## 4 Experimental Validation
As the deposition process continued, the heat transfer rate between part and substrate reached a steady state, and the local fluctuation of the  
Figure 6: Time plots of the melt pool width (MPW) and laser voltage signals for Experiment 1 (solid semicylinder with the profile tool path, 316 L stainless steel). (**a**) The data without control; (**b**) The data with conventional PID control; (**c**) The data with adaptive control. MPW would potentially lead to geometric inaccuracies. Therefore, the control action was started in the second layer at the time around 30 s. After the second layer, the MPW was stabilized and maintained within 115-120 pixels. Figure 7: The MPW data for the entire time-domain extracted from Figure 6c, showing the automatic update of the controller parameters (\(K_{p}\), \(K_{l}\), \(K_{D}\)). Figure 8 illustrates the results of Experiment 2. The samples in Experiment 2 had the same nominal dimensions as those in Experiment 1 but with different tool path settings. In particular, the samples printed in Experiment 2 did not include the profile tool path. Only the infill was built, while the outer contour of each layer was not deposited. Figure 8a,b shows the sample fabricated with the constant laser voltage (6.2 V) without control. With a higher central bulge and lower edges, this sample had a more significant distortion than that seen in Figure 5 in Experiment 1, which was the result of less material added to the edges to compensate for the distortion when the profile tool path was absent. The conventional PID control method was used for the sample in Figure 8c,d. Both the height and area of the surface bulge area were reduced compared to those in the uncontrolled sample. However, before the PID controller was deployed, system identifications and trial-and-error experiments were conducted to determine the PID gains, thus introducing extra time and material wastage. With the proposed adaptive controller employed, as shown in Figure 8e,f, the sample had a flatter surface, sharper edges, and hence a better geometric accuracy than its uncontrolled and conventional PID controlled counterparts. Figure 9 shows the time plots of the MPW and laser voltage in Experiment 2. The MPW value of the uncontrolled sample increased continuously until it exceeded 150 pixels at the end of the fabrication. The MPW value of the conventional PID controlled sample shows a slower growth compared to the uncontrolled sample. Compared to the conventional PID controller, the proposed adaptive control method was able to further stabilize the MPW while keeping it within the range of 115-130 pixels. The proposed adaptive control method was proven effective regardless of the tool path setting. Figure 8: Samples of Experiment 2 (solid semicylinder without 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 conventional PID controller; (**d**) The reconstructed surface of the conventional PID controlled sample; (**e**) The sample fabricated with proposed adaptive control method; (**f**) The reconstructed surface of the adaptively controlled sample. Experiment 3 was conducted to validate the capability of the proposed adaptive controller in improving the geometric accuracy for any random part, without extra controller tuning or system identification. Compared to the previous two experiments, Experiment 3 involved different material (LPW-35N nickel alloy instead of 316 L stainless steel), geometry (a thin-walled hollow part instead of a solid part), tool path (continuous spiral path instead of zigzag straight path segments), and process parameters (different powder feeding rates and layer thicknesses). The fabrication result of Experiment 3 is shown in Figure 10. Figure 10a shows the uncontrolled sample deposited with the constant laser voltage (6.2 V), which shows a wavy top surface with obvious bulge and dent regions.