No. 2022.16
Stabilization of forming processes using multi–dimensional Hamilton–Jacobi equations
M. Bambach, M. Gugat, M. Herty, and F. Thein
Subject: Partial differential equations, stationary state, process control, numerical simulation, mathematical models, feedback control, microstructure
Abstract
We introduce a feedback control for the stabilization of forming processes to ensure suitable microstructure of the formed workpiece. Mathematically, the underlying model for the evolution of the microstructure is given by a spatially two–dimensional partial differential equation of Hamilton–Jacobi type. The feedback control is applied at the boundary and exponential stabilization of stationary states in $L^2$– is established. The derivation is based on a Lyapunov function extending prior work to the spatially two– dimensional case. The theoretical findings are confirmed by numerical simulations.
Reference
2022 IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico, 2022, pp. 7376-7381