Encoder self-callibration apparatus and method
View Patent ↗The disclosed electronic processing apparatus calculates and applies calibrations to sensors that produce quasi-sinusoidal, quadrature signals. The apparatus includes either or both of fixed and programmable electronic circuits. The apparatus includes a circuit to calculate the phase and magnitude corresponding to the two input (quadrature) signals. The apparatus also includes a circuit for accumulating the number of cycles of the input signals. The apparatus also includes a circuit to generate Gain, Offset, and Phase calibration coefficients, wherein the circuit compares the phase space position of the measured phasor with the position of an idealized phasor, the locus of the idealized phasor in phase space being a circle of predetermined radius with no offset. The calculation of the coefficients occurs without user intervention, according to a pre-programmed rule or rules. The apparatus also includes a circuit to apply the Gain, Offset, and Phase calibration coefficients to the measured quadrature signals x i and y i according to the formulae X i =( x i +Ox i +P i ×y i )× Gx i Y i =( y i +Oy i )× Gy i where Gx i and Gy i are the scaling coefficients, Ox i and Oy i are the offset coefficients and P i is the phase coefficient and where X i and Y i are the post-calibration quadrature signals. The apparatus also includes a circuit that creates an output signal representative of the current, calibrated phase. The output signal is either a parallel, digital word or one or more serial pulse trains wherein the total number of pulses produced over time corresponds to the total phase change in the measured signal. The output signal is coded to allow phase decreases as well as phase increases.
1. A method of calibrating an optical encoder, the encoder generating two analog quadrature signals, x, y, the method comprising:
a. generating a plurality of digital samples, x i , y i , of the analog signals x, y, i having integer values from one to an integer n larger than one;
b. generating a plurality calibrated samples X i , Y i , according to the equation
X i =( x i +Ox i +P i ×y i )× Gx i
Y i =( y i +Oy i )× Gy i
Gx i and Gy i being scaling coefficients, Ox i and Oy i being offset coefficients, and P i being phase coefficients;
c. generating a plurality of magnitude M i , and phase, Φ i , samples according to the equations
M i =√{square root over (X i 2 +Y i 2 )}
Φ
i
=
A
TAN
[
Y
i
X
i
]
,
M i and Φ i defining one sample of a phasor V i , according to the equation
V i =M i exp( jΦ i ),
j being the complex number square root of negative one and where V i may be represented by a line segment having a first end and a second end, the first end lying at an origin of a two-dimensional coordinate system, the coordinate system defining an x axis and a y axis, the origin being located at an intersection of the x axis and the y axis, the second end being displaced from the first end by a length equal to the magnitude M i , in a direction defined by a angle relative to the x axis equal to the phase Φ i ;
d. providing initial values for the scaling coefficients, Gx 1 and Gy 1 , the offset coefficients, Ox 1 and Oy 1 , and the phase coefficients, P 1 ;
e. adjusting the values of the scaling coefficients, the offset coefficients, and the phase coefficients so that
Gx i+1 equals either Gx i or Gx i plus or minus an incremental adjustment,
Gy i+1 equals either Gy i or Gy i plus or minus an incremental adjustment,
Ox i+1 equals either Ox i or Ox i plus or minus an incremental adjustment,
Oy i+1 equals either Oy i or Oy i plus or minus an incremental adjustment,
P i+1 equals either P i or P i plus or minus an incremental adjustment;
the incremental adjustments being made so that a distance between the second end of a hypothetical phasor V′ i and a circle is less than or equal to a distance between a second end of the phasor V i and the circle, the circle having a pre-determined radius and being centered on the origin, the hypothetical phasor V′ i being determined by the following equations:
X′ i =( x i +Ox i+1 +P i+1 ×y i )× Gx i+1
Y′ i =( y i +Oy i+1 )× Gy i+1
M′ i =√{square root over (X′ i 2 +Y′ i 2 )}
Φ
i
′
=
A
TAN
[
Y
i
′
X
i
′
]
V′ i =M′ i exp( jΦ′ i ).
2. A method according to claim 1 , wherein the coefficients Gx i and Ox i , are adjusted once while V i lies in a half of the circle, and are not adjusted again until V k lies in the other half of the circle, k being greater than i.
3. A method according to claim 1 , the circle including a left half and a right half, the left half being left of the origin, the right half being right of the origin, wherein the coefficients Gx i and Ox i , are adjusted once while V i lies in the left half of the circle, and are not adjusted again until V k lies in the right half of the circle, k being greater than i.
4. A method according to claim 1 , wherein the coefficients Gy i and Oy i , are adjusted once while V i lies in a half of the circle, and are not adjusted again until V k lies in the other half of the circle, k being greater than i.
5. A method according to claim 1 , the circle including an upper half and a lower half, the upper half being above the origin, the lower half being below the origin, wherein the coefficients Gy i and Oy i , are adjusted once while V i lies in the upper half of the circle, and are not adjusted again until V k lies in the lower half of the circle, k being greater than i.
6. A method according to claim 1 , wherein the coefficient P i is adjusted once while V i lies in a quadrant of the circle, and is not adjusted again until V k lies in a different quadrant of the circle, k being greater than i.
7. A method according to claim 1 , wherein the circle is a unit circle.
8. A method according to claim 1 , wherein the values of the coefficients are adjusted according to the following table:
Angle (in
Angle (in
degrees)
degrees)
Magnitude > unit circle radius
Magnitude < unit circle radius
From:
To:
Space
Offset
Phase
Gain
Offset
Phase
348.75
11.25
0
Gx = Gx − 1
Ox = Ox − 1
—
Gx = Gx + 1
Ox = Ox + 1
—
11.25
33.75
1
33.75
56.25
2
—
—
P = P − 1
—
—
P = P + 1
56.25
78.75
3
78.75
101.25
4
Gy = Gy − 1
Oy = Oy − 1
—
Gy = Gy + 1
Oy = Oy + 1
—
101.25
123.75
5
123.75
146.25
6
—
—
P = P + 1
—
—
P = P − 1
146.25
168.75
7
168.75
191.25
8
Gx = Gx − 1
Ox = Ox + 1
—
Gx = Gx + 1
Ox = Ox − 1
—
191.25
213.75
9
213.75
236.25
10
—
—
P = P − 1
—
—
P = P + 1
236.25
258.75
11
258.75
281.25
12
Gy = Gy − 1
Oy = Oy + 1
—
Gy = Gy + 1
Oy = Oy − 1
—
281.25
303.75
13
303.75
326.25
14
—
—
P = P + 1
—
—
P = P − 1
326.25
348.75
15
if Magnitude = unit circle radius then no coefficients are adjusted
wherein the increment value “1” is one least significant bit.