Method and apparatus for using fast fourier transform feedback to compensate for non-linear motion

A hybrid learning feedback controller (HLC) system for controlling operation of a xerographic imaging device, the xerographic device having an input port and an output port, the HLC feedback controller system comprising:

• a feed forward controller system operative to receive an actuating signal and in response to the actuating signal output a manipulated variable, the feed forward controller system comprising:
• a feed forward controller;
• a first input summing node connected to the feed forward controller, the first input. summing node operative for summing a reference input and a first feedback signal;
• a second input summing node connected to the feed forward controller, the second input summing node operative for summing the manipulated variable and a second feedback signal;
• a first proportionality device serially connected to the second input summing node and the input port of the xerographic imaging device;
• a first feedback compensator connected to the controller;
• and
• a second feedback compensator connectable to the controller, the second feedback compensator having a learning controller system for correcting non-linear motion of the device;
• wherein the second feedback compensator comprises:
• a sampling device;
• and
• a signal generator connected to the sampling device, the signal generator operative to produce the second feedback signal,
• wherein sampling device comprises:
• fast Fourier transform (FFT) device;
• a magnitude detector connected to the FFT device;
• and
• a phase comparator connected to the magnitude detector.