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Message ID: 711     Entry time: Wed Aug 14 00:05:00 2013
Author: Giorgos 
Type: DailyProgress 
Category: SUS 
Subject: 3DoF Stability in Simulink 

Today, I achieved stability in Simulink for 3DoF, including noise to the hall-effect sensors and the coil's conditioning. We had measured the noise at the ADC to be max 20mV, but that value is amplified by the gain (91) of the HE conditioning boards. So, I included noise of 20/91 mV. I attached the final model and the script.   Maglev_3DoF_Giorgos.slx.

I also used vector fitting to find the transfer functions of the coupling between DC1 coil to all sensors. An example of the successful resemblance is shown in the figures below (DC1 coil to W sensor). The figure on the left shows the modelling of the coupling and the deviation between the fitting and the data. The right figure shows a body plot of the modelled and measured transfer function.

Vector_Fitting_Cancellation.pngDC1toW_BodePlot.png

I also calculated the amount of cross-coupling and noise inside our system in order to find the allowed gain to avoid any saturation.

Since the OP27 in the coil conditioning board also saturates at 10V, the DAC should provide no more than 400mV; beyond that point, the gain of 25 we introduced in the coils would saturate the OP27.

We had also found the cross coupling to be around 0.01 for two nearby sensors and 0.001 for the third one (in the 3DoF case we ignore all others). If our DAC never exceeds 400mV, cross coupling would get at most 0.0084V (8.4mV) at the ADC.
Similarly, if the coils get at most 10V, the maximum force they provide is 0.02N, which translates to 0.0113m (1.13cm) maximum displacement of the plate. Such displacement would produce 0.1989V at the ADC. Adding noise to these, our signal is only 0.2273V, well below the saturation of the ADC.
Inside the feedback filter, the cross coupling is cancelled down to -60dB (0.001V/V), so only 0.0012V remains, given a 400mV DAC output). The signal is thus 0.2201V. To avoid saturation of the DAC, we can afford a maximum gain of 1.8.

Attachment 2: mag_lev_20130809Giorgos3Channels.m  1 kB  Uploaded Wed Aug 14 19:12:13 2013  | Hide | Hide all
%%%%%%%%%%%%%%%%%% Magnet %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mag_mass = 0.5;
mag = 1/mag_mass;

%%%%%%%%%%%%%%%%% Negative Spring %%%%%%%%%%%%%%%%%%%%%%

omegam = 2*pi*0.3;            % resonant frequency
K = -mag_mass*omegam^2;      % F=-K*x

... 54 more lines ...
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