Laser Sintering Control for Metal Additive Manufacturing by PDE Backstepping

Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

“…The regulation of the interface s(t) to a desired setpoint s r is a crucial task in several applications that involve thermal phase change, such as creating a layer of desired thickness in metal additive manufacturing [32]. However, the actuator dynamics given in (5) introduce a major extra challenge to achieving setpoint regulation while guaranteeing the safety constraints (7), (8).…”

“…It remains to ensure h 2 ≥ 0. Since both h 1 ≥ 0 and h 3 ≥ 0 are satisfied under the input condition (32), and taking into account the fact that h 3 can be written with respect to h 1 and h 2 as defined in (13), we aim to satisfy the following inequality:…”

“…This is achieved by two QP modifications, which, when combined, give a physically natural feedback which saturates the operator's command between two safety feedback laws, one ensuring that the system is heated enough and the other ensuring that it is not overheated. d) Stefan model of phase change and its control: The Stefan model of the liquid-solid phase change has been widely utilized in various kinds of science and engineering processes, including sea-ice melting and freezing [28], continuous casting of steel [43], cancer treatment by cryosurgeries [44], additive manufacturing for materials of both polymer [34] and metal [32], crystal growth [14], and thermal energy storage systems [33]. Apart from the thermodynamical model, the Stefan PDE-ODE systems have been employed to model several chemical, electrical, social, and financial dynamics such as lithium-ion batteries [24], tumor growth process [15], neuron growth [10], domain walls in ferroelectric thin films [40], spreading of invasive species in ecology [12], information diffusion on social networks [47], and the American put option [7].…”

Control of selective laser melting processes: existing efforts, challenges, and future opportunities

“…The roughness was improved by post-processing using laser pulses and refilling the gaps. In [35], a backstepping control was designed for a nonlinear partial derivative equation model. The model was developed to capture the thermodynamics of the phase change of the melt pool.…”

“…Besides that, there are few efforts investigating the phenomena that could appear during the building process. From the control perspective, To investigate the controllability of the SLM process using feedback P and PI control Laser power Melt-pool geometry [24]- [25] To overcome the overheating problem and keyhole formation FF [17] To control melt pool temperature at sufficient time FF combined with P-controller Temperature profile [18], [26] To avoid heat accumulation Layer-wise [7] To control the temperature profile of the scanning segment Model-free-ILC [28]- [30] To investigate the feasibility of ML control system ML-ILC [31] To improve the surface quality of the product -Surface geometry [11], [34] To investigate the effect of scanning path strategy Open-loop control Scanning path Melt-pool geometry [31], [32] To investigate the Lyapunov stability Backstepping Laser power [35] Prove the feasibility of the control algorithm [40], [41] Feedback linearization…”