LP12- Power Supply- Need education

I have read a lot about different options to upgrade the analogue power supply.
A phono stage need to amplify micro signal would require very good power supply to ensure there is minimal noise interfere with the signal.
I read about Lingo and other power supply articles, however they never mentioned about the science behind it.
How could a power supply powering a motor will introduce noise to the cartridge especially belt drive?
How do you measure the noise when playing a record?
Or would  the power supply provide a more stable rotational speed, my speed measurement on the turntable shows very consistence rpm once it is playing?
I really do not understand why a Lingo power supply cost so much but cannot provide an improvement with a measurable results.
Could someone educate me.
@phoenixengr   I believe in the Linn Radikal upgrade the motor is a brushed DC design.
@daveyf- I believe that is correct. If I’m not mistaken, it also uses feedback from the platter for accurate speed control.

Mark Kelly had an innovative design for a brushed DC motor controller that did not require speed feedback from the platter, but as far as I know, he never pursued it.
@phoenixengr That is also correct. There is an optical reader that mounts under the platter and reads a mark on the platter every revolution.
@phoenixengr - Mark Kelly had two very unique designs for open loop controllers, the brushed DC controller being one of them. The other was the Synchrotron AC-1, which was an open loop controller for synchronous AC motors. That controller was the most accurate open loop motor controller I’ve ever used, and every conceivable motor parameter (frequency, amplitude, phase angle, harmonic distortion, etc) could be adjusted. This level of parametric adjustment allowed cogging to become nearly non-existent.

I still own both.
Do you mind if I ask how does Open Loop Controller work? 
If it is an open loop, it does not need a controller since there is no feedback and therefore no correction is required.