## 4 Experimental Validation

Table 1: Materials, geometries, and deposition tool paths in different experiments. \begin{table}
\begin{tabular}{c c c c} \hline
**Process Parameters** & \multicolumn{3}{c}{**Powder Material**} \\ \cline{2-4}  & **316 L Stainless Steel** & **LPW-35N Nickel Alloy** & \\ \hline Laser voltage & 6.2 & 6.2 & V \\ Printing speed & 20.0 & 20.0 & mm/s \\ Powder feeding rate & 6.09 & 7.73 & g/min \\ Layer thickness & 0.2 & 0.3 & mm \\ Infill hatch distance (for solid parts only) & 2.0 & 2.0 & mm \\ \hline \end{tabular}
\end{table} 
Table 2: Constant nominal process parameters used for direct energy deposition (DED) processes without control. also scanned and reconstructed, as shown in Figure 5f. It can be observed that the central bulge area was further flattened compared with the conventional PID controlled sample. Figure 6a-c shows the time plots of the MPW data and laser voltage signals for the uncontrolled sample, conventional PID controlled sample, and adaptively controlled sample, respectively. In Figure 6a, a progressive increase in the MPW is observed due to the accumulated heat built up in the part when using a constant laser voltage. The MPW exceeded 140 pixels at the end of the fabrication process with the trend of growing even larger. In Figure 6b, the conventional PID controller was used, and the growth of MPW was reduced compared to the uncontrolled sample. However, there was still an increasing trend in MPW. About half of the MPW data were in the range of 120-130 pixels after 250 s, suggesting an unstable heat input across the surface and the possibility of more severe geometry inaccuracy if the deposition continues. In Figure 6c, the adaptive controller showed a more significant effect on stabilizing the melt pool than the conventional PID controller. The laser voltage signal was reduced gradually to decrease the average energy density as the process continued. The MPW data were maintained at a narrower range of 115-120 pixels throughout the entire deposition process. Therefore, uneven localized heat accumulation was minimized, and the possibility of surface defect occurrence was reduced. Figure 5: Samples of Experiment 1 (solid semicylinder with the profile tool path, 316 L stainless steel). (**a**) The sample fabricated without control; (**b**) The reconstructed surface of the uncontrolled sample; (**c**) The sample fabricated with a conventional proportional–integral–derivative (PID) controller; (**d**) The reconstructed surface of the conventional PID controlled sample; (**e**) The sample fabricated with the proposed adaptive controller; (**f**) The reconstructed surface of the adaptively controlled sample. During the closed-loop control, the laser voltage output was constrained by a maximum value of 6.2 V. This value was the limit of the DED process window determined in previous experiments, in order to prevent material failure. In fact, as shown in Figure 6b,c, the laser voltage was below 6.0 V for most of the time and seldomly hit the 6.2 V limit. Figure 7 shows the PID gain variations for the entire time-plots extracted from Figure 6c, where the controller parameters (\(K_{P}\), \(K_{I}\), \(K_{D}\)) were updated in each adaptive control interval (10 s in this study). The collected I/O dataset in each interval was used to optimize the controller parameters automatically without manual tuning. The resultant controller parameters were truncated at three decimals, as shown in the plot. The resultant PID controller had zero derivative gains (\(K_{D}\) = 0), which was acceptable in this case since the negligible derivative action could reduce the system's sensitivity to noises. When the first layer was deposited, a significant portion of the input heat was conducted to the substrate, and hence the melt pool was in a transient state. Since neither surface defect nor geometric nonconformance was observed in the first layer, a constant laser voltage was applied.