Nonlinear Fixed-Time Convergence Control for Robust Melt-Pool Regulation in Laser Powder Bed Fusion

This paper presents a nonlinear fixed-time convergence control framework for regulating melt-pool dynamics in the Laser Powder Bed Fusion (L-PBF) process. Classical control methods, such as PID controllers, rely on linear approximations and fixed gains that fail to accommodate the rapid thermal fluctuations and nonlinear dynamics inherent in L-PBF, and no prior work has established fixed-time convergence guarantees for melt-pool tracking. The proposed approach ensures predictable convergence of the melt-pool cross-sectional area to its reference value within a fixed duration, independent of initial conditions. A control-oriented thermal model is formulated for Inconel 625 based on energy conservation principles, and stability is rigorously verified using Lyapunov analysis. Simulation-based studies under three representative thermal regimes: heat accumulation alone, heat accumulation with time-varying specific heat, and heat accumulation with simultaneous variation of density and laser absorption efficiency, demonstrate that the proposed controller achieves lower cumulative tracking error (Integral Error Area = 2.895 –3.499) compared with conventional PID-based methods, corresponding to a tracking accuracy improvement of up to 24.5%. These results confirm the controller’s robustness and accuracy, within a simulation environment, offering a reliable pathway for real-time melt-pool regulation and improved process stability in metal additive manufacturing.