  Precise positioning and fast traversal times are crucial in achieving high
productivity and scale in machining. This paper compares two optimization-based
predictive control approaches that achieve high performance. In the first
approach, the contour error is defined using the global position, the position
on the path is inferred through a virtual path parameter, and the cost function
combines the corresponding states and inputs to achieve a trade-off between
high speed and positioning accuracy. The second approach is based on a local
definition of both the error and the progress along the path, and results in a
system with a reduced number of states and inputs that enables real-time
optimization. Terminal and trust region constraints are required to achieve
precise tracking of geometries where a fast or instantaneous change in
direction is present. The performance of both approaches using different
quadratic programming solvers is evaluated in simulations for geometries that
are challenging in machine tools applications.
