REDUCED-ORDER STATE-SPACE MODELS FOR CONTROL OF METAL-FORMING PROCESSES

This paper describes a systematic procedure to build reduced-order ana lytical models for representing metal-forming processes. The non-linea r finite element method (FEM) is used to model and simulate the metal- forming process. The procedure for construction of the state space mod el from the finite element model is described. Available model reducti on schemes are utilized in generating reduced-order models from the fu ll size state space representation of the system. The objective of the design process is to maintain specified effective strain rates in cer tain critical elements of the workpiece. The control input (ram veloci ty) is designed off-line using the linear quadratic regulator (LQR) th eory with finite time control. Three model reduction methods are studi ed and a suitable technique applicable to the metal-forming process is identified. The selection is based on two performance measures, namel y 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.