Material grain growth consensus control: A multi-zone heating approach applied on a Monte-Carlo model

This paper considers the control of the grain growth in a copper thin film using a multi-zone micro heater array. The overall system is a multi-input/multi-output (MIMO) control system: currents of 10 micro heaters as input and local microstructure (mean grain sizes) as output. We develop a biased Monte-Carlo (MC) model to simulate complete microstructure evolution in response to the temperature field controlled by the heater input. An FEM temperature model is approximated by Artificial Neural Network (ANN) and coupled with the MC model to predict grain growth under controlled temperature field. Focusing on the metrics of mean grain size, a multi-region empirical model is generalized for efficient control analysis and tuning. We first apply consensus-based output feedback to track a desired grain size trajectory. Stability is verified by passivity theorem using the loop transformation. As an alternate approach, we have also applied Particle Swarm Optimization (PSO) based Model Predictive Control (MPC) to take constraints and the full state into account. Simulations are conducted on the empirical model for controller tuning. Both methods achieve consensus and follow the reference trajectory well. MPC is able to reach consensus faster, but relies on model accuracy. Consensus-based output feedback may not realize optimal performance, but is more robust with respect to the variability of material properties and experimental parameters. The consensus controller is then applied to the MC model to with desirable performance demonstrated as well.