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

D. ITAE Tuning Method 
Another useful method for tuning of PID is ITAE method is described in [13]. Integral time 
multiplied by absolute error (ITAE) criterion is given by: 
∫
( ) dt 
------------------------------------------------------------------------------3.38 
Where t is the time and e(t) is the error which is calculating the difference between the set 
point and the output. The controller parameters with this method are given by table 3.5. For a 
first order plus dead time model [13], solve for: 
---------------------------------------3.39 
Design for Load and Set-point changes yield different ITAE optimum. 
Type of input 
Type of 
controller
Mode
A 
B 
Load 
PI 
P 
0.859 
-0.977 
I 
0.674 
-0.680 
Load 
PID 
P 
1.357 
-0.947 
I 
0.842 
-0.738 
D 
0.381 
0.995 
Set-point 
PI 
P 
0.586 
-0.916 
I 
1.03 
-0.165 
Set-point 
PID 
P 
0.965 
-0.85 
I 
0.796 
-0.1465 
D 
0.308 
0.929 
Table 3. 5 ITAE PID controller parameter for first order plus dead time model 

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Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
38 
From table, we get 
Load Settings: 
(
⁄ )
⁄
⁄ -------------------------------------------------------3.40 
Set point Settings: 
(
⁄ )
⁄
⁄ (
⁄ )-------------------------------------3.41 
i. 
Design load point change
For PID controller

K
c
K=1.357*(0.8)^(-0.947) 
K
c
13.07=1.6763 
K
c
=0.1282 

⁄ ( )
,
⁄
=25.1838 
K
i
=0.0051 

⁄ ( )
K
d
= 1.5246 
Thus the controller transfer function is
( )
----------------------------------3.42
ii. 
Design set point change
For PID controller

K
c
K=0.965*(0.8)^(-0.85) 
K
c
13.07=1.665 
K
c
=0.08925 

⁄ ( )
,
⁄
=36.8297 
K
i
=0.0024 

⁄ ( )
K
d
= 0.5584 
Thus the controller transfer function is
( )
--------------------------------3.43 

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Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
39