Hierarchical optimal force-position-contour control of machining processes. Part II. Illustrative example

There has been a tremendous amount of research in machine tool servomechanism control, contour control, and machining force control; however, to date these technologies have not been tightly integrated. This paper develops a hierarchical optimal control methodology for the simultaneous regulation of servomechanism positions, contour error, and machining forces. The contour error and machining force process reside in the top level of the hierarchy where the goals are to 1) drive the contour error to zero to maximize quality and 2) maintain a constant cutting force to maximize productivity. These goals are systematically propagated to the bottom level, via aggregation relationships between the top and bottom-level states, and combined with the bottom-level goals of tracking reference servomechanism positions. A single controller is designed at the bottom level, where the physical control signals reside, that simultaneously meets both the top and bottom-level goals. The hierarchical optimal control methodology is extended to account for variations in force process model parameters and process parameters. Simulations are conducted for four machining operations that validate the developed methodology. The results illustrate that the controller can simultaneously achieve both the top and bottom-level goals.