Low Velocity Friction Compensation and Feedforward Solution based on Repetitive Control

One of the most significant sources of tracking error for an X-Y table is static friction, a nonlinear disturbance. Static friction, or stiction, occurs when an axis makes a zero velocity crossing, i.e. when an axis reverses direction. In traversing a circular profile for example. an X-Y table encounters zero velocity crossings at ninety degree intervals around the circle, leaving relatively large tracking errors referred to as "quadrant glitches". To eliminate errors caused by stiction, repetitive control, a subclass of learning control, is employed. Experiments are conducted on the X-Y bed of a CNC milling machine. The repetitive controller is implemented digitally in the position servo loop. The velocity loop is closed internally by an analog PI servo which is part of the original controller of the CNC milling machine. The repetitive controller undergoes successive passes in tracking a profile containing a zero velocity crossing. The repetitive controller contains an internal periodic signal generator which receives the error over repetitive cycles and generates a compensating input for cancellation of the repetitive disturbance. Experimental data indicates that perfect velocity tracking can be achieved in twelve cycles or less. Of particular interest is the velocity command input generated by repetitive control. The input contains feedforward information for developing perfect trajectoris at low velocities. An analysis for using the feedforward information for zero velocity crossings at different local accelerations is developed.