In this experiment, we used a feedback control to create a stable trap for a NdFeB permanent magnet. The block diagram is the following:
The displacement of the magnet is sensed by the Hall-effect sensor, whose output voltage is proportional to the magnetic flux produced
by the permanent magnet. It has a flat response within the frequencies we are interested in. It is driven by a 5 V power supplier and its
output has a DC voltagle of 2.5 V. We subtracted the DC voltage and used the resulting signal as the error signal. This was
simply achieved by using two channels "A" and "B". The output is "A-B" with a gain equal to one. We then put the error
signal into another SR560 as a low-pass filter with a gain of 100 above 30 Hz. We used the "DC" coupling modes in both
preamplifers. The output is then used to drive a coil. The coil has a dimension of 1.5 inch in diameter and 2 inch in length.
The inductance of the coil is around 0.5 H and the resistance is 4.7 Om. Therefore, it has a corner frequency aournd 10/2pi Hz.
The coil has a iron core inside to enhance the DC force to the permanent magnet. The low-frequency 1/f response of the magnet is produced
by the eddy current damping of the aluminum plane that is below the magnet. This 1/f response is essential for a stable configuration. In the
next stage, we will remove the aluminum plane, and instead we will use a filter to create similar transfer function. At high-frequencies, it behaves as
a free-mass and has a 1/f^2 response. Finally, the magnet is stably levitated.
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