Fuzzy pid based Temperature Control of Electric Furnace for Glass Tempering Process

CHAPTER THREE 
3 MATERIALS AND METHODS 
This chapter deals with the materials and the methods used in accomplishing the thesis. The 
materials used are digital computer and MATLAB/SIMULINK software. Modeling, designing 
and analyzing are the methods used. The following sections present each of these in detail. 
3.1 
 
Modeling of glass tempering process 
 
The first step in the analysis and design of the control system is mathematical modeling of the 
different components. The transfer function method is widely used in designing control 
systems. After proper assumptions and approximations are made to linearize the mathematical 
equations describing the components, transfer functions are obtained. Thus, using these 
transfer functions, the tempering process is modeled for temperature control. 
The block diagram in Figure 3.1 shows the main components of glass tempering process of 
heating section. Before designing the temperature control system, the appropriate model for 
each component should be obtained [28]. 
Figure 3. 1 General block diagram of fuzzy pid temperature control for glass tempering furnace 

---

Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
25 
3.1.1 
 
Modeling of electric furnace
In glass tempering process electric furnace is used to heat the glass to the desired value. Thus 
electric furnace converts electric power/energy to heat energy and heats the glass through 
conduction, convention and radiation
. 
The temperature process of electric furnace is given by 
first order plus time delay equation [28][29][30][31].
( )
-------------------------------------------------------------------3.1 
Where k is magnification value, T is time constant and D is pure lag time. 
Assuming the walls of the glass tempering furnace has ideal heat insulation and there are no 
losses into surrounding. The equation of heat balance can be written as follows [32][33]: 
-------------------------------------------------------3.2 
Where: 
 is the material density, ton/m3, 
C is the specific heat of the material, Mcal / deg .ton, 
V is the volume of the furnace, m3, 
is the temperature in zone,
 , 
is the amount heat flow with material Q1 Mcal/hour, 
Q1 is the flow rate input m3/hour, 
is the amount heat flow with material Q2 Mcal/hour, Q2 is the flow rate
output m3 /hour. 
Using the following assumptions: 
I. 
( )
( ) 
II. 
Substituting the assumptions in equation (3.2) and taking Laplace transform gives 
( )
( )
-----------------------------------------------------------------------3.3 
Where, T 
, time constant 

---

Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
26 
And considering
as input
the transfer function can be
( )
( )
------------------------------------------------------------------------------------3.4 
Where
, magnification value and
T 
, time constant
-----------------------------------------------3.5