CALIBRATING POSITION SENSOR READINGS

BACKGROUND

In applications involving articulated structures, it is often desirable to determine the position of the distal end of the most distal link of the articulated structure. This can be achieved by sensing the position of each link relative to the last along the articulated structure, from its base to the most distal link. This series of measurements can be used in combination with the known layout of the articulated structure to determine the position of the distal end of the most distal link relative to the base. Rotary position sensors are used to sense relative rotation between links. Linear position sensors are used to sense relative longitudinal motion between links.

Hall effect magnetic sensors are commonly used to sense relative motion between links. In a typical rotary position sensor, a ring has a set of alternating magnetic poles arranged around it. A sensor interacts with the ring, and is located so that the magnetic poles move past the sensor as the rotation that is desired to be sensed takes place. For example, the ring could be attached about a shaft and the sensor could be attached to a housing within which the shaft rotates. The sensor detects changes in magnetic polarity as the poles move past the sensor. By counting the number of changes in polarity the amount of rotation from a reference position can be sensed. To sense the direction of rotation two such pairs of rings and sensors can be provided, and arranged so that one sensor detects magnetic transitions of its ring at rotation positions that are offset from the positions where the other sensor detects magnetic transitions of its ring. By considering the relative timing of transitions detected by each sensor the direction of rotation can be sensed.

The field of robotics utilises articulated structures as robot arms. Accurate position sensing is important for robot arms in order to ensure their end effectors are manipulated precisely as intended. The larger the magnetic rings of the position sensor, the more accurately the relative rotation of two links of the robot arm is sensed. However, in some robotics

applications, for example in the field of surgical robotics, it is desirable for the position sensors to be very compact to fit within the available space and to minimise the weight that they add to the arm.

Thus, there is a need for an improved position sensor which balances the competing requirements of accuracy and compactness.

SUMMARY OF THE INVENTION

According to an aspect of the invention, there is provided a method of correcting a position reading from a position sensing arrangement, the position sensing arrangement being suitable for sensing the position of a revolute joint of an articulated structure, the position sensing arrangement comprising a disc having a magnetic ring with magnetic pole pairs and a magnetic sensor assembly comprising a magnetic sensor array for detecting the magnetic pole pairs of the magnetic ring, the method comprising: for each pole pair of the magnetic ring, taking a calibration pole pair position reading with the magnetic sensor array, and generating a pole pair correcting function by comparing the calibration pole pair position reading with a model pole pair position reading; averaging the pole pair correcting functions of the pole pairs of the magnetic ring to generate an average pole pair correcting function for the magnetic ring; taking a position reading with the magnetic sensor array, the position reading comprising a plurality of pole pair position readings; and generating a corrected position reading by deducting the average pole pair correcting function from each pole pair position reading.

The calibration pole pair position reading may be multi-bit.

The pole pair correcting function may comprise a periodically oscillating function. This periodically oscillating function may comprise a sinusoidal function.

For each pole pair, the pole pair correcting function may be generated by fitting a curve to the calibration pole pair position reading, and deducting a line representing the model pole

pair position reading from the fitted curve. The curve may be fitted to the calibration pole pair position reading using a method of least squares.

Suitably, the disc comprises a further magnetic ring with magnetic pole pairs, and the magnetic sensor assembly comprises a further magnetic sensor array for detecting the magnetic pole pairs of the further magnetic ring, and the method comprises: for each pole pair of the further magnetic ring, taking a further calibration pole pair position reading with the further magnetic sensor array, and generating a further pole pair correcting function by comparing the further calibration pole pair position reading with the model pole pair position reading; averaging the further pole pair correcting functions of the pole pairs of the further magnetic ring to generate an average further pole pair correcting function for the further magnetic ring; taking a further position reading with the further magnetic sensor array, the further position reading comprising a plurality of pole pair position readings; and deducting the average further pole pair correcting function from each pole pair position reading to generate a corrected further position reading.

The further pole pair correcting function may comprise a periodically oscillating function. This periodically oscillating function may comprise a sinusoidal function.

The further pole pair correcting function may be generated by fitting a curve to the further calibration pole pair position reading, and deducting a line representing the model pole pair position reading from the fitted curve. The curve may be fitted to the further calibration pole pair position reading using a method of least squares.

The method may further comprise: for each pole pair of the magnetic ring, generating a corrected calibration pole pair position reading by deducting the pole pair correcting function from the calibration pole pair position reading; generating a revolution correcting function by comparing the corrected calibration pole pair position readings for the magnetic ring with model revolution position readings; and generating the corrected position reading by: deducting the average pole pair correcting function from each pole pair position reading; and deducting the revolution correcting function from the position reading.

The revolution correcting function may comprise a periodically oscillating function. This periodically oscillating function may comprise a sinusoidal function.

The method may comprise generating the revolution correcting function by fitting a curve to the corrected calibration pole pair position readings, and deducting a line representing the model revolution position readings from the fitted curve. The curve may be fitted to the corrected calibration pole pair position readings using a method of least squares.

The method may comprise, for each pole pair of the further magnetic ring, generating a further corrected calibration pole pair position reading by deducting the further pole pair correcting function from the further calibration pole pair position reading; generating a further revolution correcting function by comparing the further corrected calibration pole pair position readings for the magnetic ring with further model revolution position readings; and generating the corrected position reading by: deducting the average further pole pair correcting function from each pole pair position reading; and deducting the further revolution correcting function from the position reading.

The further revolution correcting function may comprise a periodically oscillating function. This periodically oscillating function may comprise a sinusoidal function.

The method may comprise generating the further revolution correcting function by fitting a curve to the corrected calibration pole pair position readings, and deducting a line representing the model revolution position readings from the fitted curve. The curve may be fitted to the corrected calibration pole pair position readings using a method of least squares.

BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be described by way of example with reference to the accompanying drawings. In the drawings:

figure 1 illustrates a general representation of a shaft equipped with a position sensing arrangement;

figure 2 illustrates the dimensions of a disc 3 of figure 1;

figure 3 illustrates a portion of a magnetic ring of figure 1;

figure 4 illustrates a magnetic sensor array of figure 1;

figure 5 is a graph illustrating theoretical and actual position sensor readings;

figure 6 is a flowchart illustrating a method of determining pole pair numbers for two magnetic rings when the inner radial boundary is limiting;

figure 7 is a flowchart illustrating a method of determining pole pair numbers for two magnetic rings when the outer radial boundary is limiting;

figure 8 is a graph illustrating theoretical and actual combined position sensor readings; and

figure 9 illustrates arrangements for mounting the disc;

figure 10 illustrates the magnetic field detected by a magnetic sensor array;

figure 11 illustrates theoretical and actual sensor readings taken whilst a single magnetic pole pair passes a magnetic sensor assembly;

figure 12 illustrates a correcting function for a pole pair; and

figure 13 illustrates theoretical and actual sensor readings taken whilst a whole magnetic ring passes a magnetic sensor assembly.

DETAILED DESCRIPTION

The following relates to a position sensing arrangement for an articulated structure, and a method of assembling the position sensing arrangement. By sensing the position of each joint of an articulated structure, the position of the distal end of the articulated structure can be determined from a combination of the sensed joint positions and known layout of the articulated structure. In the example of a robot arm, a base of the robot arm is coupled to the end effector at the distal end of the robot arm via a series of links joined together by joints. These may be revolute joints or prismatic joints. In the case of a revolute joint, the rotation of the joint is sensed. In other words, the relative rotation of the two shafts which the revolute joint attaches is sensed. The angle of rotation and the direction of rotation are sensed. In the case of a prismatic joint, the longitudinal motion of the joint is sensed. In other words, the relative motion of the two shafts which the prismatic joint attaches is sensed. The movement distance and the direction of movement are sensed.

Figure 1 illustrates an example of a position sensing arrangement for detecting rotation of shaft 1 about axis 2. The position sensing arrangement detects the angle and direction of rotation of shaft 1 about axis 2. The position sensing arrangement comprises a magnetic sensor assembly and a disc 3. Disc 3 is shown in more detail on figure 2. Disc 3 is an annulus having an outer radial boundary 4 and an inner radial boundary 5. Both the boundaries of the annulus are centred on the centre point of the disc 3. The radius of the outer radial boundary is r0. The radius of the inner radial boundary is n. Disc 3 is fast with the element whose position is being sensed. In this case, disc 3 is rigidly mounted to shaft 1. There is no relative motion permitted between shaft 1 and disc 3. Disc 3 rotates about axis 2. In other words, disc 3 and shaft 1 rotate about a common axis.

Two magnetic rings 6,7 are disposed on disc 3. The magnetic rings are not movable relative to each other. The two magnetic rings are concentric. Both magnetic rings are centred on the centre of the disc. In other words, the magnetic rings are arranged in a circle having the rotation axis 2 of shaft 1 as its axis. The radial distance between the centre of the disc and the centreline 9 of the inner magnetic ring 6 is rm. The radial distance between the centre of the disc and the centreline 10 of the outer magnetic ring 7 is rn. The centrelines 9, 10 of the magnetic rings 6,7 are separated by a radial distance s. The minimum value of the radial distance s is predetermined. Suitably, radial distance s is at least the length of a pole pair. In other words, s > 2y.

Each magnetic ring carries a number of permanent magnets defining magnetic poles 8. On the sensing surface of each magnetic ring, the magnets alternate polarity between north and south poles around the ring. Inner magnetic ring 6 has m magnetic pole pairs. Outer magnetic ring 7 has n magnetic pole pairs. Each magnetic pole 8 on the inner magnetic ring 6 is the same shape and size, within manufacturing tolerance. Each magnetic pole 8 on the outer magnetic ring 7 is the same shape and size, within manufacturing tolerance. Suitably, each magnetic pole 8 on the inner magnetic ring 6 is the same shape and size as each magnetic pole 8 on the outer magnetic ring 7, within manufacturing tolerance and the fact that the arc radius of the inner magnetic ring is different to the arc radius of the outer magnetic ring. A portion of a magnetic ring is shown in more detail in figure 3. Each magnetic pole 8 has a

radial length x and a circumferential length y. In one example, y is 2mm. In this example, a pole pair (i.e. a north pole and adjacent south pole pair) has a circumferential length of 4mm.

The magnetic sensor assembly is mounted to the articulated structure so as to detect relative rotation between two elements. The magnetic sensor assembly is rigidly attached to one of those elements, such that the magnetic sensor assembly is not permitted to move relative to that element. The disc 3 is rigidly attached to the other of those elements, such that the magnetic rings 6, 7 are not permitted to move relative to that other element. In the case of the example of figure 1, the disc 3 is rigidly attached to the shaft 1. The magnetic sensor assembly is rigidly attached to the part of the articulated structure that the shaft 1 rotates relative to.

The magnetic sensor assembly detects relative rotation of the first and second magnetic rings and the magnetic sensor assembly. Magnetic sensor assembly comprises two magnetic sensor arrays 11,12. Inner magnetic sensor array 11 is disposed adjacent to and aligned with the inner magnetic ring 6. Outer magnetic sensor array 12 is disposed adjacent to and aligned with the outer magnetic ring 7. Since the magnetic sensor assembly is mounted to the articulated structure relative to which shaft 1 rotates, as shaft 1 rotates, the magnetic rings 6 and 7 revolve past the magnetic sensor arrays 11, 12. Each sensor array is capable of detecting transitions between north and south poles of the magnetic ring it is disposed over as those transitions move past the sensor array. In an exemplary implementation, the first and second magnetic rings 6, 7 are separated radially by at least the length of a pole pair. Increasing the separation of the rings reduces the interference each ring causes to the sensor of the other ring. Thus, separating the rings by at least the length of a pole pair aids the inner magnetic sensor array 11 only detecting the transitions of the inner magnetic ring 6, and the outer magnetic sensor array 12 only detecting the transitions of the outer magnetic ring 7.

Each magnetic sensor array 11, 12 comprises a set of sensors. Figure 4 illustrates an example in which a magnetic sensor array comprises four individual sensors 13a,b,c,d. Each magnetic sensor array is rectilinear. As can be seen from figure 4, the individual sensors are arranged in a straight line. The sensors of the set are all the same size and shape and have equal spacing between them. Each sensor 13 has a width t and a length u and is separated from the next

sensor by a distance v. The centres of adjacent sensors are separated by a distance z. In the example shown in figure 4 in which the magnetic sensor array has four individual sensors, z is the same as a quarter the length of a pole pair. In other words, z = y/2. Thus, whilst the centres of the sensors marked 1 and 3 are over the boundary between adjacent poles, the centres of sensors marked 2 and 4 are over the centres of adjacent poles. The centres of the outer sensors (marked 1 and 4) are separated by three quarters the length of a pole pair. In an exemplary implementation, t is less than the radial extent of the magnetic ring x. In other words, t < x.

Since the individual sensors are in a straight line whereas the magnetic ring is circular, the centre of each sensor is not consistently aligned with the centre of a magnetic pole as the shaft rotates. The offset between the centre of the sensor and the centre of the magnetic pole varies as the shaft rotates. This variable offset causes a systematic error in the sensor output. In an alternative implementation, the magnetic sensor arrays 11, 12 are each in a circular configuration centred on the centre of the disc 3. In this case, the radius of the centreline of each magnetic sensor array is the same as the radius of the centreline of the magnetic ring it is reading. Thus, the centreline of the magnetic sensor array is consistently aligned with the centreline of the magnetic ring it is reading as the shaft rotates.

The sensors could, for example, be Hall effect sensors, reed sensors, magnetoresistive sensors or inductive sensors.

Each magnetic sensor array 11, 12 is arranged to provide a multi-bit output representing the relative position of the neighbouring poles to it. The number and relative placement of the poles on the magnetic rings are arranged such that each position of the shaft within the range of rotation angles to be measured is associated with a unique set of outputs from the two magnetic sensor arrays 11, 12. The number of poles m on the inner ring and the number of poles n on the outer ring are different and co-prime. Their selection is described further below. The outputs from the sensors pass to a processing unit 14.

The circumferential positions of the magnetic sensor arrays 11, 12 and the rotational position of the disc 3 about axis 2 may be chosen so that the transitions between the poles on the inner magnetic ring 6 as sensed by magnetic sensor array 11 occur for different rotational positions of the shaft from the transitions between the poles on the outer magnetic ring 7 as sensed by magnetic sensor array 12. This allows the direction of rotation of the shaft to be inferred from the relative order of the transitions sensed by each magnetic sensor array.

The outputs of magnetic sensor arrays 11, 12 pass to the processing unit 14. The processing unit comprises a processor device 15, which could be hard coded to interpret the signals from the magnetic sensor arrays 11, 12 or could be a general purpose processor configured to execute software code stored in a non-transient way in memory 16. The processor device combines the signals from the sensors to form an integrated output signal at 17.

A method of selecting the number of magnetic pole pairs m on the inner magnetic ring 6 and the number of magnetic pole pairs n on the outer magnetic ring 7 will now be described.

The selection of m and n may be subject to any one, any combination, or all of the following constraints.

1. The inner and outer magnetic rings 6, 7 both need to fit on the disc 3. Suitably, the inner and outer magnetic sensor arrays 11, 12 are each disposed within the footprint of the disc 3 as well. The inner radial boundary 5 is at a radius n. In order to fit the inner magnetic sensor array 11 over the disc 3 without exceeding the inner radial boundary 5, the centreline 9 of the inner magnetic ring is separated from the inner radial boundary 5 by at least the portion of the radial width of the magnetic sensor assembly 11 which is disposed between the centreline 9 of the inner magnetic ring and the inner radial boundary 5. This portion may be half the radial width of the magnetic sensor assembly, i.e. Wm/2. In other words, rm > n + wm/2. If the sensor array is offset radially within the sensor assembly, then the portion may be greater. In one example, rm > n + (wm + 1)/2. The outer radial boundary 4 is at a radius r0. In order to fit the outer magnetic sensor array 12 over the disc 3 without exceeding the outer radial boundary 4, the centreline 10 of the outer magnetic ring is separated from the outer radial boundary 4 by at least the portion of the radial width of the magnetic sensor assembly 12 which is disposed between the centreline 10 of the outer magnetic ring and the outer radial boundary 4. This portion may be the radial width of the

magnetic sensor assembly, i.e. wn/2. In other words, rn < r0 - wn/2. If the sensor array is offset radially within the sensor assembly, then the portion may be greater. In one example, rn < r0 - (wn + 1)/2.

The centres of adjacent sensors are separated by a quarter the length of a pole pair. In other words, adjacent sensors are separated by y/2. This ensures that the magnetic sensor array can detect each pole transition as the disc rotates.

The radial distance s between the centreline of the inner magnetic ring 6 and the centreline of the outer magnetic ring 7 is greater than a predetermined distance. That predetermined distance is set by a desired insensitivity to stray magnetic fields. Suitably, s > 2y. In this case, the nearest magnetic pole on the inner magnetic ring 6 that the inner magnetic sensor array 11 is detecting is always closer than a magnetic pole on the outer magnetic ring 7. Similarly, the nearest magnetic pole on the outer magnetic ring 7 that the outer magnetic sensor array 12 is detecting is always closer than a magnetic pole on the inner magnetic ring 6. Thus, this prevents interference arising from the magnetic sensor array over one magnetic ring detecting a magnetic field from the other magnetic ring.

The minimum number of sensors b in each magnetic sensor array is greater than a threshold. This threshold is such that there is sufficient spatial sampling for an unambiguous position reading. Suitably, b > 4. Four sensors is sufficient where there are no magnetic harmonics detected.

The width, t, of each magnetic sensor is less than the radial extent of the magnetic ring x. In other words, t < x. The signal to noise ratio of the detected transitions is reduced if the magnetic sensor array is narrower than the magnetic ring.

The inner radial boundary of the disc may be constrained by the articulated structure. For example, in figure 1, the inner radial boundary of the disc is limited by the shaft 1. In this case, the radius of the inner radial boundary n has to be at least as big as the radius of the shaft 1.

The outer radial boundary of the disc may be constrained by the articulated structure. For example, the position sensor may fit inside a housing of the articulated structure. In this case, the radius of the outer radial boundary r0 has to be at least as small as the radius of the housing.

The position sensor is arranged to detect a maximum angle of rotation. This maximum angle of rotation depends on the element whose rotation is being detected. For a revolute joint, the maximum angle of rotation to be detected depends on the location of that joint in the kinematic chain. The maximum angle of rotation to be detected may be less than 360°. The maximum angle of rotation to be detected may be greater than 360°. The accuracy of the position measurement is proportional to the angle of rotation to be detected. The greater the angle of rotation to be detected, the higher the accuracy of the position measurement needed. The sensor reading accuracy is given by:

Accuracy = ±2y x 2 * V∑ pole pairs (equation 1)

∑ pole pairs is the sum of the number of pole pairs of all of the magnetic rings on the disc. When there are two magnetic rings on the disc,∑ pole pairs = m+n. The more pole pairs on the magnetic rings, the larger the magnetic rings. Thus, larger magnetic rings lead to more accurate position measurements. The greater the angle of rotation to be detected, the bigger m and/or n are to achieve the required accuracy. Thus, the number of pole pairs on the magnetic rings for detecting rotation of one element relative to another is constrained by the relative angle of rotation to be detected between the two elements. In the case of a revolute joint, the selection of m and n are specific to the maximum angle of rotation of that revolute joint to be detected.

Figure 5 is a graph which illustrates theoretical and actual position sensor measurements taken from a position sensing arrangement of the form shown in figure 1. The x-axis is the position sensor measurement of the outer magnetic sensor array 12, and the y-axis is the position sensor measurement of the inner magnetic sensor array 11. The starred line plot illustrates theoretical measurements with 100% accuracy. The solid line plot illustrates example actual readings. These example actual readings differ from the theoretical readings due to manufacturing variation in the magnetisation of the magnetic rings on the disc, manufacturing variation in the magnetic sensor arrays, and/or misalignment between the magnetic rings and the magnetic sensor arrays. In figure 5 the actual readings have a consistent offset from the theoretical readings which demonstrates a systematic error in the actual readings.

This offset may be due to an error when magnetising the disc. For example, the centre of the magnetic rings may be offset slightly from the centre of rotation of the disc. Figure 5 also demonstrates additional error in the readings beyond the systematic error. In order to accurately detect which sensor reading was intended, the solid line of the actual readings in the plot of figure 5 needs to be closer to the correct line of theoretical readings than another line of theoretical readings.

A method of determining the values of m and n will now be described for an example in which the inner radial boundary of the disc 3 is limiting. For example, the disc may be mounted on a shaft, and hence the radius of the inner radial boundary n of the disc 3 has to be greater than the radius of the shaft. Figure 6 illustrates the steps of this method.

At step 20, the minimum rm,min is determined. This is the minimum radius of the centreline 9 of the inner magnetic ring permitted by the limiting inner radius n. As described in constraint 1 above, at its minimum, the centreline 9 of the inner magnetic ring is separated from the inner radial boundary 5 by the portion of the radial width of the magnetic sensor assembly 11 which is disposed between the centreline 9 of the inner magnetic ring and the inner radial boundary 5. This is to ensure that the magnetic sensor assembly 11 is confined within the inner radial boundary. In one example, the minimum rm-min is given by:

rm,min Π + (Wm + t)/2 (equation 2)

At step 21, the minimum number of pole pairs m for the inner magnetic ring is determined. The magnetic ring has a whole number of pole pairs. Thus, m is an integer. rm,min is increased to the lowest value of rm, where

2nrm = raly (equation 3)

Where m is an integer.

At step 22, the minimum rn,min is determined. This is the minimum radius of the centreline 10 of the outer magnetic ring permitted by the limiting inner radius n. As described in constraint 3 above, at its minimum, the centreline 10 of the outer magnetic ring is separated radially from the centreline 9 of the inner magnetic ring by a predetermined distance. This predetermined distance is suitably large enough to reduce or minimise interference in the sensor reading of one magnetic ring as a result of the other magnetic ring.

+ s (equation 4) where rm is that from equation 3, and s is the predetermined distance.

At step 23, the minimum number of pole pairs n for the outer magnetic ring is determined. The magnetic ring has a whole number of pole pairs. Thus, n is an integer. rn,min is increased to the lowest value of rn, where

2nrn = n2y (equation 5)

Where n is an integer.

At step 24, it is determined whether the values of m and n determined at steps 21 and 23 are co-prime. If m and n are co-prime, then these are the m,n pair which provide the most compact disc. In this case, m is chosen to be the number of pole pairs on the inner magnetic ring, and n is chosen to be the number of pole pairs on the outer magnetic ring. The method proceeds to step 25 where the position sensing arrangement is constructed by mounting a disc having an inner magnetic ring with m pole pairs and an outer magnetic ring with n pole pairs to the articulated structure. The disc is rigidly attached to the element of the articulated structure whose position it is configured to sense. The disc is mounted such that it rotates about the same axis as the element whose position it is configured to sense.

If, at step 24, it is determined that the values of m and n determined at steps 21 and 23 are not co-prime, then the method proceeds to step 26. At step 26, the value of n determined at step 23 is incremented by 1. At step 27, it is determined whether the new value of n determined at step 26 and the value of m determined at step 21 are co-prime. If they are not co-prime, then the method returns to step 26, where the value of n is incremented by 1. Then the method returns to step 27 where it is determined whether the new value of n is co-prime with m. Steps 26 and 27 continue iteratively, each iteration incrementing the value of n by 1, until a value of n is reached which is co-prime with m. Each iteration thereby increments the difference between m and n by 1.

We Claim:
1. A method of correcting a position reading from a position sensing arrangement, the
position sensing arrangement being suitable for sensing the position of a revolute joint
of an articulated structure, the position sensing arrangement comprising a disc having
a magnetic ring with magnetic pole pairs and a magnetic sensor assembly comprising
a magnetic sensor array for detecting the magnetic pole pairs of the magnetic ring,
the method comprising:
for each pole pair of the magnetic ring, taking a calibration pole pair position
reading with the magnetic sensor array, and generating a pole pair correcting function
by comparing the calibration pole pair position reading with a model pole pair
position reading;
for each pole pair of the magnetic ring, generating a corrected calibration pole
pair position reading by deducting the pole pair correcting function from the
calibration pole pair position reading;
generating a revolution correcting function by comparing the corrected
calibration pole pair position readings for the magnetic ring with model revolution
position readings; and
generating the corrected position reading by:
deducting the revolution correcting function from the position reading.
2. A method as claimed in claim 1, wherein the calibration pole pair position reading is
multi-bit.
3. A method as claimed in claim 1 or 2, wherein the revolution correcting function
comprises a periodically oscillating function.
4. A method as claimed in claim 3, wherein the revolution correcting function comprises
a sinusoidal function.
5. A method as claimed in any of claims 1 to 4, comprising generating the revolution
correcting function by fitting a curve to the corrected calibration pole pair position
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readings, and deducting a line representing the model revolution position readings
from the fitted curve.
6. A method as claimed in claim 5, comprising fitting the curve to the corrected
calibration pole pair position readings using a method of least squares.
7. A method as claimed in any of claims 1 to 6 wherein the disc comprises a further
magnetic ring with magnetic pole pairs, and the magnetic sensor assembly comprises
a further magnetic sensor array for detecting the magnetic pole pairs of the further
magnetic ring, the method comprising:
for each pole pair of the further magnetic ring, taking a further calibration pole
pair position reading with the further magnetic sensor array, and generating a further
pole pair correcting function by comparing the further calibration pole pair position
reading with the model pole pair position reading;
for each pole pair of the further magnetic ring, generating a further corrected
calibration pole pair position reading by deducting the further pole pair correcting
function from the further calibration pole pair position reading;
generating a further revolution correcting function by comparing the further
corrected calibration pole pair position readings for the magnetic ring with further
model revolution position readings; and
generating the corrected position reading by:
deducting the further revolution correcting function from the position
reading.
8. A method as claimed in claim 7, wherein the further revolution correcting function
comprises a periodically oscillating function.
9. A method as claimed in claim 8, wherein the further revolution correcting function
comprises a sinusoidal function.
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10. A method as claimed in claim 7, comprising generating the further revolution
correcting function by fitting a curve to the corrected calibration pole pair position
readings, and deducting a line representing the model revolution position readings
from the fitted curve.
11. A method as claimed in claim 10, comprising fitting the curve to the corrected
calibration pole pair position readings using a method of least squares.