Receding horizon reference governor

A method for controlling an operation of a processing machine while or during positioning a worktool according to a processing pattern to machine a workpiece, the method comprising:

• using a memory having stored data including a reference trajectory defined in a spatial domain by a sequence of points for positioning the worktool, and defined in a time domain by a relative time for positioning the worktool on each point of the reference trajectory;
• using a sensor to determine a state of the processing machine;
• receiving, via an input interface in communication with the sensor, data regarding the state of the processing machine;
• using a reference governor to iteratively process the reference trajectory over a receding horizon of a sequence of future points in time including multiple windows of points, and to analytically update the relative time for positioning the worktool for at least some points of the reference trajectory within the receding horizon to satisfy constraints on the operation of the processing machine having the state, wherein the reference governor forms the receding horizon for processing during a current iteration by removing a window of points from the beginning of the receding horizon processed during a previous iteration and adding an unprocessed window of points at the end of the receding horizon, wherein the reference governor, upon detecting violation of the constraints at an infeasible point within one window of the receding horizon, updates the points by assigning the processing time allocated for the entire reseeding horizon to a feasible portion of the receding horizon ending at the infeasible point, wherein the reference governor partitions the feasible portion of the receding horizon into the same number of windows as a number of windows in the receding horizon and stretch the relative time for positioning the worktool according to a processing time of the window of the receding horizon;
• and
• controlling, via a controller, the operation of the processing machine using control inputs causing the worktool to track the updated reference trajectory, wherein the reference governor is in communication with the input interface and the memory.

A control system for controlling an operation of a processing machine while or during positioning a worktool according to a processing pattern to machine a workpiece, a memory to store a reference trajectory defined in a spatial domain by a sequence of points for positioning the worktool and defined in a time domain by a relative time for positioning the worktool on each point of the reference trajectory, wherein the points of the reference trajectory are sampled on a uniform timescale in the time domain and irregularly in the spatial domain, comprising:

• a sensor to determine a state of the processing machine;
• a reference governor to iteratively process the reference trajectory over a receding horizon of a sequence of future points in time including multiple windows of points, and to analytically update the relative time for positioning the worktool for at least some points of the reference trajectory within the receding horizon to satisfy constraints on the operation of the processing machine having the state, wherein the reference governor forms the receding horizon for processing during a current iteration by removing a window of points from the beginning of the receding horizon processed during a previous iteration and adding an unprocessed window of points at the end of the receding horizon, wherein the reference governor, upon detecting violation of the constraints at an infeasible point within one window of the receding horizon, updates the points by assigning the processing time allocated for the entire reseeding horizon to a feasible portion of the receding horizon ending at the infeasible point, wherein the reference governor partitions the feasible portion of the receding horizon into the same number of windows as a number of windows in the receding horizon and stretch the relative time for positioning the worktool according to a processing time of the window of the receding horizon;
• and
• a controller to control the operation of the processing machine using control inputs causing the worktool to track the updated reference trajectory.