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Message ID: 688     Entry time: Thu Aug 1 11:43:15 2013
Author: Giorgos 
Type: DailyProgress 
Category: SUS 
Subject: Sensing Matrix and Calibration 

Sensing Matrix
I calculated the entries of our sensing matrix S x = y, where S is the 6x6 sensing matrix, x is 6x1 vector signal from six degrees of freedom and y is the 6x1 signal sensed by six HE sensors. Haixing told me to ignore the 7th sensor (N), because in practice we could levitate the system using only the rest six. The sensing matrix contains many unknown coefficients, which we will find by calibrating the system and adjusting the values. I will post the matrix, once we know the entries are correct.

Calibration

Coil - Force

We want to get an idea of how much force is applied on the plate for different signals from the digital filter. So, we measure the DC motors output (in mV) and we also have previous measurements of how the DC motors voltage correlates to the force applied. Therefore, knowing how the digital filter output corresponds to the DC motors voltage offset, we can infer the relationship between digital signal output and force on the plate. We first worked with the first top coils: AC1, AC2, and AC3. While changing the output for a single coil, we measured the response of all the motors to consider cross-coupling effects. While measuring the response of the bottom motors, we have to make sure there is always contact betweem them and the plate; otherwise, the data will not show how the force on the motors changes.    

Calibration of Coils - Force
    AC1     AC2     AC3  
V/mV B1 B2 B3 B1 B2 B3 B1 B2 B3
0 -276 170 246 -268 -44 285 -268 -32 259
-9 -263 -28 281 -265 -38 256 -265 -27 249
-7 -262 -32 281 -265 -40 259 -267 -28 251
-5 -263 -36 283 -265 -41 260 -267 -29 253
-3 -264 -38 283 -266 -43 263 -266 -28 254
-1 -267 -41 283 -267 -44 264 -266 -30 258
1 -268 -44 285 -268 -45 266 -266 -30 260
3 -271 -46 286 -268 -46 268 -265 -29 263
5 -272 -49 287 -270 -47 271 -266 -31 265
7 -274 -52 288 -272 -45 276 -265 -31 268
9 -274 -54 287 -272 -44 277 -264 -34 275

        

 

 

 

 

 

 

 

 

 

 

When we apply feedback, current runs through the coils and creates/adjust the ambient magnetic field. However, the magnetic force the HE sensors feel from the levitated plate is so coupled with the one created by the coils. We also want to know how sensitive the sensors are to our coils, when we apply feedback and so we again took measurements.

Calibration of Coils - Sensors
    AC1     AC2     AC3  
Source/Bits AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3
0 3400 -2800 2050 3400 -2820 2040 3440 -2790 2040
-9 -680 -2810 2050 3430 -7140 2050 3430 -2790 -2040
-7 240 -2810 2050 3440 -6170 2090 3440 -2790 -1140
-5 1160 -2800 2050 3430 -5220 2075 3430 -2790 -220
-3 2075 -2810 2050 3430 -4250 2060 3410 -2820 690
-1 2980 -2800 2050 3440 -3300 2050 3430 -2810 1600
1 3880 -2810 2040 3440 -2350 2060 3410 -2820 2510
3 4780 -2840 2040 3430 -1400 2060 3410 -2800 3420
5 5680 -2840 2040 3420 -450 2050 3420 -2800 4310
7 6590 -2840 2050 3400 520 2050 3420 -2820 5230
9 7480 -2840 2040 3420 1490 2040 3410 -2800 6130

 

 

 

 

 

 

 

 

 

 

 

We also want to know how sensitive the sensors are to a vertical displacement of the plate:

HE output - plate displacement
  Inches/bits AC1 AC2 AC3
Group1 0'' 3290 -3110 1975
  0.3'' 3510 -2830 2190
Group2 0'' 3280 -3110 1940
  0.3'' 3540 -2850 2160

In all our measurements, we noticed some hysteresis so we had to follow the same order when recording the data. In case of a mistake, we had to repeat from the beginning.

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