Robust nonlinear feedback-feedforward control of a coupled kinetic Monte Carlo-finite difference simulation

Robust nonlinear feedforward-feedback controllers are designed for a multiscale system that dynamically couples kinetic Monte Carlo (KMC) and finite difference (FD) codes. The coupled codes simulate the copper electrodeposition process for manufacturing on-chip copper interconnects in electronic devices. The control objective is to regulate the current density subject to the condition that the steady-state fluctuation of the overpotential remains bounded within ±0.01 V. The controller designs incorporate a low-order stochastic model that captures the input-output behavior of the coupled KMC-FD code. The controllers achieve the objectives and the closed-loop responses implemented on the low-order model and the coupled KMC-FD code match well within stochastic variations. The nonlinear feedforward control reduces the rise time of the controller response while the feedback control ensures robustness in the presence of model uncertainty.