Abstract
We develop online feedback control for forming processes governed by nonlinear material models. A novel approach based on a description using partial differential equation governing time-dependent viscoplastic deformations is proposed. The derivation of the feedback control law is based on a Lyapunov analysis of the linearised partial differential equation. Analytically and in the spatially one-dimensional setting exponential decay of the time evolution of perturbations to desired stress–strain states is established. Also, a similar performance of the feedback control is observed when implemented in a three–dimensional finite element simulation of titanium alloy forming.
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