Dynamic modeling of friction stir welding for model predictive control

Abstract

Controlling temperature in Friction Stir Welding (FSW) is important for consistent post-weld properties. PID temperature control of FSW has been previously implemented once the process is at a quasi-steady state, but has not worked well during either starting transients or during process changes that significantly alter the system dynamics. This work develops models and theories for the application of Model Predictive Control (MPC) to FSW and assesses temperature predication capabilities in simulation.Two different model forms are developed for MPC and are evaluated in simulation. The first model is a first-order plus dead time (FOPDT) model. The second is the Hybrid Heat Source model that combines the heat source method and a 1D discretized thermal model of the FSW tool. Model parameters are determined by fitting model predictions to weld data. This is done both manually and via optimization-based curve fitting. The models’ fits are compared quantitatively by calculating the mean-subtracted SSE (MSSSE) and average absolute derivative error. The manually tuned parameter sets result in a better fit by both metrics for both models. The FOPDT model matches the post-startup-transient data better than the Hybrid Heat Source, and is expected to have superior control in this region of the weld. The Hybrid Heat Source model is expected to have superior temperature control during the startup transient.