Time optimal contour tracking for machine tool controllers

A decomposition procedure was used to optimize feedrate and voltage control of biaxial contouring systems. The optimization procedure takes into account the contour-error, voltage, and current constraints while tracking the contour in minimum time. The tracking time is first minimized with respect to the feedrate profile using a nominal linear-quadratic-regulator type of controller. Using the feedrate profile obtained, the controller is tuned by minimizing a certain objective function with respect to the Q and R weighting matrices. The process is repeated until no further improvements can be obtained in tracking time. The use of iterative decomposition avoids mismatch in sensitivity since the feedrate profile has significant effects on the constraints and tracking time, while the weighting matrices have significant effects only, on the constraints. The procedure was tested and evaluated using a model of a representative biaxial DC motor system.<>