thecontact point, oxidation occurs even in the point ofcontact. Namely, the oxide film is formed, and steel
balls are joined.

Iterative control systems can be viewed as 2D systems
because that systems have two kinds of dynamics: theone along time direction for each repetition index, andthe one with respects to the repetition index. In iterativecontrol systems, it is noted that, though there is no limit
for the iterative index, the iterated passes are always
bounded in finite time intervals. In consideration ofthese characteristics, authors have solved the asymptotic
tracking problem of nD discrete systems whose input
and output signals are bounded in, at most, onedimension. We call it the practical tracking problem ofnD systems.
Very complicated algebra calculations are necessary tosolve the practical tracking problem. So we havedeveloped Symbolic Control Toolbox and nD Control
System Toolbox. nD Control System Toolbox is an
integrated CAD Toolbox for nD system theory for use
with the software product MATLAB and Symbolic
Math Toolbox. It consists of several functional
packages which provide various basic tools andfacilities for both numerical calculation and symbolic
manipulation required in analysis and synthesis of 2D
control systems such as stability test, factor coprime
factorizations and solution of various linear matrix
equations, etc. Symbolic Control Toolbox is a algebraic
equation solution package for 1D system.

angle of robot arm

tracking error