Texas Instruments TIDA-060040, Manual

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Rotation Angle (deg)
A
ngle E
rror (d
eg)
0 45 90 135 180 225 270 315 360
-4
-3.6
-3.2
-2.8
-2.4
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
Natural Error
4 Piece Residual Error
Rotation Angle (deg)
A
ngle E
rror (d
eg)
0 45 90 135 180 225 270 315 360
-4
-3.6
-3.2
-2.8
-2.4
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
Natural Error
8 Piece Residual Error
Rotation Angle (deg)
A
ngle E
rror (d
eg)
0 45 90 135 180 225 270 315 360
-4
-3.6
-3.2
-2.8
-2.4
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
Natural Error
16 piece Residual Error
Rotation Angle (deg)
A
ngle E
rror (d
eg)
0 45 90 135 180 225 270 315 360
-4
-3.6
-3.2
-2.8
-2.4
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
Natural Error
32 Piece Residual Error
Figure 3-6. Multi-Point Linearization
As the number of samples increases, the resulting peak error is continually reduced. Depending on the required
system accuracy, 8 points to 64 points can often provide adequate accuracy. In a more advanced approach, it
is possible to match the error profile to a set of equations which are a combination of harmonics of the rotation
frequency. By performing complex analysis, it is possible to generate a series of coefficients, α
i
and β
i
, that may
be used as shown in Equation 10 :
Correction Factor = ∑
i = 1
n
α
i
sin i*θ + β
i
cos i*θ
(10)
Here, the total error is a combination of the scalar factors for each harmonic of the measured angle. Using this
approach can produce superior results to the multi-point linearization method and does not require storing as
much data in memory.
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22 Absolute Angle Encoder Reference Design With Hall-Effect Sensors for
Precise Motor Position Control TIDUC07 – MARCH 2022
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