STATE-SPACE REPRESENTATION AND OPTIMAL-CONTROL OF NONLINEAR MATERIAL DEFORMATION USING THE FINITE-ELEMENT METHOD

A state-space model for representing the non-linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal-forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state-space model from non-linear finite element formulation, optimal control strategy and numerical example cases with discussions.