Partial Differential Equation-Based Multivariable Control Input Optimization for Laser-Aided Powder Deposition Processes

This paper deals with the systematic optimization method for multiple input variables (laser irradiation power and scanning speed) in a class of laser-aided powder deposition (LAPD) processes. These processes are normally described by a coupled system of nonlinear partial differential equations (PDEs). To begin with, a desired solid–liquid (S/L) interface geometry is first approximated from a few practical process target parameters that define the desired process properties. Then, the control problem is formulated as one of seeking the optimal combination of process inputs that achieves close tracking of the desired S/L interface in quasi-steady state. The paper details the derivation of the adjoint-based solution for this PDE-constrained multivariable control input optimization problem. The effectiveness of the proposed method is illustrated via a case study on a laser cladding process.