Feedback stabilization of forming processes

TL;DR

This paper develops a novel feedback control law for nonlinear forming processes, ensuring stabilization and exponential decay of perturbations, validated through numerical simulations.

Contribution

It introduces a new feedback law based on Lyapunov analysis for controlling nonlinear viscoplastic material models in forming processes.

Findings

Proves exponential decay of perturbations under the new control law.

Demonstrates effectiveness through finite element simulations.

Provides a theoretical foundation for online control of forming processes.

Abstract

We are interested in the control of forming processes for nonlinear material models. To develop an online control we derive a novel feedback law and prove a stabilization result. The derivation of the feedback control law is based on a Laypunov analysis of the time-dependent viscoplastic material models. The derivation uses the structure of the underlying partial differential equation for the design of the feedback control. Analytically, exponential decay of the time evolution of perturbations to desired stress--strain states is shown. We test the new control law numerically by coupling it to a finite element simulation of a deformation process.