Design of Real-Time Extremum-Seeking Controller-Based Modelling for Optimizing MRR in Low Power EDM
Abstract
:1. Introduction
2. Experimental Methodology
2.1. Modelling and Design of a Low-Power EDM Process
2.2. Ignition Phase
2.3. Discharge Phase
2.4. Recovery Phase
3. Implementation of ESC on Reducing the Non-Linearity of MRR
3.1. A Non-Linear Model of the Material Removal Rate
3.2. A Non-Linear Model of the Material Removal Rate
4. Results and Discussion
4.1. Experimental Simulation
4.2. EDM Process and Model Outputs
4.3. Extremum-Seeking for Optimal Discharge Time
5. Conclusions
- ➢
- The simulated model gives less errors from 0.82% to 4.2% with the actual process output.
- ➢
- The possibility of extremum-seeking control in the search for an online optimal point with less error and more convergence speed was studied.
- ➢
- An extremum-seeking optimal search offers a 57% greater material removal rate against the average number of manual trial processes, but it offers 1.2% more efficiency than the best manual searching process.
- ➢
- The experimental validation also proved that the ESC can produce large MRR by tracking the extremum control.
- ➢
- The present study was limited to only MRR, but it is also possible to implement such algorithms for more than one response parameter optimization in future studies. In such cases, the performance measures of the process can be further enhanced which can be used for real-time complex die- and mold-making processes using EDM.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Value |
---|---|
Supply Voltage and Frequency | 240 V and 50 Hz |
Filter Capacitor | 1 F |
Ignition Resistor and Inductor | 2 Ω and 0.1 mH |
Switching Frequency for Buck converter | 30 KHz |
Process | Ig (A) | Fs (kHz) | Ton (µsec) | MRR (mm3/Min) | |
---|---|---|---|---|---|
Actual | Model | ||||
1 | 8.5 | 125 | 2.0 | 8 | 8.77 |
2 | 8.5 | 111.1 | 3.0 | 11 | 11.74 |
3 | 8.5 | 100 | 4.0 | 16 | 14.14 |
4 | 8.5 | 83.33 | 6.0 | 21 | 17.81 |
5 | 8.5 | 55.55 | 12.0 | 23 | 24.27 |
6 | 8.5 | 32.25 | 25.0 | 31 | 30.57 |
7 | 8.5 | 17.24 | 52.0 | 36 | 36.12 |
8 | 8.5 | 8.77 | 108.0 | 38 | 40.35 |
9 | 8.5 | 4.41 | 220.8 | 33 | 39.03 |
10 | 8.5 | 2.21 | 446.5 | 29 | 36.10 |
11 | 12.5 | 125 | 2.0 | 12 | 12.90 |
12 | 12.5 | 111.1 | 3.0 | 16 | 17.27 |
13 | 12.5 | 100 | 4.0 | 20 | 20.80 |
14 | 12.5 | 83.33 | 6.0 | 31 | 26.20 |
15 | 12.5 | 55.55 | 12.0 | 43 | 35.69 |
16 | 12.5 | 32.25 | 25.0 | 48 | 44.95 |
17 | 12.5 | 17.24 | 52.0 | 52 | 53.12 |
18 | 12.5 | 8.77 | 108.0 | 54 | 59.34 |
19 | 12.5 | 4.41 | 220.8 | 54 | 57.40 |
20 | 12.5 | 2.21 | 446.5 | 54 | 53.09 |
21 | 25 | 125 | 2.0 | 26 | 26.26 |
22 | 25 | 111.1 | 3.0 | 31 | 35.16 |
23 | 25 | 100 | 4.0 | 46 | 42.34 |
24 | 25 | 83.33 | 6.0 | 60 | 53.34 |
25 | 25 | 55.55 | 12.0 | 81 | 72.66 |
26 | 25 | 32.25 | 25.0 | 99 | 91.51 |
27 | 25 | 17.24 | 52.0 | 126 | 108.15 |
28 | 25 | 8.77 | 108.0 | 126 | 120.81 |
29 | 25 | 4.41 | 220.8 | 110 | 116.86 |
30 | 25 | 2.21 | 446.5 | 90 | 108.08 |
31 | 36 | 125 | 2.0 | 39 | 39.98 |
32 | 36 | 111.1 | 3.0 | 53 | 53.53 |
33 | 36 | 100 | 4.0 | 64 | 64.47 |
34 | 36 | 83.33 | 6.0 | 72 | 81.20 |
35 | 36 | 55.55 | 12.0 | 111 | 110.62 |
36 | 36 | 32.25 | 25.0 | 137 | 139.32 |
37 | 36 | 17.24 | 52.0 | 161 | 164.65 |
38 | 36 | 8.77 | 108.0 | 181 | 183.94 |
39 | 36 | 4.41 | 220.8 | 175 | 177.92 |
40 | 36 | 2.21 | 446.5 | 151 | 164.55 |
41 | 50 | 125 | 2.0 | 57 | 57.84 |
42 | 50 | 111.1 | 3.0 | 77 | 77.44 |
43 | 50 | 100 | 4.0 | 82 | 93.27 |
44 | 50 | 83.33 | 6.0 | 143 | 117.48 |
45 | 50 | 55.55 | 12.0 | 170 | 160.04 |
46 | 50 | 32.25 | 25.0 | 218 | 201.57 |
47 | 50 | 17.24 | 52.0 | 250 | 238.21 |
48 | 50 | 8.77 | 108.0 | 221 | 266.11 |
49 | 50 | 4.41 | 220.8 | 221 | 257.41 |
50 | 50 | 2.21 | 446.5 | 200 | 238.07 |
Process | Ig (A) | ESC | |||
---|---|---|---|---|---|
Optimal on Time (µs) | Maximum MRR (mm3/min) | Experimental MRR (mm3/min) | Error (%) | ||
1 | 8.5 | 136 | 40.86 | 37.85 | 7.37 |
2 | 12.5 | 140 | 60.11 | 55.68 | 7.35 |
3 | 25 | 141 | 122.4 | 112.65 | 7.97 |
4 | 36 | 142 | 186.3 | 174.92 | 6.11 |
5 | 50 | 142 | 269 | 249.5 | 7.25 |
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Ismail, M.R.M.; Thangaraj, M.; Karmiris-Obratański, P.; Papazoglou, E.; Karkalos, N. Design of Real-Time Extremum-Seeking Controller-Based Modelling for Optimizing MRR in Low Power EDM. Materials 2023, 16, 434. https://doi.org/10.3390/ma16010434
Ismail MRM, Thangaraj M, Karmiris-Obratański P, Papazoglou E, Karkalos N. Design of Real-Time Extremum-Seeking Controller-Based Modelling for Optimizing MRR in Low Power EDM. Materials. 2023; 16(1):434. https://doi.org/10.3390/ma16010434
Chicago/Turabian StyleIsmail, Mohamed Rabik Mohamed, Muthuramalingam Thangaraj, Panagiotis Karmiris-Obratański, Emmanouil Papazoglou, and Nikolaos Karkalos. 2023. "Design of Real-Time Extremum-Seeking Controller-Based Modelling for Optimizing MRR in Low Power EDM" Materials 16, no. 1: 434. https://doi.org/10.3390/ma16010434