Optimal feedrate control strategy for high-speed high-accuracy corner motions

The technique of calculus of variation is exploited to derive an optimal feedrate control law by minimizing a performance index which is a measure of machining speed and control efforts. The proposed optimal feedrate control law allows feedrate magnitude and feedrate direction to be adjusted simultaneously, resulting in an improved command of contour geometry. The proposed optimal feedrate control law has three promising properties : (i) the preview action of reshaping the original contour geometry according to the inconsistency between the individual axis dynamics, (ii) the cross-coupled effect of treating the biaxial system as a whole unit, and (iii) the adjustable feedrate tuning in an optimal manner such that a performance index which is a measure of machining speed and control efforts is minimised