Control of the fabrication of long slender workpieces of arbitrary shape—part II: Closed-loop control of the multi-axis bending process

A feedback control scheme for the multi-axis bending process is presented. The closed-loop control is derived from transfer functions that represent the bending and twisting processes. The dynamics of these processes are due to the convection of shape between the bending dies during deformation. The success of the feedback control also depends on accurate measurement of part shape. A method based on laser scanning has been developed to find the intrinsic shape representation of the measured workpiece. Shape errors are defined as the difference between the intrinsic geometric quantities of the actual and desired part. By applying shape errors to the inverse transfer functions, we can obtainincremental changes in the axis control commands. Experimental results demonstrate that the feedback control causes shape errors to decrease on subsequent iterations.