Infinite-dimensional geometric regulation in solid freeform fabrication

A distributed-parameter geometry control scheme is established to obtain a desired surface topology in material deposition processes, by modulating the feed and motion of a moving mass source. This is based on dynamic geometry shaping by a real-time optimization technique. The control strategy is founded on an analytical model of such material addition, using superposition of unit deposition distributions, composed of elementary spherical primitives. This real-time surface geometry model, with its parameters identified by in-process profile measurements, is used for Smith-prediction of the material shape in the unobservable deposition region. The methodology is tested in geometric command following on a fused wire deposition welding station, using optical sensing by a scanning laser stripe. The infinite-dimensional modeling and control methodology is applicable to solid freeform fabrication methods, generating 3-D solid objects by material deposition in successive layers made of adjacent beads