Feedrate Optimization for Machine Tool Control Subject to Contour Error Constraints

Optimization techniques are applied to feedrate and voltage control in order to improve performance of biaxial contouring systems. This is done by maintaining contour error within a prescribed tolerance while tracking the trajectory in minimum time. In addition to the error constraint, the current and voltage constraints are required to keep the motors from overloading. The design of the controllers requires two steps. First, an LQR-type innerloop controller for the armature voltage is designed for each axis to assure stability using a performance index that penalizes current, armature voltage, and axial error. Next, nonlinear programming techniques are used to find the outerloop control or feedrate profile (which determines the tracking time) and the weighting matrices (which determine the innerloop controller gains) subject to voltage, current, and two-dimensional contour error constraints for a given trajectory. Although the innerloop controllers are originally designed to minimize a weighted sum of axial error, current, and voltage, the outerloop optimization of the feedrate takes into account the two-dimensional contour error explicitly. In this manner, it is possible to tune the controllers to a particular trajectory to achieve the best performance. The method is tested via simulation using a model of a representative biaxial DC motor contouring system for an elliptical trajectory.