Time Optimal Contour Tracking for Machine Tool Controllers

A decomposition procedure is applied to the optimization of 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 decomposition procedure used in this paper consists of two phases. The first phase is the feedrate optimization phase. In this phase, the tracking time is minimized with respect to the feedrate profile using a nominal LQR-type controller. The second phase is the controller tuning phase. Using the feedrate profile obtained in the first phase, 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 iterative decomposition procedure is used to prevent any mismatch in sensitivity since the feedrate profile has dominant effects on the constraints and tracking time while the weighting matrices have dominant effects only on the constraints. The procedure is tested and evaluated using a model of a representative biaxial DC motor system.