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

A. Ziegler-Nichols Method 
The Ziegler-Nichols design methods are the most popular methods used in process control to 
determine the parameters of a PID controller. Although these methods were presented in the 
1940s, they are still widely used [9][13][14]. The step response method is based on an open-loop 
step response test of the process. Hence requiring the process to be stable, the unit step response of 
the process is characterized by two parameters L and T. These are determined by drawing a 
tangent line at the inflexion point, where the slope of the step response has its maximum value.
The intersections of the tangent and the coordinate axes give the process parameters as shown in 
Figure 3.2, and these are used in calculating the controller parameters. Since
our process model is 
first order plus dead time as indicated in equation (3.25) we can use the values of delay time 
(D/L), time constant (T) and DC gain (K) to calculate the values of
through 
different tuning correlations
. The parameters for PID controllers obtained from the Ziegler-
Nichols step response method are shown in Table 3.2.
Figure 3. 2 Response curve for Z-N method 
Controller
P 
(
⁄ )(
⁄ )
PI 
(
⁄ )(
⁄ 3.3D 
PID 
(
⁄ )(
⁄ 2D 
0.5D 
Table 3. 2 ZN PID controller parameter for first order plus dead time model 
For PID controller

K
c
=0.1148 

K
d
= 1.148( 
=10) 

K
i
=0.00269( 
=40) 

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Fuzzy PID Based Temperature Control of Electric Furnace for Glass Tempering Process
M.Sc. Thesis, Addis Ababa University, December 2016 
36 
Thus, the controller transfer function is 
( )
---------------------------------------3.36