Note: Descriptions are shown in the official language in which they were submitted.
~ W 0 95/05707 2 1 6 8 3 5~ PCTrU593/07586
ABSOLUTE ENCODER USING MULTIPHASE ANALOG SIGNALS
Fleld of the Invention
This invention relates in general to absolute encoders, and more particularly to an absolute
S encoder having mllltirh~e analog - i~iputs used in combination with digital circuits that linearize and
correct the mllltirh~e analog outp~ts.
n~d of the Invention
Absolute encoders are known for providing an output in~ir~tion of the position of a sensing
head relative to a measuring scale. For sensing rotary displ~rçmPnt the scale is in the form of a disc
with one or more tracks with one or more sensors per track. For sensing linear displ~remPnt the
scale is an elongated member co--lai-~ g one or more linearly arranged parallel tracks with one or
more sensors per track. The tracks are often formed of optically ,e~onsi~e segmrnt~ which
segmPntc are light l-~ si~e or light reflective, but the tracks can alternatively be of other forms
such as m~gnPtic, capacitive or inductive. Higher resolution is achieved by increasing the number
of tracks.
Su"""ar~ of the Invention
The present invention employs two or more sensors per track. The output of each sensor is
modulated by the track to generate a mllltirh~ce analog signal from each track. An analog to digital
converter (ADC) converts each analog signal to a digital value. A novel method is employed to
combine the mllitirh~e cyclic digital values into a single linear output per track. Other novel
methods are employed to correct, (1) zero drift in the analog signals, (2) changes in amplitude (gain)
of the analog signals, (3) deviations in the linear values from a perfect straight line. These correction
mPt-hodc are optional and can be employed in any combination. The invention applies to one, two
or more tracks per ,-.easulh~g scale and the invention includes novel methods of colllbillillg the signals
from each track to obtain a single output that increases linearly from zero to a .. ~ x ;.. ~.. over the full
span of the me~ulh-g scale. When measuring rotary displ~remPnt the mPthl ~ disclosed may be used
to combine the outputs of geared scales.
The m~thod~ used to linearize and correct the digital values are i~ tr~t~d and described in
terms of hard wired circuits. It is clear, however, that the methods described may be executed
conveniently using any general purpose microcontroller or digital signal processor ill~glal~d circuit.
Some features of the invention
A. Clipped m--itirh~ce analog signals with 1 cycle per revolution.
1. Use periphery of disc to get 1 cycle per revolution.
2. Correcting for zero drift.
t 35 3. Correcting for changes in amplitude.
4. Converting multiphase signals to single phase linear signals.
5. An example of a two phase output that is practical d~pio~h~ation of the requirements
of this invention.
6. Two examples of three phase signals that meet the requirements of this invention.
B. Correcting for non-linearity
1. Repeatability
Wo 95/0S707 2 ~ 6 ~ 3 55 PCTIUS93/07S86 ~
2. Interpolation
3. Simplified correction methods
C. An encoder that combines 1 cycle/rev. and N cycles/rev. to increase the resolution of the
encoder N times.
1. Use the periphery of the disc to get 1 cycle/rev. and a circular row of N slots to get
N cycleslrev.
2. For example, combine A32, B32, A1, and B1 to obtain linear output that repeats once
per revolution with 32 times the resolution.
D. An encoder that coll,billes N cycles/rev. and N-l cycles/rev. to increase the resolution of the
encoder N times.
1. Use a circular row of N slots and a second circular row of N-1 (or N+1) slots to get
the absolute value of N cycles/rev.
2. For example, combine A50, B50, A49 and B49 to obtain a linear output that repeats
once per revolution with 50 times the resolution of the 50 slot track.
LIST OF FIGURES
1. Disc and slits to generate a 2 phase analog signal with one cycle per revolution. (Model 10)
2A, B, C. Mçrh~nir~l design of the Model 10
3. Graph of the 2 phase analog signals from the Model 10.
4. Graph of the absolute value of the slope (DY/DX) of the 2 phase analog signals.
5. Comparison of the actual to the ideal graph of the slope.
6. Graph of the sum of the slopes of FIG. 4 and of the error resulting from the non-ideal output.
7A. Block diagram of a method to combine the digiti7ed values of the 2 phase signals of FIG. 3 to
obtain a single phase linear output.
7B. FIG. 7A plus a method to correct the amplitude of the analog signals.
7C. FIG. 7B plus a method to correct for zero drift in the analog signals.
7D. An alternate method to correct the amplitude of the analog signals using an analog multiplier.
8. Disc and slits to generate a 3 phase analog signal with one cycle per revolution.
9. Graph of the 3 phase analog signals obtained from the disc and slits shown in FIG. 8.
10. One phase of the signal from FIG. 9 and the absolute value of the slope (DY/DX) the signal.
11. Graph of the absolute value of the slopes of the 3 phase signals from FIG. 9.
12. Block diagram of a method to correct the ~mplih-de of a 3 phase signal and to combine the
signals to obtain a single phase linear ouhput.
13. Graph of one phase of an ~ltprn~te 3 phase analog signal and a graph of the absolute value of
the slope of the ~ItPrn~tP signal.
14. Graph of one cycle of an ~ltern~tp 3 phase signal.
15. Graph of the absolute value of the slopes of the 3 phase signal from FIG. 14.
16A. A method of colle~ lg the linear output using interpolation.
16B. A simplified method of coll~c~ g the linear Ouhput.
16C. Another .~implified method of CO~ g the linear output.
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17. The disc and slits of FIG. 1 with the addition of a circular row of slots and the associated slits.
18. Block diagram of a method to combine the ~igiti7Pd values of the analog signals obtained from
the disc of FIG. 17 to obtain a single phase output with increased resolution.
19. A disc with 49 slots in the outer row and 50 slots in the inner row with the slits required to
obtain a 2 phase output from each row of slots.
20. Block diagram of a method to combine the ~ligiti7ed values of the analog signals obtained from
the disc of FIG!!-l9 to obtain a single phase output.
A. ENCODERS USING CLIPPED MULTIPHASE ANALOG SIGNALS WITH l CYCLE PER
REVOLUTION .~
1. AN ENCODER THAT USES THE PE3~;IPHERY OF A DISC TO GET A TWO PHASE
ANALOG SIGNAL WITH 1 CYCLE PER REVOLUTION.
FIG. 1 shows a measuring scale dP~ignPd to measure rotary position over a range of one
revolution. The Ille&7u~ g scale is an opaque disc l with a single track formed by the periphery of
the disc. There is a center hole in the disc which is used to mount the disc on a rotating shaft. All
angles and radii described in this example are Ill~,uled from the center of this hole. This example
employs two optical sensors that generate a two phase analog signal. The two source-sensor pairs
are spaced 90 degrees apart at the periphery of the disc. The optical path between the source and the
sensor is limited by a pair of idPntisAI slit plates, one on each side of the disc, that confine the light
path to area of slits 46 and 47.
The disc 1 has a ~IIAXilll~llll radius that is constant over the angle from 345 to 0 to 15. The
radius is a ...i..i...~... over the angle from 165 to 180 to 195. From 15 to 165 the periphery of
the disc forms a spiral in which the radius (R) is reduced a constant rate with respect to the angle (0).
In this example DR/DO is .00012 inch per degree. This has the result that the II~AXilll~lll radius is
0.18 inches greater than the .. ;.. i.. ~.. radius. The periphery of the disc between 195 degrees and
345 degrees is also a spiral with the radius increasing at the rate of .00012 inches per degree.
In FIG. l, the disc is shown in the angular position where slit 48 is totally exposed and slit 47
is one-half eclipsed by the disc. I have selected the output of slit 48 to be phase A and the output
from slit 47 to be phase B. I have arbitrarily selected this position as the zero reference ~osition of
the disc. I have also arbitrarily selected counter-clockwise rotation of the disc in this view to produce
an increasing linear output from the signal conditioning circuits. In other words, the signal
conditioning circuits will be decignPd to produce an output that is zero and increasing when the output
from phase A is a IIIAX jllllllll and when the output from phase B is half-way between IIIAXillllllll and
l,,illi,,,~,-- and is decreasing.
The IIIAXillllllll radius of slits 47 and 48 is equal to the minim-lm radius of the disc. The
mAximnm radius of slits 47 and 48 is equal to the r.. Axi,.. radius of the disc. The sides of the disc
are parallel to a line through the center of the disc and the center of the slit. The area of the slit must
be less than the active area of the light source and light sensor. The width is usually equal to or less
than the difference between the mAximl-m and ...i,.i..""" radius of the slit. In this example, the width
~0 is 0.18 inches and is equal to the difference between the mAYimllm and miniml-m radius of the slit.
Wo 95/05707 2 1 6 8 3 ~ 5 PCT/US93l07S86
To ~u~ al~e, FIG. 1 shows a rotary optical encoder that produces two phase analog output
with one cycle corresponding to one revolution of the disc.
FIGs. 2A, 2B, and 2C show a m~rh:lnic~l assembly of the disc 1, the two slit plates 31 and 33,
the light emitting diodes 24 and 27 (the sources), and the phuLollA~ 36 and 43 (the sensors).
The center hole of the disc locates the disc on shaft 26. The disc is fixed in position by a cylindrical
keeper 22 that is c~ ed both to the shaft and to the disc. The shaft rotates in bearings which in
this example are simply holes drilled in the source board 29 and the sensor board 35. The axial
location of the shaft is det~rmin~d by thrust bearings 25 and 42 which are cempnt~d to the shaft.
Holes in the split plates 31 and 33 locate on pins 23 and 28 which in turn are a press fit in holes
drilled in the source and sensor boards. The axial location of the slit plates is det~rmin~d by spacers
30, 32, 34, 44, 45 and 46.
The sources are located by holes drilled in the source board and are soldered to etched foil
conductors which in turn are soldered to wires 37 and 41 which supply electrical current to the
sources. In this example, the sources are connected in series by a feed-thru connection 49 and the
same current flows through both sources. The sensors are located by holes drilled in the sensor board
and are soldered to etched foil con~ tors which in turn are soldered to wires 38, 39 and 40. Wire
40 is connected to a source of positive voltage, typically 5 to 25 volts. Wires 38 and 40 carry the
output current from sensors 36 and 43. The output analog current is proportional to the amount of
light arriving at the sensors.
The geometric relationship of the sources, the sensors, the slit plates, and the disc shown in
FIGS. 2A, 2B and 2C has the result that ill-lminAtion of the disc falls to zero at the edges of the
shadow of the slits and rises to a ~ i-"~-- at the center of the ilh~ ;llAled area. As a con~equPnre
the change in the amount of light arriving at the sensor (DY) for a change in the i~ Al~d area of
the slit is small near the edge of the slit and is a ..~xi...~,,, near the center of the slit. In p~a~"aph
5, I discuss how this effect is used to improve the linearity of the encoder output.
2. COMPENSATING FOR ZERO DRIFT
To correct zero drift in the analog signals, I first convert the analog signals to digital values
and store the ...i..i...~.. digital value of each analog signal. I have designed the measuring scale so
that each of the two phase signals remain at the minimllm value over 30 degrees of the input. This
permits me to store in fixed colll~uLer memory, a range of digital values of phase B that ill~n~ifi~.
when phase A is at a minimllm In this example, if phase B is between 375% and 62.5% of full
range, then phase A is a ...;..i...~... or a m~Yirnllm If phase A is greater than one-half its range, then
it is stored as a IllA~ llll and if it is less than one-half its range, then it is stored as a minimnm
Similarly, phase A is between 37.5% and 62.5% of full range when phase B is a l,.illil,,,ll~, or a
IIIAXillllllll To allow for variations that will occur during the "~A~ r~ hlg process the range is
reduced, for example to 40% to 60~o.
To correct for zero drift, I subtract the stored Illillil~ value from all subsequent digital values
of the related analog signal.
3. COMPENSATING FOR CHANGES IN AMPLITUDE
To correct for changes in the amplitude of the analog signals, I use the same procedure to store
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the m~ximl-m digital value of each analog signal. For each analog input the stored ,.. ~xi.. , value
is used to compute a gain factor. The numerical value of the gain factor is the desired ,,. ~xi,.......
value divided by the difference of the stored ,..~xi,,,,l~,, value and the stored ",i"i,...-... value.
The corrected digital output of each phase is called the norm~li7Pci value. The norm~li7Pd value
of any phase is equal to the gain factor of that phase multiplied by the difference of current value of
the output of the analog to digital co,lv~lle. and the stored ",i.,i.. value of that phase.
4. CONVERTING MULTIPHASE SIGNALS TO SINGLE PHASE LINEAR SIGNALS
I have also dP~igned the me~llring scale to shape the mllltiph~ce signals so that they can be
combined to form a single phase signal whose output increases linearly in proportion to the
mP~h~nic~l motion of the llleasulillg scale. A ch~ te~i~tic of a linear output is that the ratio of the
inc,~",t"Li~l output DY to the inc-e",e"lill input DX is a constant. I have discovered that I can
simplify the co",pul~lion of the single phase linear output if the sum of absolute values of the ratio
DY/DX for each phase of the multiphase signals is a constant.
The method used to combine the norm~li7ed mllltirh~e signals to obtain a linear single phase
output also requires that at the l.. i~ and ll.~xilll --ll values of the mllitirh~ce signals the ratio
DY/DX must be zero over a definite range of values of the input X. As described in the previous
pala~ hs, this feature is also required for the operation of the circuits used to correct for zero drift
and to correct for changes in signal amplitude.
It is possible to devise many different mllltiph~ce analog signals that meet these two
requir~",t"~.
I. that the value DY/DX be zero for at least lt25 of a cycle at the ,..~xi....~,. and
minimllm values of Y for each of the mllltirh~ce signals, and
II. that the absolute values of DY/DX for each phase when added together will equal a
constant
2S
5. AN EXAMPLE OF TWO PHASE ENCODER OUTPUT
FIGURE 3 is an example of a set of two phase signals that meet requirement I andclosely approximate requirement II. The slope DY/DXis zero over 30 degrees at both the ",illi",~
and m~ximllm values of the signals (,e.~uire",ent I). The absolute value of the slopes DY/DX of
phase A and phase B is shown in FIGURE 4. The shape of these curves reflects the non-uniform
illumin~tion of the disc ~ cll~ in palagla~h 1. The sum of these slopes is not exactly constant
but I will show first that the error is small and secondly I will show a method to correct the result
and elimin~te the error. FIGURE 5 shows both the ideal values and the practical values of DY/DX
for phase A. The curved line shows the slope obtained from the optical en~oder~ described in
paragraph 1. The ideal slope is constant at that .. ~xil~ value of the slope over 30 degrees of the
input as shown by the second curve in Figure 5. I will de~ocsl~a~e by this example that small
deviations from the ideal waveshape product acceptable errors in the linearized output. This
disclosure will also describe methods to remove these and other errors from the final output.
The upper curve in FIGURE 6 shows the sum of the slopes from Figure 4. Requiremene Il
states that this sum should be a constant. In this example, the sum varies from a constant by about
WO 95/0S707 2 1 6 ~ 3 5 5 PCT/US93/07S86
10%. The lower curve shows the resultant error in the linearized output obtained from the signals
shown in Figure 3. The error is about + or - 1 part per 1000 (O.l~o) of the ,.,;.xi,.,..", linear output.
This error is small co-.,pdred to other errors in a typical encoder and is acceL,Lable. This error and
other encoder errors are repeatable and can be corrected by the methods described in this ~ clQsllre.
FIGURE 7A is a block diagram of a method of co-l-bi,-hlg the normAli7ed values of a two phase
encoder to obtain an output KLIN whose amplitude is proportional to the mPrhAnirAI ~licplAremPnt
of the input X. FIGURE 7B is an eYpAn~ion of Figure 7A with the addition of the blocks required
to correct the amplitude of the analog signals. FIGURE 7C is an eYpAn~ion of Figure 7B with the
addition of the blocks required to correct for zero drift in the analog signals. FIGURE 7D is a block
diagram of an AltPrnAte method to correct the amplitude of the analog signal. The method shown in
4D uses the analog to digital COIl~ l as an analog multiplier as a s~bsl i~ e for the digital multiplier
shown in Figure 1 lB. In some applications, the method shown in Figure 7D may increase the speed
and/or reduce the cost of the signal processing circuits.
6. TWO EXAMPLES OF THREE PHASE SIGNALS THAT MEET THESE
REQUIREMENTS
FIGURE 8 shows a disc similar to Figure 1 morlifip~d to produce a three phase output. The disc
has a ,.. ~xi.. radius that is constant over the angle from 330 degrees to 0 degrees to 30 degrees.
The radius is a ...i"i". ~... over the angle from 150 degrees to 180 degrees to 210 degrees. From 30
degrees to 150 degrees the periphery of the disc forms a spiral in which the radius (R) is reduced a
constant rate with respect to the angle (O). In this example DR/DO is .00015 inch per degree. This
has the result that the .. ~ ... radius is .018 inches greater than the .. i"i,............. radius. The
periphery of the disc between 210 degrees and 330 degrees is also a spiral with the radius inc.~asi.lg
at the rate of .00015 inches per degree.
In Figure 8, the disc is shown in the angular position where slit 98 is totally exposed. Slits 97
2~ and 99 are one-fourth eclipsed by the disc. Because of the non-uniform illllminAtion ~i~cuc~e,d in
pAr~grarh 1, the normAIi7e~ output at this position is ~pro~ lld~ely 7/8 of the l.. A~i.. ....I have
selected the output of slit 98 to be phase A, the output from slit 97 to be phase B, and the output from
slit 99 to be phase C. I have arbitrarily selected this position as the zero reference position of the
disc. I have also arbitrarily selected counter-clockwise rotation of the disc in this view to produce
an increasi.. g linear output from the signal conditioning circuits. In other words, the signal
con~litioning circuits are clç~igrlP~ to produce an output that is zero and i..~reasillg when the output
from phase A is a l~.~xill~ and when the nnrmAli7Pd output from phase B is about 7/8 of the
,,,,.xi,,,...,, and is decreasing. At zero, the normAli7ed output from phase C is equal to phase B and
is increasing.
The ,.... illi,,,~.,, radius of slits 97, 98 and 99 is equal to the ,,,i.,i,,.. l,,, radius of the disc. The
II~Axill~llll radius of slits 97, 98, and 99 is equal to the ,,,~xi,.. , radius of the disc. The sides of the
disc are parallel to a line through the center of the disc and the center of the slit. The area of the slit
must be less than the active area of the light source and light sensor. The width is usually equal to
or less than the difference between the IllAxillllllll and minimnm radius of the slit. In this example,
the width is 0.012 inches and is less than the dirrerence between the ".~xi". "" and "~ i"~.l"~ radius
2 1 68355
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of the slit.
To su~ lali~e~ Figure 8 shows a rotary optical encoder disc and slit layout that produces a
three phase analog output with one cycle corresponding to one revolution of the disc. One example
of a suitable three phase signal is shown in FIG~E 9. In this example, full scale input (X) is 360
degrees. The ."~xi,.. value of the nr~rm~li7ed output (Y) is 10,000 and the .. illi~ value is zero.
At the ,.. ~ ", and ",i.. ;.. ~ values, the output is corLr.tant and DY/DX is zero over a range of 60
degrees of the input.
FIGURE 10 shows one phase of the three phase signal together with the absolute value of the
slope. The encoder is ~l~signP~l so that the signal Y has a slope DY/DX that rises linearly from zero
to a Ill~xilll.llll slope that occurs when the output Y is one-half the ~ -- The slope the decreases
linearly so that the slope again reaches zero when the output Y reaches the .. ,.,.in.. An encoder
similar to that shown in Figures 2A, 2B and 2C but with three source sensor pairs and with a disc
as shown in Figure 8 produces an output that closely a,Jplo~illlalec7 the shape shown in Figure 10.
It is possible to produce similar outputs using magnPtic, capacitive, or inductive tr~n~c~u~er.~.
FIGURE 11 shows the absolute values of DY/DX for each of the three phase signals shown
in Figure 9. From inspection of Figure 11 it can be seen that for any value of the input X, the sum
of the three values of DY/DX is a constant value which in this example is 10,000.
FIGURE 12 is a block diagram of the method used to combine the signals from a three phase
encoder first to correct for changes in signal ~mp~ e and second to obtain a linear single phase
OUhpUt whose ~mrlihlrie is proportional to the mP~h~ni~ pl~emPnt of the input.
The values A', B' and C' are digital values col-~ onding to the analog inputs Al, B~ and C~.
The values Ap, Bp, and Cp are the ...~xi..~... values of A', B' and C'. The values Am, Bm, and Cm
are the desired ",~xi." , values of the norm~li7ed ouhputs A, B and C. The values Am, Bm, and
Cm, are stored in colllpuler ...c...o.~. The norm~li7e~ value A is obtained by multiplying A' by the
ratio Am/Ap. B and C are colll~uled in a similar fashion. The peak value Ap is obtained by sorting
the value of A' when A is greater than Am/2 and when B and C are nearly equal (i.e., when the
absolute values of the difference B-C is less than k, where k is a number stored in co..-~uler memory.
In this example, k might be chosen as 1000) Bp and Cp are stored in a similar fashion.
The linear output, KLIN, is obtained by adding or subllàcling the norm~li7~ values A, B and
C using the rules listed in Figure 12.
The analog signals shown in Figures 9, 10 and 11 are obtained when the encoder is dP-signPd
to produce a signal such that DY/DX has a triangular wave shape as shown in Figure 11. I have
chosen this example because the optical encoders described in this ~ closllre produce an output that
closely ay~loxilll~tp~ this example. Many other waveshapes are suitable, it is only necessary (as
stated above) that the absolute values of DY/DX summed over all phases closely approximate a
constant value. The closer the approxim~tion, the more accurate the encoder.
To illustrate that other signal wave shapes produce similar results, I have shown in Figures 13,
14 and 15 the signals from a 3 phase encoder in which DY/DX has the value l-Cosine 3X over a 120
degree sector and has a value zero of the adjacent 60 degree sector. FIGURE 14, shows three such
signals spaced at 120 degree intervals to form a three phase output. A three phase signal can also
Wo 95l0s707 2 1 6 8 3 5 5 PCT/1159311)7586
be formed using 60 degree intervals, this is equivalent to inverting phase A, i.e., A inverted = Am -
A.
FIGURE 13 shows the relationship of the output Y to the slope DY/DX for phase A of figure
~ 14. For purposes of illustration, DY/DX is 10(1-Cosine 3X). FIGURE 15 shows the absolute value
of DY/DX for all three phases. It can be seen from inspection, that in this example, the sum of these
three signals is 20 for any value of X.
In ~ullullal~, Figures 9, 10 and 11 show a set of three phase encoder signals that can be closely
d~prc"~ ed by the optical encoder designs described in this ~ closllre. Figures 13, 14 and 15 show
an ~Itern~t~ set of three phase encoder signals that may be more easily created using m~gn~tic7
capacitive or inductive tran~lrer.~. Beyond these two eY~mples, other wa~l-apes may be chosen
to fit other re.lui,~
Either set of three phase signals can be norm~li7ed and ~ A~ d using the method shown in
Figure 12.
B. CORRECTING FOR NON LINEARITY
1. REPEATABILITY
Figure 6 shows one source of error in the encoder output KLIN. Similar errors result from
mPrh~nic~l imperfections in the parts or the assembly of the encoder.
Typically these errors are independent of changes in the operating environment and are constant
over the life of the encoder. For this reason, it is practical, as a part of the m:~mlf~rtnrjng process,
to store calibration data for the encoder. If the encoder includes a microprocessor, the calibration
data are loaded directly to non-volatile memory. If not, the calibration data are shipped sry~ ely~
for eY~mrle, in a floppy disc to be loaded by the encoder user into his signal processing eyui~ e.lL.
2. INTERPOLATION
FIGURE 16A is a block diagram of a method to correct the output KLIN. This method uses
interpolation to reduce the amount of calibration data that must be stored in the co---~uler memory.
The method sep~-~t~ KLIN into the most ~i~nifi~nf digits (KLA) and the least 5ignifi~ ~nt digits
(KLB). For ey~nnrle~ if KLIN ranges from 0000 to 9999, KLA has 100 possible values from 0000
to 9900. KLB also has 100 possible values from 00 to 99. The correction table stores a correction
term (OFn) for each value of KLAn. To speed the colll~u~ion, a second lookup table may be used
to store the value DDOF = OFn+ l-OFn. .Alt~rn~t~ly, DDOF may be colll~uled each time from the
contents of the OFn lookup table.
The corrected output (COR) is col--pu~ed as follows:
COR = KLN - (OF + (KLB * DDOF))
3. SIMPLIFIED CORRECTION METHODS
3~ FIGURE 16B omits the second lookup table, the mllltirlier and the adder. This method is used
when the encoder errors are small and DDOF is not greater than plus or minus one.
FIGURE 16C shows a method that may be used for low resolution encoders. This method is
fast but requires a larger lookup table and it reduces the useful resolution by a factor of two. The
example in Figure 16C employs 9 bits to represent KLIN1 and provides an 8 bit output to represent
COR1.
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C. AN ENCODER THAT COMBINES 1 CYCLE/REV. AND N CYCLES/REV. TO INCREASE
THE RESOLUTION OF THE ENCODER N TIMES.
1. USE THE PERIPHERY OF THE DISC TO GET A CYCLE/REV. AND A
CIRCULAR ROW OF N SLOTS TO GET N CYCLES/REV.
Figure 17 shows an encoder disc that combines the rotary disc shown in Figure 1 with a second
track formed by row of 32 slots inside the ~ lll radius of the disc. The edges of the slots are
formed by 64 equally spaced radial lines, i.e., the edges are spaced at 5.625 degree intervals. These
slots ml d~ te the light between two source-sensor pairs that are aligned with slits 125 and 126 to
produce a two phase analog signal with 32 cycles per revolution of the disc. The l,-~i",~l" radius
of the sli~ is slightly less than the ll~ lll radius of the slot. The l,.;"il.~." radius of the slit is
slightly greater than the ~ radius of the slot. The edges of the slit are radial lines and the
angular width of the slit is 5/6 the angular width of the slot. In this example, the angular width of
the slit is 4.6875 degrees.
These tiimPn~ ns product a cyclic analog signal with a lI-~-Iilll-llll and ",i"i",~-,- value that is
constant over an angle equal to 1/6 of the angular width of the slot or .9375 degrees. This angle
mllltirliP,d by 32 is 30 degrees. This results in an analog signal that has the same shape as the two
phase signals shown in Figure 3, but repeated 32 times per revolution.
Phase A32 is generated by a source-sensor pair aligned with slit 125. Slit 125 is shown located
in the center of one of the slots. This position of the disc has been arbitrarily selected as the zero
position for the X32 output. In this view, positive rotation is counter-clockwise. To be col~c;~
with p~ragrarh A1, the center of slit 126 which ge,le.~,les phase B32 must be aligned with ~e
clockwise edge of one of the other slots. For the best ac. ~dcy it is ~fer~.~le to select the nearest
slot cQ~ with the physical size of the sources and sensors.
The source-sensor pairs aligned with slit 127 generate phase A1 and the source-sensor pairs
aligned with slit 128 generate phase B 1 of the one cycle per revolution signal . Slits 127 and 128 have
an angular spacing of 90 degrees. At the position of the disc shown in Figure 17, phase A1 output
is about equal to the phase B1 output and referring to Figure 3, these values correspond to the disc
having a rotary position of about 135 degrees with respect to the zero position defined in p~dglayh
1.
2. FOR EXAMPLE, COMBINE A32, B32, A1 AND B1 TO OBTAIN LINEAR
OUTPUT THAT REPEATS ONCE PER REVOLUTION WITH 32 TIMES THE
RESOLUTION.
FIGURE 18 uses the method shown in Figure 7B to obtain KLIN1 from phase Al and phase
Bl and to obtain KLIN32 from phase A32 and phase B32. KLINl is co"e~-~ed to obtain COR 1 and
KLIN32 is co,le~;led to obtain COR32 using the method shown in Figure 16A or 16B or 16C as
required by the size of the error to be corrected.
COR1 is multiplied by 32 and the result is separated into the most ~ignific~nt digits 32CORlA
(which have a range of values from 0 to 31) and the least significant digits 32CORlB (which have
the same range of values as COP.32). In this example, COR1 and COR32 have a range of values of
0 to 9999. The range of values selected for convenience in COIllyu~illg and is limited by the resolution
wo 9S/05707 2 1 6 ~ 3 5 5 PCT/US93/07586
-10-
of the ADC and by the requirements of the application. Usually the m~l~imllm value is 1 less than
some power of 2, for example 511, 1023 or 4095.
32CORlB is subLIa~;~ed from COR32 to obtain DIF. If DIF is negative, 32CORlA is increased
by 1. If the result is 32, s~bstit~lte 0. The result iA~ntifit-~ which of the 32 slots gPn~r~tPd phase A32
and phase B32. In this example, the result is the two most cignifir~nt decimal digits of a six decimal
digit number NX id~lifying the position of the disc.
The value NX was computed using the value COR32 which is the colle~l~d value of KLIN32.
The correction using Table 1 is complete only if all 32 slots are iAPntic~l. In general, the slots are
not iAentir~l and a further i-..~ ,.--e--l in ac~ u~a~;y may be obtained using a third lookup table that
employs the most 5ignifir~nt digits of NX as a table address. The example in Figure 18 uses the three
most cignific~nt decimal digits of NX, the values 0 to 319, to locate the correction terms OF and
DDOF. The co-~;Led output N equals NX - (OF + DDOF*NXB). In this example, NXB is the
three least .cignifir~nt decimal digits of NX.
D. AN ENCODER THAT COMBINES N CYCLEStREV. AND N-1 CYCLES/REV. TO
INCREASE THE RESOLUTION OF THE ENCODER N TIMES.
1. USE A CIRCULAR TRACK OF N SLOTS AND A SECOND CIRCULAR TRACK
OF N-l (OR N+ 1) SLOTS TO GET THE ABSOLUTE VALUE OF N CYCLES/REV.
Figure 19 shows an encoder disc with a circular periphery, with a first track formed by a row
of 49 slots inside the ."i.,; " ." ", radius of the disc and with a second track formed by a row of 50 slots
inside the row of 49 slots. The edges of the outer row of slots are formeA by 98 equally spaced radial
lines, and the edges of the inner row of slots are formeA by 100 equally spaced lines, i.e., the edges
of the inner rows are spaced at 3.6 degree intervals. The inner row of slots m~ te the light
between two source-sensor pairs that are aligned with slits A50 and B50 to produce a two phase
analog signal with 50 cycles per revolution of the disc. The outer row of slots mnd~ te the light
between two additional source-sensor pairs that are aligned with slits A49 and B49 to produce a two
phase analog signal with 49 cycles per revolution. The ."~i",~,.. radius of each slit is slightly less
than the ~ xi",..", radius of the associated row of slots. The ",i..i~ l" radius of each slit is slightly
greater than the "i,-;",-"" radius of the ~csoci~t~A row of slots. The eAges of the slits are radial lines
and the angular width of the slits is 5/6 the angular width of the associated slot. In this exarnple, the
angular width of the slits A50 and B50 is 3.0 degrees.
For the inner track, these dimPncions produce a cyclic analog signal with a Ill~xillllllll and
minimllm value that is constant over an angle equal to 1/6 of the angular width of the slot or .6
degrees. This angle multiplied by 50 is 30 degrees. This results in an analog signal that has the same
shape as the two phase signals shown in Figure 3, but repeateA 50 times per revolution.
For the outer track, the angular dim~mions are increased by the ratio of 50/49. The result is
a two phase signal of the same shape but repeated 49 times per revolution.
Phase A50 is generated by a source-sensor pair aligned with slit A50. Slit A50 is shown
locateA in the center of one of the inner row of slots. This position of the disc has been arbitrarily
selected as the zero position for the X50 output. In this view, positive rotation is counter-clockwise.
To be consistent with p~agld~)h Al, the center of slit B50 which generates phase B50 must be aligned
21 68355
W0 95/05707 PCT/US93/07~86
with the clockwise edge of one of the other slots. For the best accuracy, it is preferable to select the
nearest slot cQn.~ e~l with the physical size of the sources and sensors.
Phase A49 is generated by a source-sensor pair aligned with slit A49. Slit A49 is shown
located in the center of one of the outer row of slots. This position of the disc is also the zero
position for the X49 ou~put and the center of slit B49 which generates phase B49 must be aligned with
the cloclcwise edge of one of the other slots in the outer track. The source-sensor pairs aligned with
slit B49 generate phase B49 of the 49 cycle per revolution signal.
2. FOR EXAMPLE, COMBINE A50, B50, A49 AND B 49 TO OBTAIN A LINEAR
OUTPUT THAT REPEATS ONCE PER REVOLUTION WITH 50 TIMES THE
RESOLUTION OP THE 50 SLOT TRACK.
FIGURE 20 uses the method shown in Figure 7B to obtain KLIN49 from phase A49 and phase
B49 and to obtain KLIN50 from phase A50 and phase B50. KLIN49 is collecled to obtain COR49
and KLIN50 is corrected to obtain COR50 using the method shown in Pigure 16A or 16B as required
by the size of the error to be co~ Led.
To obtain COR1, COR50 is ~ublidcl~d from COR49. If the result is negative, a constant
(10,000 in this example) is added such that COR1 is always positive.
COR1 is multiplied by 50 and the result is separated into the most gignifi~nt digits 50CORlA
(which have a range of values from 0 to 49) and the least ~ignifi( ~nt digits 50CORIB (which have
the same rage of values as COR50). In this example, COR49 and COR50 have a range of values of
0 to 9999. The range of values is selected for convenience in computing and is limited by the
resolution of the ADC and by the requirements of the application. Usually the ...~xi...~.., value is 1
less than some power of 2, for example 511, 1023 or 4095.
50CORlB is subtracted from COR50 to obtain DIP. If DIP is nega~ive, 50CORlA is increased
by 1. If the result is 50, ~b~ e O. The result i~lentifiPs which of the 50 slots (0-49) generated
phase A50 and phase B50. In this eY~mple, the resul~ - the two most significant decimal digits of
a six decimal digit number NX identifying the position : the disc.
The value NX was co~ uled using the value COR50 which is the co--e~;led value of KLIN50.
The correction using Table 1 is complete only if all 50 slots are iclçntic~l In general, the slots are
not i~l~nti(~l and a further hl.~.o\,~llle"L in ac.;u,a~ y may be obtained using a thW lookup table that
employs the most signifi-~nt digits of NX as a table address. The example in Figure 18 uses the three
most sig~ific~nt decimal digits of N~ the values 0 to 499, to locate the correction terms OF and
DDOP. The corrected output N equals NX - (OF + DDOF*NXB). In this example, NXB is the
three least signific~nt decimal digits of NX.
.
