# Dynamic Observer Modeling and Minimum-Variance Self-Tuning Control of EDM Interelectrode Gap
## 5 Test Verification
### Comparison and Verification of Process Targets under Different Gap Conditions  
EDM uses the high-temperature plasma generated by the discharge to remove the workpiece. The plasma energy is mainly determined by the interelectrode voltage and the loop current, while the material removal rate and the surface roughness in EDM are influenced by the interelectrode voltage and loop current. The literature [27] has studied the effect of the interelectrode gap on the interelectrode voltage and loop current. Therefore, it is of great significance to study the effect of the interelectrode gap on the material removal rate and surface roughness of EDM. A single-crystal silicon processing experiment was conducted by using the minimum-variance self-tuning control, and the interelectrode gap desired value was 60, 50, and 40 \(\upmu\)m. The test processing time at the three desired gaps was 100 s. The tracking effect of the three different desired gaps is shown in Figure 13.  
Figure 12: Sine wave tracking: (**a**) The original image; (**b**) partial enlargement; (**c**) parameter identification result.  
After the test was completed, the mass of single-crystal silicon before and after machining was measured by the JD500-3 precision electronic balance (Shenyang Longteng Electronics Co., Ltd, Shenyang, Liaoning, China) to calculate the material removal rate. The balance's maximum measurement mass is 500 g, with an accuracy of 0.001 g. The surface morphology and roughness of the processed single-crystal silicon was measured by the Leica DCM 3D white light interferometer (Leica, Solms, Hessen, Germany). The three-dimensional surface and two-dimensional shape of the workpiece surface are shown in Figures 14-16. The measurement results of material removal rate and surface roughness are shown in Table 4.  
Figure 14: Three-dimensional surface topography and two-dimensional surface topography (\(d\) = 40 \(\upmu\)m). (**a**) Three-dimensional surface topography; (**b**) two-dimensional surface topography.  
Figure 13: Three different desired tracking effects.  
In the EDM system, the plasma channel diameter and pit size formed by a single-pulse discharge are determined by the current and the effective discharge time [28, 29], and the higher the current and longer the effective discharge time, the larger the plasma channel diameter and the crater. In continuous pulse machining, the higher the current and the longer the effective discharge time, the greater the material removal rate and surface roughness. The quantitative relationship between the plasma channel diameter and the interelectrode gap is given in Reference [27], and the larger the interelectrode gap, the smaller the loop current. Therefore, when the interelectrode gap increases, the loop current decreases, which leads to a reduction of the material removal rate and surface roughness. From Table 4, it can be seen that the material removal rate and surface roughness decrease with the increase of the interelectrode gap. The above analysis fully proves the rationality of the test results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Interelectrode Gap (\(\upmu\)m)** & **Material Removal Rate (mg/min)** & **Surface Roughness (\(\upmu\)m)** \\ \hline
40 & 51 & 7.35 \\
50 & 46 & 5.66 \\
60 & 39 & 4.58 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Material removal rate and surface roughness data.  
Figure 16: Three-dimensional surface topography and two-dimensional surface topography (\(d=60\)\(\upmu\)m). (**a**) Three-dimensional surface topography; (**b**) two-dimensional surface topography.  
Figure 15: Three-dimensional surface topography and two-dimensional surface topography (\(d=50\)\(\upmu\)m). (**a**) Three-dimensional surface topography; (**b**) two-dimensional surface topography.