Reduced-order state space models for control of metal-forming processes

This paper describes a systematic procedure to build reduced-order analytical models for representing metal-forming processes. The non-linear finite element method is used to model and simulate the metal-forming process. The procedure for construction of the state space model from the finite element model is described. Available model reduction schemes are utilized in generating reduced-order models from the full size state space representation of the system. The objective of the design process is to maintain specified effective strain rates in certain critical elements of the workpiece. The control input (ram velocity) is designed off-line using the linear quadratic regulator theory with finite time control. Three model reduction methods are studied and a suitable technique applicable to the metal-forming process is identified. The selection is based on two performance measures, namely the designed velocity schedule and the infinity norm of the reduced-order system. The method of building the reduced-order process models is explained and demonstrated using two case studies.