Hierarchical optimal contour control of motion systems

Many motion control applications utilize multiple axes to traverse complex trajectories. The hierarchical contour control methodology proposed in this paper treats each axis as an individual subsystem and combines the Internal Model Principle with robust tracking and optimal hierarchical control techniques to track a desired trajectory. In this method the objectives are divided into two levels. Measurable goals of each subsystem are included in the bottom level and unmeasurable goals, which are estimated using the bottom level states, are considered in the top level where the subsystems are synchronized. The proposed methodology reduces system complexity while greatly improving tracking performance. The tracking error for each axis is considered in the bottom level where the Internal Model Principle is used to compensate for unmodeled nonlinear friction and slowly varying uncertainties. The top level goal (i.e., zero contour error) is propagated to the lower level by an aggregation relationship between contour error and physical linear axis variables. A controller is designed at the bottom level which simultaneously satisfies the bottom level goals (i.e., individual axis tracking) and the top level goal. Experimental results implemented on a table top CNC machine for diamond and freeform contours illustrate the performance of the proposed methodology. While this methodology was implemented for a two-axis motion system, it can be extended to any motion system containing more than two axes.