Nonlinear Temperature Control of Additive Friction Stir Deposition Evaluated on an Echo State Network

Abstract

Additive friction stir deposition is a recent innovation in additive manufacturing allowing the deposition of metallic alloys onto a metallic deposit bed, creating a purely mechanical metallic bond. The deposition can be done in a layer-by-layer manner, and the purely mechanical process eliminates the need for high energy consumption and can be deposited at a much higher rate than beam-based welding. The mechanical nature of the process allows the bonding of dissimilar alloys and a reduction in size of the heat-affected zone. The additive friction stir deposition process is difficult to model and existing literature has focused on numerical analysis, which is not amenable to online closed-loop control. In this work, a form of reservoir computing called an echo state network is used to model the additive friction stir deposition process from online process data, and validation is performed on a reserved dataset. Subsequently, a model-free controller using Lyapunov-derived combination of the robust integral of the sign error, and a single hidden layer neural network design is developed to control the additive friction stir deposition process. Control efficacy is given by way of a Lyapunov analysis which shows the system is globally exponentially stable, and simulation results with the echo state networks. Stability proof shows that under one assumption, the controller can be extrapolated to the real system. The mean squared error of the tracking result using the controller and echo state network simulation is 2.05 °C.