A method for the optimal control of forging process variables using the finite element method and control theory

In this paper, a new method is advanced for optimal control of the thermomechanical parameters during hot plastic-working processes of advanced materials, based on the finite element method and modern optimal control theory. The proposed method can be described as follows. First, the optimal trajectories of the thermomechanical parameters were defined from a grain size evolution model and the stable regions of the thermomechanical parameters. The stable regions were determined by combining artificial neural networks (ANN) with the dissipative structure theory. Second, the finite element models were transferred to suitable state–space models. Third, the optimal profile for the process parameters was fixed based on the state–space models and linear quadratic regulator (LQR) theory in order that the thermomechanical parameters of selected locations within the forging conform to the optimal trajectories and physical constraints. Applying the proposed method to an upsetting process of IN718 alloy, the ram velocity profile was determined to obtain high quality forgings. The proposed method lays the theoretical foundation for the open-loop control of forging processes for difficult-to-deform materials.