Minimize the chattering of a linear stage driven by a voice coil actuator(VCA)

I have a linear stage driven by a voice coil actuator (VCA), a capacitive probe is used to measure the movement of the stage. A picture is attached to show the basic mechanical design of the stage. Even though the resolution of the VCA is 0.5 um, the overall resolution of the stage is not that good. When I use controllers to achieve position controller of the stage, the stage is always chattering around the set value. It can only achieve 5 um in open loop and around 10 um in PID control. Is there any method to improve the performance by modifying the controlling VI?
I am using NI 6363 to give voltage signal to a LAA amplifier and the amplifier will convert the voltage signal to current signal and drive the VCA. It seems that the output of the LAA amplifier is not constant and it is the LAA amplifier that generate those chattering. The command voltage given to the amplifier is extremely constant with error less than 2mv, which will cause only 0.5 um displacement of the stage by theory. Such kind of motion is similar to the resolution of the sensor but it is only 1/10 of the actual motion noise which is on the scale of 5 um.
The stage has a natural frequency of 30 Hz, which is determined by the stiffness of the springs and the mass of the moving stage. When I use FFT to analysis the movement of the stage, I found that the main noise comes from 30 Hz and 50 Hz (both for open lood and close loop PID). I also use FFT to analysis the command voltage given to the VCA in close loop PID control, the peak frequencies are 10 Hz, 30 Hz, 40 Hz, 50 Hz, 70Hz, 90Hz....
Do I need to use some filter between the amplifier and VCA so that it can reduce the noise without influence the accuracy? Or I can reduce such noise just by using some noise block in the VI program?
Thanks
best
Attachments:
VCA stage.png ‏160 KB
FFT of Error motion with constant voltage_f1.jpg ‏1782 KB
FFT_command voltage_PID_f1.jpg ‏444 KB

Hi Paolo,
It seem the influence from the magnetic field is not a big issue in the position control of a voice coil stage(VCS). I attached some picture of the commecial design of similar VCS and all these stages do not shield the cable connecting the VCA and controller. Anyway, I will try this method to see if it can make the result better.
BTW, for the filter, could you please recommend some model for me? As the current noise is just around the level of 1 mA, I think I may need a very precise filter.
Thanks
best
Attachments:
vcs 1.jpg ‏49 KB
vcs 2.jpg ‏54 KB
vcs 3.jpg ‏22 KB

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Minimize the chattering of a linear stage driven by a voice coil actuator(V​CA)

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Minimize the chattering of a linear stage driven by a voice coil actuator(VCA)