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

 
 
 
 
 
 
 
 
 
 

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LIST OF FIGURES 
 
 
Figure Page 
Figure 2. 1 Block diagram of thermal glass tempering process ............................................................... 6 
Figure 2. 2 Viscosity of Glass from 500°c to 730°c ................................................................................... 8 
Figure 2. 3 General block diagram of PID controller .............................................................................. 12 
Figure 2. 4 Fuzzy logic system chart showing both input and output chart ........................................ 16 
Figure 2. 5 Fuzzy logic controller operations .......................................................................................... 17 
Figure 2. 6 Membership function shapes: (a) S, (b) Z, (c) Λ, and (d) Π. ................................................ 18 
Figure 2. 7 Fuzzy set with five membership functions ........................................................................... 18 
Figure 2. 8 Fuzzy logic rule matrix. ......................................................................................................... 19 
Figure 2. 9 (a) Fuzzy input grades and (b) the resulting output grades. .............................................. 20 
Figure 2. 10 Fuzzy inferencing using Mamdani’s max-min compositional operation ......................... 21 
Figure 3. 1 General block diagram of fuzzy pid temperature control for glass tempering furnace .... 24 
Figure 3. 2 Response curve for Z-N method ............................................................................................ 35 
Figure 3. 3 Simulink model of PID controller .......................................................................................... 39 
Figure 3. 4 General structure of fuzzy logic controller ........................................................................... 41 
Figure 3. 5 Fuzzy interface block ............................................................................................................. 42 
Figure 3. 6 Surface viewers of KP, KI and KD .......................................................................................... 43 
Figure 3. 7 Output membership function for Δkp and Δkd .................................................................... 46 
Figure 3. 8 Output membership function for Δki ................................................................................... 46 
Figure 3. 9 Bode diagram for first order pade approximation .............................................................. 49 
Figure 3. 10 Bode diagram for third order pade approximation ........................................................... 50 
Figure 3. 11 Step response of the original and pade approximate transfer function .......................... 50 
Figure 3. 12 Over all Simulink model of fuzzy pid and pid controller ................................................... 52 
Figure 3. 13 Model components under fuzzy pid block ......................................................................... 52 
Figure 3. 14 PID controller block model components under fuzzy pid block ...................................... 53
 
Figure 4. 1Step response of continuous and discrete closed loop PID control system ....................... 55 
Figure 4. 2 Step response of closed loop system with different PID tuning mechanisms. .................. 55 
Figure 4. 3 Simulation results of FPID and PID controllers ................................................................... 57 
Figure 4. 4 Response of the PID and FPID controllers with ±50% delay time ..................................... 58 
Figure 4. 5 Response of the PID and FPID controllers with ±50% time constant ................................ 59 
Figure 4. 6 Response of the PID and FPID controllers with ±50% DC gain ......................................... 60 
Figure 4. 7 Disturbance signal added to control signal after settling time ........................................... 61 
Figure 4. 8 Disturbance rejections of PID and FPID controllers ............................................................ 62 

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