each halbach array permanent magnet 58 as illustrated in fig4 b the net force between the two arrays at a given distance can be found by summing the forces between all the magnetized surfaces of the two arrays permanent magnet dimension a 7 9375 mm 5 16 in is predicted to meet the assistive force requirements of the stage using two identical halbach arrays for each permanent magnet i e there are a total of four arrays for each passive assist device in some embodiments a cascaded p p feedback fb controller with velocity and acceleration feed forward ff is used to control the position of scanning table 18 it can be implemented using a real time controller running at 10 khz sampling frequency to achieve a closed loop bandwidth of about 290 hz additional feed forward permanent magnet force and disturbance compensators are implemented to reject known disturbances as illustrated in the block diagram of fig5 the role of the permanent magnet force compensator is to cancel the spill over assistive forces in the constant velocity region of each scan based on the measured f pm d curve of the permanent magnets the disturbance force compensator cancels out the position and velocity dependent disturbance force ripples associated with the linear motor fig6 a illustrates an in house built prototype of magnet assisted stage system 10 as described herein the predicted and experimentally measured f pm d curves of each passive assist device are illustrated in fig6 b they are in good agreement and confirm that the stage is capable of providing the needed maximum assistive force 525 n at a gap of 3 2 mm between the magnets while providing less than 4 n of assistive force at a gap.