JPH04212008A - Converter - Google Patents

Abstract

PURPOSE:To provide a phase/angle measurement method which can obtain high measurement accuracy even when accuracy of a mechanical part of a rotor system or the like is not very high. CONSTITUTION:Each rotor generates two periodic signals of the same cycle (wherein P phenomena occur during a cycle in one signal while Q phenomena occur during a cycle in the other signal). Reference points are determined respectively in cycles of the respective periodic signals, relative timing of phenomenon occurrence with respect to the reference point is obtained to calculate the average, and the average is assumed to be one virtual occurrence timing of the phenomenon. From difference in virtual phenomena occurrence timing of the two periodic signals, phase difference between the periodic signals and, furthermore, difference in angles between the rotors can be calculated.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a converter used in a phase measuring device that can perform highly accurate phase measurements without the use of particularly high-precision parts. Note that the phase referred to in this specification naturally includes the concept of angle.

0002

BACKGROUND OF THE INVENTION Many prior art phase measuring devices and their applications, angle converting devices, generate AC signals whose phase difference corresponds to the phase or angle of the input. For example, U.S. Patent 2,930,033
No. 3,278,928. The accuracy of these devices is related in part to the mechanical precision with which the signal-generating elements interact to create the signal, and also to the precision of the means used to measure the resulting phase. . Some known configurations of this type include one or more rotating poles coupled either optically, capacitively, or inductively to corresponding fixed and movable sensors. The other configurations are the same except that the mechanical roles of the poles and the sensors are interchanged. In order to improve the accuracy of such a device, first, for all cycles of the two generated signals (i.e. from the fixed side and the movable side), the input angle must be faithful to the phase difference between the two signals in corresponding cycles. I have to make it look like it's translated into
generally considered. Averaging is often performed to increase the reliability of the measured phase. Averaging simply measures the phase over a large number of cycles, or increases the number of sensors and sums their outputs electrically. However, averaging does not necessarily eliminate pole placement errors accurately, and unless special provisions are made in the phase measurement algorithm, variations in the signal period resulting from pole angular placement errors can cause errors in the measurement results. There is sex. In particular, the method of summing multiple sensor outputs may itself introduce errors if the amplitude of the sensor signals varies. For example, if the sensor is mounted eccentrically, the distance between the sensor and the pole may change, which causes a corresponding change in the amplitude of the sensor signal.

[0003] Commonly used techniques to reduce certain eccentricity errors actually depend on the accuracy of the mechanical placement of the poles for these prior art angle transducers to achieve their performance. may rely even more heavily on for example,
Techniques include analog summation of signals originating from one or more pairs of diametrically opposed sensors. By continuing to add until almost zero, the opposing phase errors essentially cancel each other out. Essentially, this technique combines two or more signals into one and uses this as one of the two components in the phase measurement. If the error in pole placement is large or the sensors are not truly diametrically opposed, the desired effect that would result from diametrically opposed placement of opposing sensors will cancel out or be negated. That is, unless the error components that are to be averaged by directly adding the sensor signals substantially match and have unequal periods, the desired error cancellation will not occur. This increases the need to arrange the poles regularly and adds the requirement that the poles have the same shape.

[0004] It is desirable that the accuracy of the shift signal phase angle conversion device does not fundamentally depend at all on the accuracy of the pole placement, but only on the accuracy of the phase measuring means. It is also desirable that techniques for reducing eccentricity errors do not rely on the accuracy of the pole placement or the symmetry of its shape.

To briefly explain the eccentricity error correction, the error component to be canceled is the phase error. In principle, the instantaneous cancellation described above can be achieved almost exactly if the amplitudes of the signals from both diametrically opposed sensors are equal. Unfortunately, due to the nature of the eccentricity error, there will also be an amplitude difference between the two signals. Therefore, it is desirable to be able to cancel the phase error regardless of the amplitude difference. These precautions apply to certain other errors as well.

Changes in the angular velocity of the rotating element can have a significant effect on the accuracy of the phase measuring means. Such fluctuations change the period of the signal whose phase difference is to be determined. The phase measuring means detects the steady state change in angular velocity (
It is highly desirable to be essentially insensitive to changes in average values, etc.) and to periodic changes that occur during each revolution of the rotating member. If it is insensitive to periodic changes, it generates angular momentum to smooth out these fluctuations (the "flywheel effect")
Mass requirements are reduced, thus reducing the weight of the device.

[0007] Crosstalk between the fixed and movable sensor signals can result in phase distortion, which greatly reduces the accuracy of this phase. Such crosstalk can often be reduced or eliminated by providing shielding, but this adds cost, mechanical complexity, weight, and possibly size. The technique used to generate AC signals is
be such that it generates an AC signal with properties such that it can accurately convey that information even in the presence of crosstalk, and that phase measurement techniques are inherently insensitive to crosstalk and provide true phase information. It is highly desirable to be able to obtain this accurately.

Prior art phase measurement techniques using all types of transducers that generate signals of variable phase difference often produce results that are best characterized as "fine" measurements. This precise result is the remainder (modulo)
value and must be combined with the result of the "coarse" measurement. Depending on how this is done, the device is generally incremental or absolute.
solution) is decided. Examples of devices to which these precautions apply include certain angle conversion devices and distance measuring devices. There is nothing inherently wrong with "coarse-fine" measurements, but by directly obtaining a uniform high-precision, high-resolution result, it is possible to avoid the problems caused by averaging the coarse and fine components separately and then combining them. It would certainly be advantageous to use a phase measurement technique that does not have to avoid the well-known pitfalls of Some of this problem arises from the modulo nature of the measurement, which is the tipping point at which the result of the measurement changes from very small or very large values (i.e., near the modulus for taking the remainder) to zero. It is related to how to handle values that are very close to . All of these problems have hitherto been dealt with conveniently, but their solutions have not been cost-free. Therefore, it is desirable to be able to eliminate these concerns while maintaining all of the accuracy and resolution of such a "coarse-fine" method. Such phase measurement techniques must also remain insensitive to signal period variations (pole placement errors, motor speed variations) and crosstalk.

An important consideration in phase measurement techniques is freedom from the so-called "phase matching problem." This is commonly experienced in what may be called the "start-stop" method of phase measurement. This method measures the phase between two signals of the same frequency and known period. Here, the phase is measured by starting a timer at a zero crossing or edge of one signal and stopping the timer at a corresponding zero crossing or edge of the other signal. That is, the time measured by the timer is a fraction of a period and therefore represents the phase. A common averaging technique for this method is simply to remember n measurement intervals and divide the result by n periods.

However, this method, especially when used with such averaging, suffers from significant difficulties when start and stop conditions become very close to each other. Noise can cause them to be observed incorrectly, making it very difficult to distinguish and average between very large and very small angles. A common solution to this problem is to introduce a 180 degree offset when the measured value normally falls within a selected region on either side of zero and remove it later. It is desirable to eliminate this extra effort while preserving the advantages of taking the average.

[0011] Very often in devices with rotating members, the absolute measurement coarse or other information is obtained from a signal indicating the completion of each revolution. It is desirable that no extra poles or sensors need to be provided to generate these once-per-rotation signals.

Finally, it would be advantageous if all of the previous advantages could be achieved digitally, minimizing the need for precision, low-drift analog circuitry. In particular, algorithms that take advantage of the computational and judgmental capabilities of a microprocessor to handle the large amount of logical complexity of the transducer as a whole, along with taking advantage of suitable structural features of the measurement hardware. It is desirable to move to

[0013]

OBJECTS OF THE INVENTION It is an object of the present invention to overcome the problems of the prior art mentioned above and to achieve what has been stated as desirable.

[0014]

SUMMARY OF THE INVENTION These and other advantages can be realized by utilizing the teachings summarized below. The result is a relatively low cost precision angle transducer that requires fewer mechanical parts but is capable of making measurements in the second (1/60 degree) range.

The angle converter described in the embodiment eliminates the need for high precision in the placement of the rotating pole by using a phase measurement technique that is in principle insensitive to pole placement errors. This technique is also inherently insensitive to non-uniformities or variations in the sensor-to-pole gap. In the angle converter of the embodiment,
The rotating pole consists of two standard commercially available gears supported on a common shaft and driven by a motor. As the gear rotates, four AC signals are generated from fixed and movable magnetic sensor pairs located independently (i.e., separately and with outputs not summed analogously) on opposite sides of the diameter.

[0016] In addition to eccentricity errors, similar errors can be corrected very precisely with sensors placed independently on diametrically opposite sides. Moreover, such a correction does not require that the spacing of the gear teeth be regular or accurate, nor does it require that the sensor pairs be placed on exactly diametrically opposite sides. The various independent sensors each generate their own individual signals in which at least one rotation of transition information occurring in the included rotations is captured by periodic sampling and stored in a memory device. When making a measurement, the transition information for each sensor is aggregated and combined with similar aggregates for other sensors. In this way all self-cancelling phase information is presented and cancellation occurs when the sum is combined. However, the phase error due to eccentricity does not necessarily need to be sensed in parallel, as when analog sensor signals are aggregated in real time. It is because of this simultaneity of opposing errors due to the symmetry of the sensor at both ends of the diameter that the pole placement must be ideal to maximize error cancellation. By processing the phase information stored in the signal of exactly one revolution or an integral number of revolutions, the essential property of symmetry of errors in the sensors at both ends of the diameter is preserved, but the need for simultaneity is eliminated. In this way, the width of the poles no longer needs to be equiangular to the axis of rotation, ie, arranged at regular angles around the axis.

Also, since the measurements for the various sensors are made during the same revolution, various other errors that are self-cancelling but not the same from revolution to revolution are arbitrarily reduced to a maximum. This example is a ball bearing in which only one of several ball bearings is larger in size.

The aforementioned aggregate metric is formed in the process of measuring the phase between the signals of two independent sensors. A number of different phase measurements are taken, one for each combination of sensors. That is, the phase is measured for each combination of fixed and movable sensors. This phase measurement is independent of the amplitude of the signals involved. Once all of the various phases are available, they can be averaged to cancel out the phase error introduced by eccentricity. In short, instead of averaging phase and amplitude as inseparable entities (so the amplitude difference affects the phase difference) and then measuring the phase, we first measure the phase and then average only the phase. Phase errors due to eccentricity are therefore almost exactly canceled out, as well as any additional amplitude fluctuations introduced by eccentricity or non-uniformities in the pole-to-sensor distance.

Since both signals whose phase is measured are of different frequencies, crosstalk does not affect the angle converter described below. That is, the phase information carried in the signal from the movable sensor is orthogonal to the phase information carried in the signal from the fixed sensor. If the frequencies are selected appropriately, the result of integrating the crosstalk exerted on each frequency will be zero in principle. In reality, due to the discrete sampling nature of digital methods, error cancellation is only approximately achieved, but this approximation can, in principle, be as close as possible to the exact value. . The different frequencies are selected such that no frequency is an integer multiple of any other. The phase measuring device according to the present invention generates a signal at such a frequency by a simple means of using gears having different numbers of teeth.

With the phase measurement technique according to the invention, signals of different and possibly non-constant frequencies can also be used, provided that only the following conditions are met: First, for every P cycles of one frequency, there must be exactly Q cycles of the other signal. Second, some means must be used to repeatedly identify or track the absolute reference position for one or both signals. An absolute (i.e., non-incremental) integrated (
In other words, results (coarse and fine are not determined separately) are obtained. It is also possible to divide the results into coarse and fine. If there is only one absolute reference mark, a fine measurement result is obtained, and coarse information is obtained by a separate absolute measurement or by incremental accumulation. Depending on the details discussed later, the absolute reference mark may be obtained either hard (i.e., as an actual signal) or soft (i.e., the microprocessor extracts a certain cycle that should be the mark). For extraction, the microprocessor uses the interval of each cycle to be extracted as a mark (so as not to lose sight of the mark). In the former case, a constant useful in the phase measurement technique can either be found and permanently stored for use by the microprocessor, or the microprocessor can automatically set its value each time the device is powered up. You can use it by either finding it and storing it. In the latter case, it is not possible to store the constants permanently, since the above-mentioned constant values can change depending on which cycle is chosen as the reference mark. To find the constant automatically in the latter case, the operator must enter one or two known static conditions into the device so that it can discover the value of the constant. In either case, there are ways to avoid having to find the value of the constant.

In the angle conversion device according to the present invention, absolute reference marks can be easily generated by simply removing arbitrarily selected teeth from each gear. That is, in this case the microprocessor detects in each sensor signal a periodic disturbance corresponding to the removed tooth. This detection determines the relative position of the absolute reference mark. Once this position is determined, the microprocessor uses the signals generated by each sensor (or the position obtained from it) if those removed teeth were there.
(time information) can be accurately approximated. This provides insight into the impact that the missing tooth would have had on the phase measurement itself (which is currently unknown) and on the associated error reduction mechanisms (if any of these were present) if this action had not been taken. (known to be susceptible to secondary effects) is minimized.

The phase measurement itself can begin at any time between P or Q cycles of the two signals. For each signal, the microprocessor indicates, in units of whole cycles, the difference between the start time and the time at which its respective absolute reference mark most recently occurred. Start measuring at the time when one of the signals next crosses zero, using it as a local reference time,
The local reference time and the zero crossing times of P and Q consecutive cycles of each signal are measured and stored in a table. In the embodiment of the invention described below, only positive going zero crossings were considered, but instead negative going
oing) Zero crossings can also be used. The system can easily use either zero crossing. The data in the table is used to sum each of the P transition times of one signal and the Q transition times of the other signal. These sums are arithmetically combined with the time required for the P or Q cycle, the measured difference between the start time and the absolute reference, and the values of P and Q to calculate the phase.

This technique avoids the "phase matching problem" mentioned earlier. This is because all that is required here is to independently measure P and Q consecutive times, each from a single reference time. Noise introduces only unavoidable uncertainty because its value cannot be known precisely. However, this uncertainty is reduced by the averaging inherent in this technique. However, since there is no special correspondence between P times and Q times, such noise is modulo
There is no chance of introducing a measurement value that is erroneous by the value of lus). This is consistent with the advantage that the poles can be arranged arbitrarily. What matters is the change in the difference between the two mean times of occurrence of what we will call the "equivalent unipolar" below. However, since these average times are determined separately from each other, the problem of phase matching does not occur at all.

The measurements and calculations described above are performed by coupling a zero-crossing detector to the output of a separate sensor. A delay mechanism provides a delayed signal for each zero crossing detector output. The transition detection circuit compares both delayed and non-delayed signals for each signal and detects that one of the signals has transitioned. When a transition is detected,
What transitions are made is immediately captured along with the time in the digital clock circuit. Sequential transition and time data are temporarily stored in a circular buffer that can be read/written independently of each other. As a result, even if asynchronous data is generated in bursts over a short period of time, this data can be captured independently of the microprocessor using interrupt control and fetching it into the storage device at its own pace. You will be able to do this. The up-down counter circuit interrupts the microprocessor when new information is available in the circular buffer. Under the control of the interrupt handling routine, the microprocessor executes transitions stored in tables in read/write storage.
Update time versus information. This table contains data for at least one rotation. When a request is made to take an angle measurement, the microprocessor uses a table to make various phase measurements between the sensors and compiles the results into the appropriate answer.

[0025]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a perspective view of an assembled mechanical part of an angle converting device constructed in accordance with the present invention. A reference stator 2, which is a stationary base, supports an input stator 3, which is a rotatable housing, and also contains an electronic circuit and a motor. Electrical signals originating from circuits within mechanical part 1 are provided by an umbinical cable to additional circuitry (not shown) including a microprocessor. The microprocessor performs operations on the phase information contained in the timing of the transitions of the four signals, providing the system in use with absolute angular data that can be accurate to seconds in degrees.

[0026] The stator 2 is rigidly attached to the instrument or device in which angle measurements are to be made. For example, it can be mounted on a pedestal, or it can be mounted on a tripod, such as a theodolite.
It can be attached to the reference member e). The movable member whose angle is to be measured is mechanically coupled to a rotatable input stator 3. In this way, the input angle is expressed as the angular displacement between the input stator 3 and the reference stator 2, which are connected by the movable member.

The electronic circuit in mechanical part 1 generates four square wave signals. The angular information is contained in the various phase differences of a modulus between each signal of a selected set of four square wave signals in relation to each of the remaining signals of the other set. . These four signals, for example, A, B
, X and Y, the signals A and B will have the same frequency and correspond to the input stator, for example. Also, signal X and signal Y have the same frequency, but this frequency is different from signal A,
It is preferable that it is not the same as B. Signals A, B correspond to the reference stator. The multiple comparisons described in the second sentence of this section do not refer to comparing the phase of signal A to the phase of signal B; they also refer to comparing the phase of signal X to the phase of signal Y. It's not like I'm doing it. What is stated there is to find the phase difference between "signal A combined with signal B" and "signal X combined with signal Y." To do this, the actual phase measurements made are A:X, A:Y, B:X
, and B:Y. From now on, you can easily change these to AX, A.
Let's say something like Y. The reasons for performing these phase measurements will be explained in detail below at appropriate points. The additional circuitry mentioned in the previous section obtains timing data indicative of these phase differences, and the microprocessor converts this data into highly accurate absolute angle measurements.

As shown in FIG. 1, the mechanical part 1 can be of relatively simple construction. In one practical embodiment, mechanical portion 1 has a diameter of approximately 114.3 mm (approximately 4.5 mm).
inches) and has a height of approximately 57.15 mm (approximately 2.25 inches).

Referring now to FIG. 2, the mechanical part 1 of the angle conversion device is shown partially exploded. The input stator 3, which is a rotatable housing, has been removed and turned upside down. The rotor shaft 4 is securely supported by an invisible bearing on the bottom of the reference stator 2, which is a stationary base. The rotor shaft 4 is free to rotate around the shaft, but is fixed against forces in the direction of extension of the shaft. Bearing on the rotor shaft 4 by a pair of bearings (of which only the upper bearing 12 is visible) is a reference rotor 6, which is a motor-driven two-ring member with magnetically permeable teeth. The two annular members are preferably firmly attached and separated by a spacer 19 of low magnetic permeability. The reference rotor 5 and the input rotor 6 are each screwed to a spacer 19 and cannot move relative to each other. They can only rotate as a unit around the rotor axis 4. It has been demonstrated, as explained below, that the phase accuracy of the teeth of the reference rotor 5 and input rotor 6 has little effect on the accuracy of the angle converter, so standard stock steel gears may be used.

The reference rotor 5 and the input rotor 6 are driven by motors, not visible in this figure, which are arranged in recesses in the stationary base reference stator 2 below the printed circuit board 7. The preferred motor for the configuration shown here is a DC Hall effect commutated three phase motor whose rotational speed is electrically regulated to three revolutions per second. (A speed of at least 2 to 10 rotations per second seems to be practical. The above lower limit is determined by the fact that as the rotation speed decreases, the signal amplitude from the magnetic sensor also decreases.On the other hand, the upper limit is Due to the processing power of the processor and the power consumption of the portable motor, it is currently limited to 10 rotations per second.In principle, the rotational speed of the rotor should be able to be increased considerably if desired. ) The field windings of the motor are fixed inside the aforementioned recesses, while the armature consists of permanent magnets attached to magnetic rings fixed to the underside of the reference rotor 5.

A pair of independent self-biasing magnetic sensors 8, 9 are arranged around the reference rotor 5 on diametrically opposed sides. As the reference rotor 5 rotates, mutually independent reference sensors 8, 9 sense the temporal changes in the reluctance of the associated magnetic circuit formed by each sensor and its immediate gear teeth. The signals generated by each of the reference sensors 8, 9 are each shaped into two of the four square waves mentioned above (X and Y mentioned earlier).
become.

Another set of independent self-biasing magnetic sensors, input sensors 10, 11, are located under the input stator 3, which is a rotatable housing. Input sensors 10 and 11 also generate separate signals in response to temporal changes in reluctance due to rotation of input rotor 6. Each of these separate signals is shaped into a square wave, resulting in the remaining two square wave signals (A and B above).

In addition to the motor speed control circuit, the printed circuit board 7 also includes an amplifier and the generally sinusoidal outputs of the four magnetic sensors 8-11 with their associated square wave signals A, B, X.
and a zero-crossing detector for converting into Y.

When assembled, the rotatable input stator 3
is locked to the rotor shaft 4, and the rotor shaft 4 is reliably supported in rotation by a bearing (invisible) under the rotor at the bottom of the reference stator 2, which is a stationary base, as described above. The rotor axis 4 provides a stable axis of rotation for the rotating input stator 3, through which the input angle is applied. The input stator 3 is further supported to the reference stator 2 by a series of ball bearings 15 which are held in place by a retainer 16. The hardened and polished bearing surfaces 13, 14 each form a race in which an intervening ball bearing 15 runs. Thereby, the input stator 3 is firmly supported on the reference stator 2 so as to rotate smoothly and with low friction around the stable axis of the rotor shaft 4. This bearing configuration allows the theodolite telescope to be mounted directly above the angle converter.

Other mechanical configurations are also possible. for example,
The rotor shaft 4 is firmly attached to the reference stator, while
The input stator may be supported by a bearing on the rotor shaft.

The input stator 3 must be able to freely rotate whatever input angle is to be transformed. For this purpose, four circular slip rings 17 are arranged on the underside of the rotatable housing of the input stator 3, corresponding to four sets of elastic contacts 18. Elastic contact 18
transmits signals from input sensors 10, 11 to printed circuit board 7. Therefore, in this input stator 3, there are no restrictions regarding the direction and magnitude of the input angle.

By inputting the angle, a phase difference corresponding to the input angle is created between the signals from the input sensors 10 and 11 for the input rotor 6 and the signals from the reference sensors 8 and 9 for the reference rotor 5. is generated. To see why this is the case, the input stator 3 is connected to the input sensors 10 and 1.
1 are located directly above the reference sensors 8 and 9, respectively. Further, it is assumed that the same gears are used for the input and reference rotors 5 and 6, and that the teeth of both gears are mounted so that they exactly overlap when viewed from the rotor axis direction. Under this rather restrictive condition, there will be no phase difference between the reference sensor signal and the input sensor signal, since corresponding sets of signals occur simultaneously. Assuming that the rotor has n teeth, for example 3
Even when a mechanical angle of 60/n degrees is input,
Due to the spatial arrangement described above, there will be no electrical phase shift between the input and reference sensor signals since both signals will be generated simultaneously. In other words, n teeth are 360/n
A signal with a mechanical modulus of mechanical degree (
In other words, it generates a residual signal for this modulus). Within this mechanical law (i.e. the rotor is i×36
While rotating from 0/n degrees to (i+1)×360/n degrees), the sensor output exhibits a complete cycle of 360 electrical degrees (ie, the phase of the sensor output signal rotates 360 degrees). If the mechanical input is 1/4 of 360/n degrees, the output signal of the sensor will have a phase shift of 1/4 of 360 degrees, or 90 degrees.

Since the phase of the sensor output signal rotates exactly n times for each mechanical rotation, the electrical phase difference is conveniently expressed as "
It can also be said to be a measurement of ``spirit''. The input angle can be measured by combining the "coarse" value, which indicates how many "fine" cycles are included in the input angle, and the "fine" value. The coarse value is usually obtained either by incrementing the currently stored coarse value in response to finding that the phase has rotated exactly one time during a fine measurement (so-called incremental method), or by directly measuring it. (the so-called absolute law). The preferred phase measurement techniques discussed in detail below are compatible with this coarse/fine concept and are compatible with the incremental and absolute measurement concepts. However, if the advantages of the present invention are utilized to the fullest, the measurement result becomes the final "answer" as it is, so the measurement result cannot be clearly separated into coarse and fine components. Therefore, the concept of coarse and fine becomes unnecessary. In a sense, these concepts still exist. For example, when the teeth of a gear are arranged regularly, ``coarse'' and ``fine'' have somewhat similar meanings to their original meanings. (In the present invention, it appears that the number of poles on each rotor must be equal for the concepts of coarse and fine to have their traditional meaning). However, as mentioned above, these are unnecessary conditions that the rotor does not have to satisfy. If the gears used in both rotors have unequal numbers of teeth, or if the teeth are irregularly arranged, the words "coarse" and "fine" have rather special meanings. This will be discussed in more detail at the end of the section describing phase measurement techniques.

A preferred use of the phase measurement technique of the present invention requires provision of means for generating a hard mark that appears once per revolution of each rotor. This is equivalent to identifying a pole on each rotor as the "absolute reference pole." However, also as an example of the flexibility of the technique described here, the phase measurement itself
If you only want to generate a "precise" answer while still needing a "perfect" answer, use the incremental measurement method (the input rotor's
You can omit the "once per rotation" mark) or the two "
The "once per revolution" mark will be used to take separate coarse measurements. In either of the following two cases, the rotor rotor 5 (unless P=Q)
The marks placed once per rotation provide reference pole information for the reference rotor 5 in the actual measurement. The software marks for one revolution will be explained elsewhere. The need for marks is the same in any case. The difference is mainly in the way the mark is generated. (As written here, these notes are separate from, and may not be fully recognized as, supporting items that appear in various subsequent chapters. (It is described to illustrate the flexibility of the phase measurement technique of the present invention.)

The use of separate once-per-revolution marks provides a means of making coarse measurements that can be correlated with fine measurements to produce absolute (ie, non-incremental) angle measurements. Such rough measurements are also performed by phase comparison. However, since each signal whose phase is to be measured has only one electrical cycle per mechanical revolution, 360 degrees of electrical phase corresponds to exactly 360 degrees of mechanical rotation of the input rotor 3. Additionally, n fine cycles per rotor revolution can be used as a clock in determining the coarse phase measurements between two revolution once marks. This considerably reduces the influence of motor speed changes on coarse measurements. Instead of installing separate sensors on the input and reference rotors to generate a hardware signal for each rotation, this signal can be easily obtained by simply removing one tooth from each of the input and reference rotors. . In FIG. 2, teeth 20 and 21 have been removed from reference rotor 5 and input rotor 6, respectively. A microprocessor can recognize periods as long as one revolution mark and can make highly accurate estimates from the missing cycle of what would have happened if it had actually been there.

In addition to marking once per revolution, a possible use is to indicate the time interval for collecting exactly one revolution's worth of data. Exactly one rotation's worth of data is important in the phase measurement technique of the present invention. However, in such a method, the starting point of such a time interval is limited (ie, the starting point can only be one mark detected per revolution), which slows down the progress of the measurement considerably. Since a processor is available and the number of rotor poles does not change, the preferred method of collecting exactly one revolution's worth of data is to count cycles. In this way, phase measurements can begin when any pole passes any sensor.

Errors resulting from sensor eccentricity (and other conditions such as motor tilt, etc.) are determined by the analog sum of multiple input sensor outputs and the analog sum of multiple reference sensor outputs, as in prior art devices. can be further reduced by not making the phase comparison beforehand. Instead, the signals remain separated and the phase information from each independent sensor is sought by measurements that are strictly related to the timing of those signals. This allows eccentricity correction based only on phase. As mentioned above, in the conventional technology, when performing algebraic addition of a plurality of signals, the phase of a large amplitude signal inevitably suppresses the phase information of a small amplitude signal. The present invention does not have this drawback. This is important because the presence of eccentricity also causes significant (and non-linear) variations in signal amplitude.

Techniques that first measure the phase and then average the results generally reduce "once-per-round" errors,
It is also advantageous in reducing other types of errors, such as those known as "two-round-one" errors. The one-round error is the error in the measurement angle, which is a periodic function of the input angle, and is 360
It has a period of input degree. The 1-round 2-times error has a period of 180 input degrees (the error function is 2 times during one rotation of the input).
(repeat several times). In order to reduce the one-round error, it is best to average it and place the sensor on the opposite side of the diameter. In order to reduce the two-per-round error, it is best to average it and to arrange two pairs of sensors arranged on opposite sides of the diameter, shifted by 90 degrees. The effectiveness of these and related techniques can be significantly improved by first measuring the phase and then averaging it.

Finally, crosstalk between the input and reference sensors can significantly affect the accuracy of the converter. This effect can be almost entirely eliminated by measuring over a period of just an integral number of revolutions of the rotor and by suitably selecting the gears of the input rotor 5 to be unequal to the number of teeth of the reference rotor 6.

It is clear that the above features are difficult or impossible to implement with conventional phase comparator circuits. However, it can be effectively and efficiently performed using microprocessor-based devices, as described in detail below. Here, the microprocessor creates a table in memory of the transition directions of the four square wave signals from the sensors and their times of occurrence. This table is created by an interrupt handling routine that is activated by the transition of any of the four signals. When not in an interrupt state, the microprocessor can begin processing data already in the table as soon as a measurement request is made. Tables can be made circular so that sufficiently old data is automatically replaced with new data.

Block Diagram of Angle Converter FIGS. 3A to 3C are simplified block diagrams of an angle converter having the features described above. If any of the components in FIGS. 3A to 3C correspond to those in FIGS. 1 and 2, the corresponding reference numerals in FIGS. use

Referring first to FIG. 3A, reference rotor 5 and input rotor 6 are mounted such that shaft 22 rotates about an axis corresponding to rotor shaft 4 of FIG. For simplicity and ease of explanation, the more complex rotor mounting and drive mechanism in FIG. 2 has been replaced with what is shown here. A motor that drives the rotating shaft 22 and a bearing that supports the rotating shaft are not shown. However, the structure depicted here works reliably and, if used, the rotor shaft is made of a non-magnetic material, such as brass.

The number of poles of the input rotor 6 is a certain integer Q,
The number of poles of the reference rotor 5 is another integer P. In the actual example, Q is 120 and P is 144. but,
In order to make it easier to see, rotors 5 and 6 and the number of poles are much smaller in this figure. Therefore, this causes the missing pole 20
, 21 can be clearly shown. When using a depleted pole (e.g., a gear with teeth removed) as a single rotation indicator mark, as is the case with the preferred embodiment described herein, the physical number of teeth is (P-1), respectively. Although there are only (Q-1) poles, the expressions P poles and Q poles are still used. Of course, its meaning is (P-1) and (
Q-1) There are "actual poles" and two "nominal poles", the latter of which can be detected independently due to its absence. In other words, a missing pole is counted as a pole. Of course, it is not always necessary to think in this way; for example, in this example, the number of poles Q=1
It is also easily possible to characterize the structure as 19 and P=143 and not interpret the depletion poles as poles. In other words, in this other interpretation, the missing pole is considered to be an entirely different one-turn indicator mark that falls exactly between the two poles. In the light of the following explanation, these two methods, in the final analysis, look at the same thing equally.
It becomes clear that there are two methods.

The reference sensors 8, 9 are located on diametrically opposite sides with respect to the reference rotor 5. Each reference sensor has a magnet 23
, 24, magnetically permeable pole pieces 25, 26 and sensing windings 27, 28
have. The reference sensors 8, 9 are part of the reference stator 2 and are placed in fixed positions. The input sensors 10 and 11 have the same structure and are arranged on diametrically opposite sides of the input rotor 6. These input sensors 10,
11 is a part of the input stator 3, which moves together in accordance with the direction and magnitude of the input angle.

Each of the independent reference sensors 8, 9 and input sensors 10, 11 provides corresponding data separately, the output of which is not algebraically added to the output of the other sensors. To do this, independent reference sensors 8, 9
and input sensors 10, 11 are coupled to amplifiers 29-32, one each. The outputs of amplifiers 29-32 are coupled to respective zero-crossing detectors 33-36, one each.

For convenience of later explanation, the signals and data related to the sensors 10 and 11 on the input stator 3 are labeled A.
, B, and the reference sensor 8 on the reference stator 2
, 9 are named X and Y, respectively. A, B, X, and Y generally refer to the information content of the associated signal path and do not refer to the particular electrical form of the signal at any particular point on that path.

Referring to FIG. 3B, data A, B, X,
and Y are sent to a corresponding one of delay circuits 37-40, respectively. The manner in which the delay circuits 37 to 40 are implemented is not itself important. These can be realized in various ways as long as certain specifications are met. This specification requires that sufficient delay be provided so that a signal transition can be detected by comparing the delayed signal and the non-delayed signal in the first stage circuit. Second, to ensure that each transition can be detected reliably, the delay must be less than 1/2 the period of the signal being delayed. Thirdly, if the transition timing is quantized by a certain clock, the amount of delay must be less than or equal to 1/2 of the clock period. The third specification ensures that when two consecutive transitions are quantized, they are separated as different states, so that they are not buried in a single detection result. . To illustrate this with respect to FIG. 3B, this means that even though there are two consecutive transitions, a signal called EVENT is issued for each one separately. Although there are various techniques that can be proposed to achieve such a delay, the circuit shown in FIG. 3B simply and conveniently satisfies the above specifications. One of the four identical delay circuits 37 to 40 will be described below as a representative.

The delay circuit 37 includes two D-type latches 41 and 42. The D input of the D-type latch 41 is connected to the output of the zero-crossing detector 36. Clock signal circuit 45
Clock signals CLK43 of mutually opposite polarity generated from
, /CLK44 (/ represents overline)
At the leading edge of , the value of signal A currently present at the D input is latched and appears on the Q signal of D-type latch 41 . Q output is D type latch 42
This time, the clock signal /CLK44 is applied to the D input of
The time is measured by The value latched in the D-type latch 41 is latched in the D-type latch 42 at the leading edge of the clock signal /CLK44 and delayed by a half cycle of the clock signal CLK43.
appears in its Q output. After another half period of clock signal CLK43, another (and possibly different from the previous) quantized sample of signal A is latched into D-type latch 41. The transition of signal A appears as a situation in which the values of two Q outputs separated by a half cycle of clock signal CLK43 are different.

XO for each of the delay circuits 37 to 40
One R gate 46 to 49 corresponds to each other. For example, for signal A, XOR gate 46 is connected to the two Q outputs of delay circuit 37. At each transition of signal A, XOR gate 46 detects a half period in which the last quantized value An is not equal to the previously quantized value An-1. Detection of such a difference generates a corresponding signal ΔA. Other signals ΔB, ΔX, ΔY, and ΔY are each XO
Generated at R gates 47-49.

Signals ΔA to ΔY are input to the OR gate 50, and EV, which is a signal indicating that one of the signals A, B, X, and Y has made a positive or negative transition.
Generates ENT51. The pulse width of EVENT51 is C
This is 1/2 of the period of LK43. The data for the transition direction and time table described above is collected in the circuit described below. The frequency of the clock signal 45 mentioned earlier is 500KH.
It is z. The 500 KHz signal CLK43 is also provided to a 12 bit counter 52 which provides information indicating the progression of time. The values of 500 KHz and 12 bits are somewhat arbitrary. These values are approximately determined by convenience, cost, performance, etc. Other frequencies and other numbers of bits are certainly possible.

Each time signal EVENT51 occurs, time and status data at its leading edge is stored in one of several temporary latches. New data counter 53 indicates which temporary latch is stored. Signal EVE
New data counter 53 is advanced at the trailing edge of NT. In this example, the new data counter 53 is 0, 1, 2, 3, 0,
I count... New data counter 53 provides its count value N to decoder/multiplexer 54, which selects the next of the four temporary latches (following the count of N) as the temporary latch destination for time and status data. The status data is from Xn-1 to An-1 from delay circuits 37 to 40.
This is the signal up to. This 4-bit information represents the value of each of signals A, B, X, and Y just before the most recent transition, and is latched on the leading edge of EVENT. By comparing these with previous signals that have been previously captured and stored, the nature of the most recent previous transition can be determined. The nature of the recent transition that caused the current occurrence of signal EVENT will become apparent on the next occurrence of signal EVENT. The same applies below.

Each time the signal EVENT is generated and the next one of the temporary latches 55 to 58 is selected for storage, the state data for Xn-1 to An-1 is updated to the current calculated value of the counter 52. and stored in the selected temporary latch.

The step count value N of the new data counter 53 is now also 0, 1, 2, 3, 0 . ．． ．． ．． This is not equal to the count value I of the interrupt catch-up counter 59, which is calculated as follows. As a result, the comparison circuit 60 detects the N of the counters 53 and 59,
A comparator circuit 60 coupled to the I output generates a signal N≠I, meaning that the two counts do not match. signal N
≠I is applied to the interrupt request input of microprocessor 61. This tells microprocessor 61 that there is additional data to add to the table. Microprocessor 61 then executes an interrupt service routine (ISR) to retrieve new data from the temporary latches and place it into the table. The details will vary depending on the particular microprocessor used, but this is a general description of what happens. The ISR increments the interrupt catch-up counter 59. The incremented count value I is sent to the decoder/multiplexer 6
Added to 2. Decoder/multiplexer 62 then selects the next count (in the order of I counts) of temporary latches 55-58 as latches that send state and time data to the microprocessor.

In this manner, an interrupt request is generated when new data is stored. Status and time information is
As long as the microprocessor never lags by more than 5 transitions,
The data is stored by a temporary latch until the microprocessor is able to store the data in storage. This mechanism allows any or all of the A, B, X, and Y signals to change at each transition, allowing successive quantization transitions to be captured.

FIG. 3C shows, with a simplified table, what microprocessor 61 does to store state and time data. First, under interrupt control,
The microprocessor builds up a table of state transitions and their associated times in random access storage 63. Although actual configurations are much more complex than can be easily shown in Figure 3C, and certain features may vary from one specific configuration to another, this figure provides a good illustration of the general idea. . The state data is examined to determine the nature of the transition, and some symbolic representation thereof is prepared and stored. The associated time is also stored. In the preferred embodiment described herein, the microprocessor is a 12-bit 5
The time information of 00 KHz (4096 counts at 2 μsec per count, or 8,192 μsec to fill the counter) is converted to a point on the absolute time axis starting at a certain time To. Although it is not particularly important when time To begins, it is convenient for it to coincide with the starting point of the measurement. (This means that when a measurement request is received, instead of simply using the data already stored in storage, it waits for other data to occur in the rotation. Both methods work equally well.) For this purpose, counter 52 can be easily operated from a maximum value back to zero as desired. The firmware detects that the count value has suddenly decreased by returning to zero, and adds back the necessary 4096 counters to generate the correct count value. The modified count value is then added to the previous value obtained on the resulting absolute time scale. This now becomes the new value and processing continues. This works well when the rotation speed is 3 revolutions per second and 120 teeth per revolution. , at most 2.778μse between successive positive transitions
This is because c. Starting and restarting absolute time scales is a convenient implementation.

The microprocessor continues to add new positive transition data to the table. Data regarding negative transitions is simply ignored. Since tables are structured cyclically in nature, old sections that contain data that is older than one rotation are used to store new data. The microprocessor keeps an eye on the chipped teeth and flags them for easy later positioning by some means or, preferably, a pole counter in the firmware associated with that rotor when a chipped tooth comes. restart. In the following explanation, the count values of these counters are expressed as P#(
(for the reference rotor) and Q# (for the input rotor). The designation P# and Q# means that there is only one pole counter per rotor. Depending on the implementation, this may be the case, or preferably there is a pole counter for each sensor. This point will be discussed later.

A chipped tooth is detected because its cycle is abnormally long (that is, because the tooth detection interval is large). A simple and satisfying way to indicate a missing transition is to put it where it should be. For example, place the positive transition at the midpoint of adjacent positive transitions. More sophisticated methods, such as averaging, are also possible.

When the system in use requires angle measurement, it generates a measurement request signal. This also causes an interrupt to the microprocessor. This causes the microprocessor to process the data in the table starting with the earliest entry. This continues for the data of one previous complete revolution of the rotor. Full rotation required (full rev
transition) is detected by counting the transitions stored in the table. Once the calculations for the measurements are completed, the answers are placed in storage and a measurement complete signal is sent to the user system. Alternatively, it may also be desirable to collect data related to a new rotation following the occurrence of the measurement request signal and process that data to determine the angle. The choice of whether to use the data of the rotation just completed or the data immediately after the measurement completion signal is a matter of actual equipment design.

It is also desirable to hold the data for the previous half-turn as soon as a measurement request signal is received and combine it with the data occurring in the subsequent half-turn to produce the answer. It can also be seen that in this way, even if the input angle changes at a constant rate less than a certain maximum value, the effects of this change can be canceled out. The answer is therefore essentially an exact answer representing the value of the input angle around the time the measurement request signal was issued.

Different but equivalent ways to organize state and time data in tables will become apparent as the explanation of how that data is used proceeds.

Phase Measurement Techniques FIGS. 4-9C are idealized schematic representations of an input rotor and a reference rotor with each associated one input sensor and one reference sensor. These figures are for single phase measurements A
This is useful in explaining how X, AY, BX, BY are performed.

The structures of FIGS. 4-9C are not limited to high permeability poles rotating past in front of the magnetic sensor. The phase measurement technique of the present invention can be used to measure the phase between two "signs" with the same period. The only conditions required for these two signs are that a known number of events occur within each sign, and that the position of each event within the sign does not change from period to period. This technique is also not sensitive to non-uniform spacing between events within the sign.

That is, the rotor may be a grooved disc or other optical encoder cooperating with an optical sensor, or the value may be periodically determined as a function of the displacement, or in the present example as a gear with a magnetic sensor. The phase of the signal so generated can be easily measured by this technique. The number of signal changes occurring per revolution (or unit time) need not be the same from rotor to rotor, nor does the period of each cycle of the signal from the rotors need to be constant. In particular, for the example considered with respect to the gears of an angle transducer, the phase measurement technique of the present invention is in principle and in practice insensitive to gear tooth alignment errors.

Referring now to FIG. 4, a reference rotor 5 and an input rotor 6 are schematically depicted. One sensor for each rotor (i.e. reference sensor 8 and input sensor 10)
) is provided. The diametrically opposite second sensor has been omitted for simplicity in explaining this feature of the invention. The phase of the signal generated by the second sensor is measured simultaneously in the same general manner as described for each one of the sensors shown. These are measured during the same rotation but have their own values P# and Q#. How the phase for the four sensors is measured as and then combined to eliminate the effects of eccentricity will be discussed in a subsequent section. For now, it is assumed that there is no eccentricity in the idealized schematic structure of FIG.

Let P, Q be the number of poles (individual teeth of a gear) on the reference rotor and input rotor, respectively, and let R be the length of time it takes for the rotor to complete one rotation.
The angle experienced by the input rotor (in radians) is given by the equation below (1
) is given by

[0071]

[Math 1]

The derivation method and interpretation of equation (1) will be described in detail below, but the symbols used in this equation will also be explained here. In equation (1), ΣTQ[i
] and ΣTP[i] are the times of occurrence of successive leading edges of the signals from the sensors involved, starting at one of several convenient start times and summing until exactly one revolution is completed. be. (Note that Q[i], P[i], etc. represent Qi and Pi, respectively.Due to the specifications of electronic application documents, it is not possible to lower a partial line by two or more steps, so all subscripts after the second step are Expressed by putting it in [].)ΣTQ[
i] is the sum of Q consecutive transitions for the input sensor and ΣTP[i] is the sum of P consecutive transitions for the reference sensor. The time R does not need to be the same each time equation (1) is used. The value of the respective time R can be determined when carrying out the respective phase measurement. This time R
can be measured, for example, by comparing the occurrence times of two events that are P cycles apart in the reference sensor output, or by comparing the occurrence times of two events that are Q cycles apart in the input sensor output. It can be done easily. P#
, Q# is where the addition starts for each rotor,
Counted from each fixed reference point. P# ranges from 0 to P-1 and Q# ranges from 0 to Q-1. For convenience, the reference point of each rotor may be its missing pole. The term Ψ is a constant that depends on the shape of each rotor, certain inaccuracies in its pole alignment, etc., and must be determined only once for each signal pair for each individual transducer. The term Ψ is not a function of θ. If we use the phase measurement technique of equation (1) to obtain individual measurement results by subtracting the first result from the successively obtained results, we obtain successive angular shifts from the initial setting. In some cases, it is not even necessary to know the value of Ψ. That is, all of the respective Ψ's are canceled out, leaving only the differences between the various values of θ.

There are rules for making a sum and finding the values of P# and Q#. The request to measure the input angle can occur at any time related to the rotation of the rotor. Summing can begin at any leading edge obtained from the reference rotor, such as the first leading edge following a measurement request. (All measurements could alternatively be made using the trailing edge.) Whether or not to start with an estimated location of the defect is a design question in making the actual device. Designers can choose the best for their respective systems. Set any pole of the reference rotor 5 as the current starting pole (i-th pole of P poles), start measurement with a certain To=0 as the time reference, and compare the sum of P consecutive times with each other. Add together. Referring briefly to Figure 4, P
1 is the starting pole and the time when P1 passes the sensor is 0 (temporary convenient assumption), then TP[i
] is the same as the sum of the time intervals shown in equation (2) below.

[0074]

[Math 2]

Before proceeding with the discussion, it is orderly to note the use of the Σ symbol. For example, regarding equation (2),
It is somewhat inconvenient that the upper and lower limits 1,y are not numerical values of subscripts appearing in TP[i]. The implication, of course, is to start with the particular value needed to define the interval from 1 to y and take the corresponding P values of i mod P. These and subsequent equations can, of course, be expressed using entirely conventional notation. However, doing so would likely result in an increase in the amount of symbols without a corresponding increase in information content. If I understand correctly, the notation I have taken here for the Σ symbol gives us
The result is a descriptive symbol that is clear and relatively simple and which itself performs its intended role well. This is especially the case when introducing the symbols Δθ and ΔφJ,K. Although these configurations include intervals of arbitrary size and are included in the sum, they are always i mod P
is not satisfactorily expressed by the value of .

Expression (2) is expressed for each time interval 1, m, n, . ．． ．．
．． When summarized for each y, it is expressed as follows.

[0077]

[Math 3]

Furthermore, addition of TQ[i] is similarly expressed as follows.

[0079]

[Math 4]

Here, even if it is assumed that "addition starts from time zero", the above equation does not lose its generality. This assumption also has the advantage of simplifying the formulas in the following explanation. Looking only at equation (1), even if addition starts from a time that is not 0, the effect will cancel itself out, so such an assumption of "initial time equal to 0" is not necessary. How this happens will be pointed out as the explanation progresses.

In FIG. 4 and equations (2) and (3), symbols 1, m, n, . ．． ．． ．． y,z represent the incremental time (time interval) between the poles of the reference rotor. Assuming a constant rotational speed, the time 1, m, . ．． ．． ．． z will be equal. It should be emphasized here that neither the reference rotor nor the input rotor needs to be poled with particularly high precision to enable high-precision phase measurements. In principle, the time intervals 1, m, n, . ．． ．． ．． z is the corresponding time interval a, b, c, . ．． ．． ．． Together with k, it can represent any arrangement of different pole spacings on the rotor. In practice, the time intervals 1, m, n, . ．． ．． ．． z is the time interval a
, b, c. ．． ．． ．． Like k, it tends to be equal. There are good reasons to want to do this. Such regularity helps to reliably detect missing poles, prevent undue transients in the sensor, and suppress crosstalk. However, in principle, the lack of such uniformity does not reduce the accuracy of phase measurement. Through the following examination, the time interval 1, m, n
、． ．． ．． ．． z and a, b, c, . ．． ．． ．． k is treated as a discrete number and is in no way assumed to represent equally spaced poles.

The addition of the time of the input rotor 6 is based on the reference rotor 5.
It starts at exactly the same time as in the case of . Generally, this start time will not begin coinciding with the transition obtained from the input rotor 6, but is a function of pole placement and input angle, and may begin coinciding. In any case, the same general rules apply. Starting from the start time, input rotor 6
The times of the next Q poles are added. Referring again to FIG. 4, similar to the reference rotor 5, the incremental times or time intervals between the poles of the input rotor 6 are a, b, c, . ．． ．． ．． It is displayed as k. Typically, the first term of the sum is a, b, c,
．． ．． ．． ．． k is a fraction of one time interval. The proportion is determined in part by the input stator 3.
It is determined by the rotation angle of , that is, the input angle.
I will call it.

For example, in FIG. 5, input stator 3
input sensor is Δθ from pole Q at the start of addition.
If the input rotor 6 is located at the front, the total for the input rotor 6 is as follows.

[0084]

[Math 5]

In each sum, the time intervals a, b, c
、． ．． ．． ．． one of y, z and time interval 1, m, n
、． ．． ．． ．． It can be seen that one of j and k does not appear. i.e. for example

[0086]

[Math 6]

At first glance, it appears as if the addition is not completed by summing just one round, and that useful information is being discarded. however,
The times associated with each pole are all used. The time for one pole on the reference rotor is (temporarily) taken as the reference for the remaining poles on that rotor as well as for all poles on the input rotor. Accounting for ``missing'' times for missing poles involves ``double use'' of two poles. Furthermore, the rules given here have desirable properties that can be seen from equation (5). That is, the count of the Δθ term is just Q, rather than Q+1 or Q-1. Why this is useful will become clear as the explanation progresses.

Finally, the terms P# and Q# (in equation (1)) are calculated based on how many poles on each rotor have passed from the time the absolute reference pole of each rotor passes until the time when the addition starts. Determined by attention. The absolute reference pole may conveniently be a regular pole or a missing pole. For example, if P1 and Q1 are the absolute reference poles for the reference rotor and input rotor, respectively, then
P# is 0 when P1 is the starting pole, 1 when P2 is the starting pole, 2 when P3 is the starting pole, and so on. Similarly, P# is 0 when Q1 is the first Q pole from the start of the P side, i.e. the reference side, 1 when Q2 is the first pole, 2 when Q3 is the first, The same applies below. The values of P# and Q# for any particular measurement are readily determined by microprocessor 61 by examining the transition and time data stored in memory.

Returning now to FIG. 4, by analyzing a series of possible cases starting from the one shown in FIG.
It can be seen that yields the required result.

FIG. 4 shows the reference rotor 5 having P poles and Q
2 shows an input rotor 6 in a schematic diagram with poles. 2
The two rotors are mounted on a common shaft for rotation. The P poles of the reference rotor 5 are P1, P2, P3, . ．． ．． ．．
PP and rotates past the reference sensor with a constant angular velocity of one revolution per time R, then the time interval 1, m, n
、． ．． ．． ．． It is divided by the angular displacement that produces z. The Q poles of the input rotor 6 are Q1, Q2, Q3, . ．． ．． ．． It is QQ. The time intervals for this are a, b, c, . ．． ．． ．．
It is k.

Although FIG. 4 is somewhat simplified, it may represent the case where the input angle is 0 degrees. This means that when looking at the position of the input sensor 10 on the input stator 3, it is exactly above the reference stator 2 when the input stator 3 is at 0 degrees, and under such conditions, P1 and Q1 respectively connect their associated sensors at the same time. pass (i.e., TP[1]=TQ
[1])). The fact that this assumption can be made will become clear as the following explanation progresses, but to put it simply, it is as follows. In other words, even if these assumptions do not hold, a certain offset will be applied to each answer. But as you can see, there is a certain offset in the answer anyway. It doesn't matter what exactly the offset is, and not having to separate it into two parts simplifies the explanation. In practice, it means whether the sensors are directly on top of each other at 0 degrees, or whether the sensors are directly above each other at 0 degrees, or the TP at 0 degrees.
There is no need to pay attention to whether [1] is equal to TQ[1].

However, with these assumptions, TP
The equation (
6b) and the difference shown in equation (7).

Before returning to these equations, it is appropriate to explain how to derive equation (6b). First of all, the formula (6
It is clear that b) is a correct equation, but there is no mention of what precedes this equation. (To show that equation (6b) is an equation, add equation (3) to the left side.
) and formula (3') may be applied). Although it can be proven that equation (6b) is an equality, equation (6b) still
It is fair to ask where each term on the left-hand side of . The answer is that it is convenient and convenient for consideration, and nothing else. It is gained by experience and serves as a convenient place to pose questions to the phase measurement technique of the present invention. In a sense, you are simply asking the question: : ``Suppose we make this difference [that is, each term on the left side of equation (6b)]. What will happen then?'' One answer is that the obtained equation can be rearranged to create an equation for θ, and finally, this difference is calculated by multiplying the quantity appearing in equation (1) by the count Q. It is something. That is,

0
094]

[Math 7]

The amount in parentheses on the right side of equation (6a) can be considered to be the difference in time obtained by subtracting the average time of occurrence of the poles of the reference rotor 5 from the average time of occurrence of the poles of the input rotor 6. Later on, we will have to say a lot about the average time of such occurrences and their differences. However, for the time being, we must again discuss what can be obtained by examining equation (6b).

[0096]

[Math. 8]

If you think about it carefully, you will find that ψ is a constant determined by the rotor (assuming that the rotation time R is constant) because there is no constraint that the poles are equally spaced. . The value of ψ is estimated to be large and one end is −QR.
, and others are in the range between +QR, but the specific values cannot be foreseen. In general, the signal pair AX. If we measure the phase of AY, BX and BY, each will have its own separate value of ψ. Nevertheless, ψ is useful, and we will probably mention it again. Note that in the example shown in FIG. 4, both P# and Q# are zero.

Referring now to FIG. 5, what is changed compared to FIG. 4 is that the input stator 3 is rotated by a small positive angle θ. As described with respect to FIG. 4, addition starts from TP[1]. Assuming that the angle θ is small enough, TQ[1] is the first transition detected after TO for input stator 3. That is, the first transition is not TQ[Q] nor any of the transitions that occur prior to TQ[Q]. Let us assume that the same difference as in equation (6b) is made between the measured sums. That is,

0099

[Math. 9]

Note that the term 2πψ/QR is another constant for ψ. Therefore, write as follows. (13) Ψ=2πψ/QR If we rewrite equation (12) using this notation, we get

0101
]

[Math. 10]

Note that for the example of FIG. 5, P# and Q# are each still equal to zero.

Next, consider the situation shown in FIG. Here P# is equal to 1 and Q# remains 0. The question here is, "What is the formula for θ under this article?"

To bring the rotor into this state, the poles P2, QQ and QQ-1 must be rearranged and θ must be increased so that they can be clearly subdivided. These changes do not affect the validity or rigor of the proof in any way. This is because something has to change in order to change P# from 0 to 1. Such free deformation does not cause problems in the case of practical transducers. This is because the poles are fixed and do not move around. And finally (and with respect to all of FIGS. 4-9C), rather than actually rotating the rotor across in front of the sensor, the sensor is shown out-of-phase around the stationary rotor by a corresponding amount. There is. Not only is this generally easier to draw, it also facilitates "back-and-forth" overlays and generally makes the diagram simpler and easier to follow.

Returning now to the subject, consider the same differences in sums measured for the particular case shown in FIG.

[0106]

[Math. 11]

Substituting Δφ=Δθ−l shown in FIG. 6, we get

[0108]

[Math. 12]

However, l+m+n+...+z is 1
Since it is equal to the rotation time R of

[0110]

[Math. 13]

The following equation is obtained from the left side of equation (15) and equation (20).

[0112]

[Math. 14]

Comparing equation (22) and equation (14), it can be seen that they are not the same. Equation (22) includes 1/P in parentheses, which is not present in equation (14). The difference between these two sets of situations is that in (14) P# is equal to 0 and the equation (
22) is equal to 1. Consider adding below 2
The relationship between P#, Q# and the difference is strongly implied for the equations obtained from the two specific cases. This relationship is confirmed from the last generalized example, and formula (1) is obtained.

Next, consider the situation shown in FIG. In order to create a state where Q# is equal to 1 while P# remains 0, θ is set to a very large positive value (or slightly negative). We start deriving the formula from the same difference as in the previous explanation.

[0115]

[Math. 15]

However, in FIG.

[0117]

[Math. 16]

Since the following holds true, R-Δθ+Δφ=a, that is, Δφ=Δθ+a−R is obtained. This is expressed by the formula (23
), the following formula is obtained.

[0119]

[Math. 17]

However, as shown above in equation (19), a
If we transform the above equation using the fact that +b+c+...+k is the time R for the rotor to rotate exactly once, we get

[0121]

[Math. 18]

[0122] If we solve the left side of equation (23) and equation (28) for Δθ, we get

[0123]

[Math. 19]

[0124] The term on the right in the parentheses of equation (30) is +1-1
/ Becomes Q. +1 has the effect of increasing the answer by 2π radians, or exactly one revolution, when multiplied by 2π outside the parentheses. Since θ and θ+2π are equivalent answers, -(1-Q)
/Q may be simply replaced with -1/Q. Therefore, the following formula is obtained.

[0125]

[Math. 20]

As before, equation (31) is not the same as equation (14) or equation (22).

Now consider the case where both P# and Q# are not 0. Let's consider what happens when each of these is equal to 1. Such a situation is illustrated in FIG. Proceed as before. In equation (33), Δφ shown in FIG. 8 is substituted.

[0128]

[Math. 21]

Now compare equations (14), (22), (31), and (36). (+0
-0)/R, the following items and the values of P# and Q# associated with each can be listed. From (14) +0-0 P#=
0 Q#=0(22) to +1/P-0
From P#=1 Q#=0(31) +0-1/
From Q P#=0 Q#=1 (36)
+1/P-1/Q P#=1 Q#=1

0130
Inspection of these results suggests that P#/P-Q#/Q can generally be used in place of each term on the right in parentheses. A more rigorous proof will show that this is exactly the case.

Let the values of P# and Q# be any non-zero values smaller than P and Q, respectively. This situation is illustrated in FIG. 9A for a small positive input angle φ. Since the sensor on the input stator is shown advanced in the direction of rotation of the rotor from the sensor on the reference stator by an angle φ, only the angle φ is positive. Positive (1) is equivalent single pole (single eq
This can be understood in light of the concept of the average time of occurrence of the uivalent pole. When the input stator is moved in the direction of rotation of the rotor, there is a time delay in the equivalent single pole of the input rotor, and when the time of the equivalent single pole of the reference rotor is subtracted,
During the rotation time R of the rotor, the time difference increases positively and proportionally to the input angle. For convenience, it is also assumed that TP1 and TQ1 match when φ=0. That is, P1
and Q1 are arranged vertically on the rotor. This will make the explanation easier to follow, but at the end of the proof it will be seen that equation (1) does not require such an assumption.

Although it is necessary to describe various items so that operations can be performed based on their subscripts, the symbols used in FIGS. 9A through 9C are somewhat different from those used in FIGS. 4 through 8. Input rotor 6 with Q poles
The time intervals a, b, c, . . . k are here named y1 to yQ. Similarly, time intervals l, m, n for a reference rotor with P poles
,...z has the names x1 to xp.

Let the value of P# be J and the value of Q# be K. J
and K are used as the corresponding values in one index for xi and yi, respectively. Furthermore, J and K are also used as double subscripts regarding Δφ. The term ΔφJ,K indicates the Δφ obtained for given values of J and K. Generalized forms of individual sums for a certain input φ are shown in equations (37) and (38). The same difference as before is made in equation (39).

[0134]

[Math. 22]

(The caveats mentioned before equation (6b) regarding its origin also apply to equation (39). Equation (6b) and equation (
39) are the same except for the difference in symbols. )

01
36] Now, ΔφJ,K that can be applied to equation (39)
Consider the replacement of . For reasons that will become clear shortly, Δ
We are interested in replacing φJ,K with the term Δφ0,0.

By examining FIG. 9A and with the help of the slight superposition shown in FIG. 6, the following permutation can be obtained. (40) ΔφJ−1, K=ΔφJ, K+xJ

01
[38] The physical interpretation of such a substitution is that for the summation of TQi, the same set of poles Q on the input rotor 6 are used, but a local reference (local reference) from the reference rotor 5 is used for the start of the summation. reference) is shifted forward in time by one pole on that rotor due to this displacement. This may correspond to repositioning of the sensor on the reference stator, but is not something that can be expected in a real transducer. A more useful interpretation is to leave the physical relationship between the rotor and the sensor unchanged, but adjust the way the data in the time and state transition tables are summed. In other words, ΣTP[i] and ΣTQ[i] overlap only slightly in time.

In any case, the particular permutation of formula (40) cannot be said to be sufficient unless K is already 0 and J is 1. Equations (41a) to (41b) show what happens to this replacement when a pole is present on the reference load 5 and skipped. (41a) ΔφJ-2, K=ΔφJ-1, K+xJ
−1 Substituting equation (40) into this right-hand side, (41b) ΔφJ−2, K=ΔφJ, K+xJ+x
J-1

Thus, the general permutation when J, is reduced to 0 is clearly as follows. (42a) ΔφO, K=ΔφJ−1, K=ΔφJ,
K+xJ+xJ-1+...+x1, (42b) ΔφJ, K=ΔφO, K-xJ-xJ-
1-...-x1

Next, consider what permutation can be used to reduce K to 0. Referring to FIG. 9B, the value given for J determines the time in the revolution at which addition of TQ[i] should begin, but which pole Qi is the "first" following the occurrence of TP[J]. Whether it should be recognized as a pole depends on the value of K. Usually "first" means "next in time" and J forces a value of K that depends on the surrounding conditions. To proceed with the replacement,
We retain that rule and reverse the process by fixing the value of K to 0 and giving different Δφ for the same J.

Similar to equation (42b), ΔφJ,K and Δφ
Look for the relationship with J and O. The next TQ[ after a certain TP[J]
I mentioned the rule to start ΣTQ[i] at
Under this the quantity ΔφJ,O seems to become somewhat abstract. This rule allows J to effectively determine K for any input angle, and although K may sometimes be 0 for a given J, it is not usually the case. No. The direct question here is "What does it mean to let K be 0 for any J?" This question is easy to answer, and understanding that the rules stated for addition are overly restrictive removes much of the abstractness of ΔφJ,0, at least for purposes of proceeding with the required permutations. (This does not mean that this rule is too strict in practice. The effect of this rule is that ΣTQi
and ΣTPi are generated from the same rotation of the rotor as much as possible. This is desirable because it minimizes the adverse effects caused by motor speed changes. )

As a first step toward ΔφJ,0, we will begin by examining the concept of ΔφJ,0 as an example of a more free addition rule and also because it is actually useful. This is probably easy to understand and useful in understanding ΔφJ,0. If ΔφJ,K is the ordinary time interval between JP[J+1] and JQ[K+1] (recall that J,K is the number of skipped poles), then TQ[ K] precedes TP[J+1] but TQ[K+1] does not precede TP[J+1], then ΔφJ,0 is (43) ΔφJ,O=ΔφJ,K+yK+1+...
...+yQ.

This physical interpretation is simple, and TQ[K
+1] to TQ[Q], do not look at it as "next",
Instead, it waits patiently for TQ[1]. K
Apart from raising ΣTP[i] to the value of Q, the only effect of this is to increase the interval between the start times of both ΣTP[i] and ΣTQ[i]. However, the quantity ΔφJ,Q is still TP[J+
1], and TQ[Q] still occurs after TP[J+1]. This is different from the case of ΔφJ,0. By skipping this pole, we aim to raise Q# to the value Q. This normally would never happen by itself since there are only Q poles. In other words, Q# normally takes a value up to Q-1 at most. Nevertheless, if Q# becomes Q (this is ΔφJ
, Q), we can consider what happens, and we can consider the relationship between such a search for ΔφJ,Q and ΔφJ,0.

Difficulties are likely to arise in illustrating ΔφJ,0. This is because under the old rules, ΔφJ,0
This is because it seems to require that we consider the measurement ``finished before it begins.'' However, the ΔφJ,K-type quantities under consideration here merely represent a time interval with a beginning and an end. Under the old rules,
The subscript J defines the beginning, such that the subscript J, which is always later in time, always defines the end of the interval. ΔφJ
, 0 is still a time interval with a beginning and an end, only now the subscript on the K side (i.e., the second subscript) defines the beginning, and the subscript on the J side defines the end. As far as the absolute value of the time interval is concerned, even if the earlier of the two is "started" and the later is "stopped", no difference will occur. The rotor is still rotating in the same direction, and positive increments in time intervals will still be measured (however, for future sign changes,
The zero point of reference must be kept in mind). Similarly, there is no harm in skipping some poles during the measurement process.

The following hypothetical situation is helpful in understanding ΔφJ,0. As noted in connection with FIGS. 3A-3C, it is assumed that there is some means for preserving the recent history of the relationship between the input rotor 6 and input stator 3 sensors. TP[
J+1], check the history to find when pole Q1 passed the input stator sensor and use this as the start time of the time interval. The time at which TP[J+1] occurs ends the time interval, but is also the assumed zero point for the addition, as well as the virtual zero point for the Δφ type time interval that carries the actual angular information. Therefore, if ΔφJ,K is considered positive, ΔφJ,0 is a negative value. These are on opposite sides of TP[J+1] from each other. The value of the interval ΔφJ,0 is found by simple subtraction. Although we do not actually do this, if we add ΔφJ,K to the negative value of ΔφJ,0 and combine it, we can obtain something else that can be easily measured without relying on recent history. be equal. That is, (44a) −ΔφJ,
0+ΔφJ, K=y1+y2+...+yK

There are other aids in understanding ΔφJ,0. Rotating systems such as the one under consideration are essentially modulo
o). In a sense, there is little meaningful difference between the value of Q and K with a value of 0. It can be explained as follows: When the Qth pole reaches the sensor, we have to decide whether to count it as Q or as 0. If you choose Q, TQ[Q]
becomes the "stop" signal for the interval, and the previous TP[J] becomes the "start" signal. If you choose 0, it becomes a "start" signal for the next TP[J+1] (i.e., TP[
J+1] becomes the "start". However, in either case, we are considering the same two points A and B on the circumference. In one case, you are measuring from A to B, and in the other case, you are measuring from B to A, or, equivalently, from A to B but in the opposite direction. . Since the sum of these two measurements in the same direction is exactly one revolution, (44b) −(ΔφJ,0)+ΔφJ,Q=R

0
Note that, taking equations (43) and (44b) as starting points, equation (44a) can be obtained by subtracting equation (44b) from equation (43).

By performing a term shift on equation (44a), a desired result in which ΔφJ,K is expressed by ΔφJ,0 can be obtained. That is, (45) ΔφJ, K=yK+yK-1+...y
1+ΔφJ,0

Physically interpreting -ΔφJ,0 resulting from equation (44a), in order to create the sum from y1 to yK, the value -Δφ is added to the actually measured time interval ΔφJ,K.
This means that J,0 must be added. TQ
The new sum for [i] is
Although it is not possible to make a direct measurement in the same sense as measured by slipping J backwards by −1, etc. until J becomes 0, one can certainly consider ΔφJ,0. So Δφ0,K and ΔφJ,0
(although neither is actually measured).

At this point, it is possible to substitute equation (42b) into equation (39) and transform the result of this substitution in the same manner as for equations (16) to (22) with respect to FIG. . From this, an equation regarding ΔφJ,K and Δφ0,K is created, and equation (45) can be substituted into this. Continuing to transform the equation further, ΔφJ, K and Δφ
Equations regarding 0, 0 are created. This is in fact its immediate purpose. The order of assignments can be reversed in a similar way. That is, first, K is set to 0, and then J is set to 0. This can be proven by simply following the steps shown above. Furthermore, the two assignments may be combined in the interest of brevity and perhaps a more elegant proof. This will cut the amount of counting in almost half. This is the method we are going to proceed with from now on.

Now, referring to FIG. 9C, Δφ0
, 0 are simply the time intervals that occur prior to TP[
1] and the subsequent TQ[1]. Once the orientation of each rotor on the coupling axis is given, Δφ0,
Note that 0 is strictly a function of the input angle. Further, Δφ0,0 is exactly what is expected from the input angle when both P# and Q# are 0. Based on the observation, it can be written as follows. (46a) Δφ0,0−ΔφJ,O+ΔφJ,K=
Δφ0,K

[0153] Next, the equation (46a) is replaced by the equation (46
Substitute b) and (46c). (46b) Δφ0, K=ΔφJ, K+xJ+xJ−
1+...+x1 (from formula (42a)) (46b) -ΔφJ,O=y1+y2+...+
yK−ΔφJ,K (from equation (44a))

[0154] If we solve for ΔφJ,K and simplify it, the result is (47) ΔφJ,K=y1+y2+...+yK-
x1-x2-...-xJ+Δφ0,0

Equation (47) can also be obtained by looking at a diagram (not shown) similar to FIG. 9C, which represents the following situation. That is, the angular displacement between the reference sensor and the input sensor is determined by rotating the reference sensor and the input sensor as one unit around the rotational axis of the rotor until the reference sensor is exactly opposite the pole P1 at which the addition started. remains constant regardless of the situation. The angle by which the pole Q1 rotates after TP[1] occurs until TQ[1] occurs is φ0,0.

Equation (47) is a "killer" permutation that combines everything into one. This equation relates ΔφJ,K to Δφ0,0 for any value of P#, Q#. Let us now substitute equation (47) for ΔφJ,K in equation (39).

[0157]

[Math. 23]

Let us "subtract R" from the y and x terms as we did for the equations related to FIGS. 6-8. R is equal to the sum of all time intervals from x1 to xP (including x1 and xP), and from y1 to yQ (y
Recall that it is also equal to the sum of all time intervals (including 1 and yQ). Consider the y term in equation (48b). Note that all yi exist and the minimum count is K. Obviously, by subtracting the K R's from the y term, we are left with a sum of the familiar form. Similarly,
The x term contains all x1 with J as the minimum count. Thus, by subtracting J R's from these terms, we are left with another familiar form of summation. Tables 1 and 2 below show the subtraction of KR and JR, respectively, in tabular form.

[0159]

[Table 1]

[Table 2]

[0160] Therefore, clearly

[0161]

[Math. 24]

Recalling that J=P# and K=Q#, and solving for φ0,0, we get

[0163]

[Math. 25]

The term in the parentheses on the left side of the right side of equation (48e) is exactly the same as equation (1) if only the difference in the type of symbol is ignored.
is the term in parentheses. The product of 2π and the term in parentheses on the right side of equation (48e) defines the constant Ψ in equation (1).

It will be shown here that the product on the right side of the right side of equation (48e) above actually becomes the value of Ψ in equation (1). Substituting equation (7) into equation (13), we get

[0166]

[Math. 26]

Therefore, the symbol of formula (49a) is replaced by formula (49b
) or the symbol of formula (49c) may be substituted. By doing this and rearranging, we get the following formula.

[0168]

[Math. 27]

Equation (49d) shows that the right part of the right side of Equation (48e) is actually correct and equivalent to Equation (1).

As shown above, we derived equation (1) and clarified the properties of the angle θ obtained from equation (1) in the process. Furthermore, Ψ was defined precisely. We have shown that the angle θ is φ0,0, which simply means that the related P
This is the angle obtained if # and Q# never start adding unless they are 0. Of course, in that case P# and Q
Stricter rules would be needed compared to the fact that #(J and K) can be given arbitrary values. Formula (1)
The advantage of equation (48e) is that such strict rules are not required. The definition of Ψ is essentially the residual offset obtained when φ0,0 equal to 0 is the input angle. The sum required to find Ψ is Σ when P#=0
TP[i] and ΣTP[i] exactly when Q#=0 (ie, no Δθ remains). Δθ with 0 degree input
is equal to 0. In other words, TP[1] is equal to T
This means that it matches Q[1]. However, in both equation (1) and equation (48e), when inputting "0 degree", TP[1
] does not require that TQ[1] match TQ[1]. This is because Ψ is the input value that the user wants to be ``0 degrees'' and provides an exact reference no matter what arbitrary state is obtained between TP[1] and TQ[1]. This is because it is possible. This includes not only arbitrarily defining the "0" position of the input stator, but also arbitrarily setting the mutual positional relationship between the rotors connected on the shaft. Recall that such correspondence between TP[1] and TQ[1] was one of the simplifying assumptions made at the beginning of the proof. It can now be shown that this special assumption is unnecessary. To see why this is so,
Observe that there is one mechanical input value where TP[1] and TQ[1] match, regardless of the "0" position of the stator or the orientation of P1 with respect to Q1. If it is convenient, such an input condition can be taken as 0 degrees, or if it should not be 0 degrees, it can be taken as some arbitrary value α. Even if the latter is selected, the only effect is that an offset of α is introduced into the measured results. The amount of offset α is TP[1] when the mechanical input changes.
Although it is certainly possible to find out by monitoring the points where and TQ[1] occur at the same time, it is not necessary to know exactly. The difference between the mechanical input angle that causes the simultaneity of TP[1] and TQ[1] and the mechanical input angle that is desired to be zero is α. To avoid finding α directly, the mechanical input is sometimes set to an arbitrary reference value θref, such as "0", "10", etc. Therefore, in order to find the fundamental value of θref by measurement, a modified equation (1) that does not include the term −Ψ is used. However, its value is expressed as follows. (50) θref=α−Ψideal

[0171]
Of course, the actual values of α and Ψideal are unknown, only their difference θref is known (by measurement and modified equation (1)).

Next, consider the result of increasing the mechanical input angle by the amount γ from the original value of θref to θnew. What we want to do here is find γ. However, θnew is a measurable quantity whose value can be obtained. (51) Solving for θnew=α+γ−Ψidealγ, (52) γ=θnew−(α−Ψideal)

0
[173] Applying equation (50) to the right-hand side of the above equation, the following equation is obtained. (53) γ=θnew−θref

That is, γ is an input value measured with θref as a reference, and the value of θref is arbitrary. Note that the actual values of α and Ψideal never need to be known exactly. Also, from the above discussion, equation (1) can be rewritten as equations (1') and (1'') as shown below.

[0175]

[Math. 28]

As explained in relation to equation (48e), θ in equation (1') does not necessarily have to be equal to φ0,0;
It may be different from φ0,0 by a certain constant. Whether the two are equal or not depends on the conditions chosen to represent "0 degrees." When the condition is "0 degrees", TQ[1] and T
If P[1] matches, θ is actually φ0
, equals 0. This arises from the definition of Ψ in equation (49) and from the effect of the "0 degree" condition in equation (1) or (1''). For equation (1), the term in parentheses then has the value of Ψ, and Ψ-Ψ is zero. In the case of formula (1”), “0 degree”
The value obtained as θn' is also Ψ, so equation (1') works exactly the same as equation (1) in which Ψ is known. However, "θ is equal to 0 degrees" means that TP
If [1] does not match TQ[1], θ becomes φ
It is obtained by adding or subtracting a constant offset, which is the value of the difference between both "zero conditions", to 0,0. However, in any case, the change in θ is equal to the change in φ0,0.

[0177] Those skilled in the art will appreciate that there are several possible ways to take advantage of the properties described above. The method is to actually set α and Ψide
find al (for a given fixed configuration only one
From finding only degrees or finding them on demand, such as at power-up, to initially finding only θref at power-up and measuring each angle as a displacement from the new θref to a different θnew. It spans. These are design questions that should be determined by criteria that make the most sense for a given application.

Depending on whether Ψ is found and used, the conditions under which 0 degrees is considered, how the poles are placed on the rotor, etc., Equation (1) or even Equation (1'') may change over time. It is possible to get a negative answer by from,
There's no problem.

Let us now return to equation (1) and consider again the other simplifying assumption made at the beginning of the previous proof. With reference to FIGS. 4 to 8, equation (2)
Recall that in and (3) we assumed that we start from "time equals 0". This means that
Applying it to FIGS. 9A to 9C, TP[1]
is equivalent to assuming that is equal to 0. This time, T
Let's consider what kind of results can be obtained assuming that P[1] is not 0. Let TP[1] be a certain non-zero value β, and consider the effect this has on equation (48e). The conclusion can also be applied to equation (1). This is because these expressions are equivalent.

[0180] All the explanations so far have been based on the time interval (a, b
, c, ... and l, m, n, ... or y1, y2, y3, ... and x1, x2, x3.
) has been used to express it. Equations (2) and (3) mean summing the ending times of these time intervals (Equation (1)
) and summing time intervals (which is more explanatory). β is not an increment for any of the time intervals (i.e. the value of these time intervals remains unchanged), but for each It is important to remember that the common increment of the end time measurements of the time interval. Formula (1
), the sum of Q such terms is taken for TQ[i], and the sum of P terms is taken for TP[i]. Since each of the Q TQ[i] increases by β, the total increases by Qβ. Similarly, T.P.
The sum of [i] increases by Pβ. Various TP[i
] does not matter in what order, nor does it matter in what order the various TQ[i] are added. That is, for a certain sum Δφ, the equation (4
Whether in the left parenthesis on the right side of 8e) or in the right parenthesis as Ψ, ΣTQ[i] each increases by Qβ and ΣTP[i] each increases by Pβ. Within each pair of parentheses,

[0181]

[Math. 29]

Therefore, it is clear that β≠0 is a self-cancellation condition.

Finally, we would like to emphasize the meaning of equation (1) in view of equations (2) and (3) and in the light of the earlier caution regarding simplifying assumptions. When Equation (1) was introduced, and as it is repeated here, we pointed out that Equation (1) requires the sum of P consecutive transition times and Q transition times. Since we have focused several paragraphs on time interval-based explanations, the unwary reader may find that in order to arrive at the answer, a series of multiple subtractions must be performed for each time interval. You may be under the mistaken impression that you actually need to find out. However, this is not the case. It is convenient to use time intervals in explanations and proofs. This is because the time intervals correspond to the placement of the poles on the rotor. However, as pointed out earlier, the expression (
2) and (3) relate the time interval to the sum required by equation (1). These sums are simply Q consecutive TQ[
i] and then simply adding consecutive P TP[i]. No subtraction is necessary to make these sums. The first of the added TP[i]
th need not be 0, and TP[i] and TQ[i
] do not have to match. When measurements are taken, only a small number of subtractions and other operations such as multiplications need to be performed on the sums thus built up.

Here, formula (1) and formula (48e)
It seems useful to consider the "meaning" of Although there is no doubt that we have derived these exactly above, and in fact it is clear that these formulas can be measured well, it may feel like something has been cheated about ``why it really works''. do not have. There is a basic principle underlying why it really works. I think it would be helpful to extract the principle and explain it briefly. Knowing this, let us now provide an interpretation of an equation for finding the angle θ.

Consider the rotating four-pole rotor shown in FIG. During exactly one rotation of the rotor in time R, the sensor generates a signal at each time from T1 to T4. As in the first example, let the time intervals between the poles be a, d, c, and d. The only restriction on a through d is that they sum to R. In particular, we do not assume that they are equal. Therefore, the following formulas or conditions (a) to (e) hold true. (b) T1=T1 (T1 is zero or a certain preceding time T
0=0 as the starting point) (B) T2=T1+a (C) T3=T1+a+b (D) T4=T1+a+b+c (E) R=a+b+c+d

Here, equation (f) shown below indicates the result of averaging four consecutive transition times in order to find the "average time of a pole", that is, the occurrence time of an "equivalent unipolar".

[0187]

[Math. 30]

It is important to understand that this averaging or equivalent time is with respect to starting addition at pole number 1. If we now averaged four consecutive times starting at "pole number 2" (delay of "a" in starting the average), what change would there be in the average time or the new equivalent unipole? ” Let's think about that. Having read the above discussion, it is quite reasonable to expect that the onset time of the new equivalent monopole will be delayed by a time interval "a". However, this is precisely the average time interval between the poles. Indicate the new values in the following expressions (G) to (N).

[0189]

[Math. 31]

As shown in equation (l), the difference between these two values (that is, equation (f) and equation (l) is exactly 1 rotation time)
/4, that is, R/4. It will be seen that if two poles were skipped, the difference would be 2/4 of a revolution. Furthermore, if there were five poles instead of four, the corresponding differences in this case would be 1/5 and 2/5 of a revolution, respectively. What we get here is P#/P and Q
It is clear that this is a summary of the law for what we call #/Q. The important point of this law is that Q arbitrary time intervals a, b, c,...k between Q poles are individually known except that their sum is R. Even if it is not, the average time increases by exactly R/Q for each pole that is skipped before starting the addition that determines the average time of pole occurrence. This is an interesting and perhaps unexpected result, since it allows us to reduce an arbitrary and unknown magnitude (the amount skipped) to one whose magnitude is clearly marked and known in advance (the magnitude of the correction).
relate to.

[0191] The principle of this correction is that consecutive occurrence times are
It applies equally to averaging over time over rotations. Now let me explain about this possibility. Let us take an average over n revolutions and consider that the number of skipped poles is less than the number of poles on the rotor. In this case, equation (g) and equation (nu) can be expressed as follows.

[0192]

[Math. 32]

That is, the rotation speed does not affect the magnitude of the correction regarding the number of skipped poles. Although this is a specific example regarding a four-pole rotor, it is clear that the generalized principle holds true for any number of poles on the rotor. The above requirement of skipping fewer poles than the number of poles on the rotor is consistent with the rules given for determining P# and Q# in connection with the preferred embodiment. This is because if multiple revolution measurements have to be made, P# forces Q#, and these two values are obtained during the first revolution. Therefore, the difference is less than one rotation at most.

Originally, other matters in equation (1) change for the measurement of n rotations. The sum ΣTQ[i] will be divided by nQ and the sum ΣTP[i] will be divided by nP, but the difference between the two quotients will still be divided by R. Also, the correction term (P#/P)-(Q#/Q) remains the same.

Other possibilities for multiple rotations are worth briefly considering. Consider that the rotor must rotate n times for each sum of ordinary P and Q poles. Furthermore, let us assume that this sum is not guaranteed to start within the same revolution (we do not consider variations in motor speed). Here, n rotations of one rotor may have almost no common part (time overlap) with n rotations of the other rotor. In other words, in this case, the total time period can be approximately 2n times. ) If we persist, the way to do this would be to treat each rotor as a "superrotor" with nP and nQ poles, respectively, for one "superrotation". Under this treatment, P#, Q# can be greater than P and Q, except by using nP instead of P, nQ instead of Q, and nR instead of R. If so, measurements are easily made using any of the equations already mentioned. A slight extra effort is to recognize every nth mark of the actual one-turn mark as a "super-one-turn mark."

[0196] By any of the above multiple rotation methods, 2
It has some utility when you want to average more than one overall measurement. Instead of making n measurements of one revolution each, one measurement of n revolutions can be made once. This would require more memory, but would probably be faster to measure and would have much less difficulty in combining answers that are very close to 0° or 360°.

For simplicity of explanation, a more formal explanation of the principles of FIG. 10 will not be presented here. However, this proof is not very difficult;
It should be noted that B and the text related to them can be interpreted as the basis of the proof. No doubt many variations of this principle have been demonstrated. The goal of this explanation is the phase angle formula, that is, Equation (1)
Recalling that the purpose of illustrating Figure 10 and its associated principles is simply to make some useful principles that can be clearly seen, That's true. Having said this, I will now proceed to its interpretation.

Perhaps the easiest point to start interpreting is equation (48d). In this equation, the time Δφ0,0 corresponds to four other times and two correction terms (JR/P and K
R/Q, that is, P#/P and Q#/Q). The reason it is preferable to start from this formula is firstly because most of the units are time, which is the original unit of measurement, and furthermore, all the terms reduce the arithmetic effort but do not imply structural relationships between the quantities. to obscure or absorb
This is also because it is presented strictly without any "restructuring for the sake of brevity." Equation (48d) is expressed as Equation (5) shown below.
5) can be rewritten as follows.

[0199]

[Math. 33]

In equation (55), the term (A) is the second average time of the Q pole reflecting the input angle, and the average starts after J and K poles are skipped. It is. Term (B) corrects the change brought about in the average time by skipping K poles. The term (C) is the second averaging time of the P poles, the angle is zero, and the averaging starts after J poles are skipped. Term (D) corrects the change brought about in the average time by skipping J poles. Term (E) is the first averaging time of the Q pole when the angle is zero, and this averaging begins when the beginning of the P pole is detected. The (F) term is the first averaging time of P poles when the angle is zero, and this averaging starts when P heads are detected.

The item (■) is the result of correcting the second average time of the equivalent single pole of the P pole, which reflects the input angle, to that from the beginning of the Q pole. Note that skipping J poles does not inherently affect the above amount other than skipping K poles. And here, the purpose of the correction made is to eliminate this effect. ■
The term is the result of correcting the second average time of the equivalent monopole of the P pole when the angle is zero to that from the beginning of the P pole. The term (2) is a fixed reference value that is the difference between the equivalent monopole of the P pole and the equivalent monopole of the Q pole, and represents the condition of a true angle of zero. However, as stated elsewhere, if this term is canceled by taking the difference, there is no need to determine the actual value of this term. Normally, the value of this term cannot be determined.

Term (a) is the modified difference between the average time of the P pole and the new average time of the Q pole reflecting the input angle. This difference is compared to an initial reference difference representing the other boundary of the input angle. That is, the current position of the transducer minus the input angle. The initial reference difference may be a fixed reference value or may simply be the result of a previous measurement (such as this difference measurement).

That is, the measurements of terms (A) to (D) are carried out during the same rotation period, but the measurement of Ψ, that is, term 2, is often carried out during a different rotation period. Also,
Item (2) represents Ψ, but if this measurement were actually performed, the measurements of items (E) and (F) in this item would be performed during the same rotation period.

The conclusion that can be drawn from the above explanation is the 2 on the left.
The difference between the two brackets is the difference measured in terms of the new angle. The amount that must be subtracted from this difference value is the difference value that was initially measured for the reference state that is the reference point when measuring the angle. The reference state may be Ψ, or it may be a difference value measured at some selected state that corresponds to a redefinable zero angle state. In addition to the explanation given in the introduction for Ψ and equation (1), Ψideal, α, and equation (
50) to equation (53), and especially equations (1') and (
1”).

The above measured difference is the average time of occurrence of the Q pole relative to the average time of the P pole. The two averages are taken over essentially the same revolution. Both average times are taken for the starting poles on their respective rotors. From this point of view, the reference rotor and its sensors provide a stable reference point for measuring time intervals due to the average time during rotation of the input rotor. Note that the value given to J essentially determines the value of K, depending on the shape of the respective rotor and the position of the input rotor. Once ΔφJ, K and Δφ
Once M and N are adjusted to the value of Q#=0, Δφ
In a certain sense, J, K and ΔφM, N are proportional. That is, the times ΔφJ,O and ΔφM,N differ by the time interval between the two P poles J and M. (If R varies from measurement to measurement, it is correct to question which rotation. This will be explained below using equation (56)). In other words, the reference rotor provides different reference points for the two measurements. The exact amount of this difference is found by zeroing out J and M. In this process, J and M (and K and N for that matter) are free to represent different parts of rotation, which may have different speeds.

If we ignore the terms in parentheses on the right side of equation (55) (these correspond to Ψ), then equation (1') and equation (
1'') deals with the case where Ψ is canceled by subtraction, it is not difficult to interpret equation (1'') in light of equation (55). The only difference is that by dividing the equation by R and then making some transformations, we get Δ
It is a conversion from finding θ to finding θ. Dividing by R is particularly desirable. This is because it normalizes the rotation speed, which can vary in various ways.
This is because P#/P and Q#/Q, which represent a certain percentage of one rotation, are obtained, unlike a specific time. Also, this allows 2π as in equation (1)
When multiplied by , the result is an angle in radians and is no longer a fraction of a revolution. Equation (1'') may be said to give the ratio per revolution between two equivalent monopoles, each related to an arbitrary starting pole. The sum of TP[i] as a subtraction is too large and has not yet been adjusted back to the initial starting point, so P
#/P is added back. Also, Q#/Q is subtracted because the reduced sum of TQ[i] started out too large by that amount and has not yet been adjusted back to the original starting point.

Further insight into how the reference rotor and its summation acts as a "0 reference" is provided by equation (56).
This can be obtained by considering the following.

[0208]

[Math. 34]

In equation (56), the term (G) is the second average time of the Q pole reflecting the input angle, and is the second average time of the Q pole reflecting the input angle.
It is a value that starts to be averaged after skipping two poles and is based on a certain second T0. Term (H) corrects the change brought about in the average time by skipping K poles. The term (J) is the first average time of the Q pole, and is the case where the angle is zero. This average is a value starting from the beginning of the Q pole and based on a certain first T0. The (K) term is the second average time of the P pole when the angle is zero. This average is a value that is started after skipping J poles and is based on a certain second T0. The (L) term corrects for the change introduced in the averaging by skipping J poles. The (M) term is the first average time of the P pole when the angle is zero, starting from the beginning of the P pole, and at a certain first T0
The value is based on

[0210] Item (■) is the value obtained by correcting the second average time of the Q pole that reflects the input angle to a value based on the beginning of the P pole. This cancels out the effect of skipping J P poles on this difference (here, the effect of skipping J is only to cause K skips). This average time is based on the second T0. The term (2) is the second average time of the P pole for angle zero. This value is corrected based on the beginning of the P pole, but is based on the second T0. Note that the (M) term and the (■) term generally have different values. This is due to the timer reset to give a different T0 for each summation, and also due to variations in motor speed.

The term (b) shows the change in the average time of the Q pole depending on the input angle, but also includes the offset between the two T0. The term (c) is an offset between the first and second T0. There is no change based on input angle. This is because the reference stator does not move.

[0212] Thus, equation (56) strictly represents the change in average time at the Q pole due only to the input angle. Although many of the notes are the same, the grouping of terms in equation (48d) is different. That is, all terms related to TP[i] are grouped together to create a difference. According to the aforementioned principle, the formula (56
) is 0 if each sum is based on the same T0. That is, the sum of "new but adjusted" TP[i] is equal to the sum of "old" TPi. Clearly, in this equation, only TQ[i] produces "angular information", which is what we would expect given that the reference sensor does not move.

[0213] Then why do we conduct a detailed study on TP[i]? The answer, at least in part, is that even in an ideal converter the value of the term in the right parenthesis will generally not be zero for at least two reasons. The first reason is that the two sums are the same T
Even if taken with respect to 0=0, they still take place at different times, thus giving rise to non-zero differences in the average times of occurrence (of course, the same applies to what is in the left bracket). However, the difference between the terms in the parentheses on the right may ``happen'' to be zero, because any clock is forever counting monotonically increasing time from an arbitrarily given time T0 = 0. This is because it is not possible. Since the clock must be reset at some point (e.g. by counting to the highest value that the clock's registers can hold), the two sums in the right parenthesis are obtained relative to the same T0=0 of the clock. It will probably disappear if you use it. As the conditions change in this way, there are cases where the sums that should not be the same become equal. (The same goes for the sum in parentheses on the left). However, this situation is not a problem. That is because the two sets of parentheses each contain the same difference between any separate T0, and so that (5
6) As you can see from the formula, the "same difference" is the difference between the two. Creating this difference between the two is the main reason for finding two ΣTP[i]. This allows the offset of the difference between the two ΣTQ[i] to be found and removed. The second reason is to perform error cancellation similar to the first reason, but we are considering another error cause. The different totals result from slightly different motor speeds and clock rates. Because these sums are different, there will be a measurable offset in the left bracket that must be removed, but this offset will also commonly occur in the right bracket.

It can be seen that none of these events (measuring at different times, resetting the clock, changing motor speed or clock rate) need be of concern. This can be easily understood by considering equation (56). In other words, due to the differential nature of this calculation, offsets caused by steady-state deviations due to these effects are canceled. Of course, care may be taken not to reset the clock in the middle of rotation during the time when phase measurement is being performed.

Two interpretations of equation (1) are shown below. The construction and measurement rules of FIGS. 3A-3C, the principles described above, and the concept of an equivalent monopole are assumed herein.

[0216]

[Math. 35]

In equation (1) expressed in the above form, the term (M) is the average time at which one Q pole appears due to the input angle and skipping Q# poles (Q# poles are skipped). Pole skipping itself results from skipping P# poles at the current input angle). This time is the time when the equivalent single pole of the Q pole appears. The (N) term is the average time when one P pole appears due to skipping P# P poles. This time is the time when the equivalent monopole of the P pole appears. The term (O) is the time required for one rotation. The term (P) is a value based on TP[1], and is the ratio of the reduction in the equivalent pole spacing due to skipping P# P poles to one rotation. This is because this skip increased the total average of TP[i] but did not result in a corresponding change in the total of TQ[i]. The term (Q) is a value based on TP[1], and is the ratio of the increase in the equivalent pole spacing due to skipping Q# poles to one rotation. This is because this skip increased the total average of TQ[1] but did not result in a corresponding change in the total of TP[1]. The (R) term is the residual spacing at the original reference angle between equivalent poles. This value may or may not be actually determined. It is usually not determined and is canceled out as a common mode component of two different measurements of θ.

[0218] The ■ term existed before the input angle was given (
i.e. TP[1]≠TQ[1]), due to the input angle itself (which delays the appearance of the equivalent monopole of the Q pole), and due to the skipping of poles (i.e.,
(starting the sum without waiting for TP[1] and TQ[1]).

The term (d) is the time interval expressed as a percentage of the rotation of the rotor.

[0220]

[Math. 36]

In equation (1) expressed in the above form, (
S) term is obtained by reflecting the initial time interval, input angle and skipping Q# Q poles, and further correcting for skipping P# P poles, 1 It is the ratio to rotation.

[0222] The term ■ is the ratio to one revolution based only on the initial time interval and input angle. In other words, the correction was made to obtain the values that would have been measured if the respective sums had been started at TP[1] and TQ[1] when the first pole appeared.

The term (e) is the ratio of only the input angle to one revolution, based on starting the respective sums at TP[1] and TQ[1]. Here, Ψ can be calculated and subtracted as in equation (1), or as shown in equation (1'
) or equation (1''), it may be canceled by subtracting the measured values for two different values of the input angle.

[0224] In equation (1) as a whole, TP[1] and TQ
[1] The rotation of the rotor between two equivalent monopoles reflecting the input angle is expressed in radians based on the first difference between [1].

Now, equation (1), equation (1'), and equation (1
”) turns out to be indeed true. It also turns out that there is no need for the number of poles on each rotor to be equal to each other, nor is there any need for the poles to be uniformly spaced on the rotor. The above proof clearly shows that the poles can be placed arbitrarily.In practice, it is likely that the poles on the rotor will be located fairly uniformly, and this will optimize the response of the sensor and avoid excessive This is desirable to help suppress conditions and crosstalk if present. Such uniformity helps indicate absolute position on the rotor and also It also allows reliable detection of missing poles, which serves as a basis for keeping track of the This can also be achieved by providing an indicator associated with the pole and a separate once-per-rotation sensor for detecting this. In principle, positioning on the rotor can be achieved by such means (with no cross-talk). In short, deliberately placing the poles haphazardly is not recommended unless there is a good reason to do so, but the phase measurement technique of the present invention improves accuracy. It is possible to make phase measurements where the polarity is not limited by the accuracy of the pole placement; depending on other factors, one may still have to have an essentially regular pole placement anyway.

Equations (1), (1') and (1'') are neither ``coarse'' nor ``fine'', provided only that they deal with device-dependent constants Ψ, but are probably It gives an absolute answer that is an integrated high-resolution solution with as high precision as accuracy and stability. To accomplish this, a time base and zero-crossing detector would be used. Due to the differential nature of the measurements, the timebase only needs to have good short-term stability. The component due to lack of long-term stability in differences between measurements taken at different times is offset by "common mode" effects. Although there are mechanical factors that can affect the accuracy of the angle converter as a whole,
Some of these will be explained in separate chapters below. However, these factors are generally expressed by formula (1) or formula (
1”) principle does not adversely affect accuracy.

The integrated answer given by equations (1) and (1'') is
"Averaging", ie the contribution given by this large number of poles, results in a high resolution answer. In this sense, it appears as if there are two unipolar rotors and the transitions of the signals from each sensor can be determined by locating with great confidence.

To this end, slight variations in pole range and motor speed may actually help increase resolution, as long as these variations are at least of a pseudo-random nature. As is well known, such "perturbations" can increase the accuracy of arithmetic data collected at a fixed number of poles.

The integrated answers in equations (1) and (1'') have easily discernible ``coarse'' and ``fine'' characteristics even when the poles are arranged essentially regularly. Contains no ingredients. The sum term appears to represent the fine part of the answer, while the terms P#/P to Q#/Q appear at first glance to represent the coarse part. An easy way to fall into this trap is to mistakenly conclude that since regularity appears to give modulo properties to the difference in quotients with respect to the sum, with regularly arranged poles it does not matter which pole the sum begins. It is.

However, such an interpretation would erroneously conclude that similarity of causes precedes similarity of effects. It is true that if the rotor has regularly spaced poles, the same things that determine P# and Q# also determine the coarse portion of the results measured with certain different phase measurement techniques. However, this does not mean that "P# with Q#" and "coarse" are the same thing. This happens simply because the conditions that mark them as different are not available or properly recognized. It can be seen that for this interpretation to be correct, P must be equal to Q and the spacing between the poles must be regular.

[0231] If we briefly consider an extreme case, we can see that the summation term is not, in principle, simply a partial part of the answer; on the other hand, P#/P,Q
It must be clear that #/Q is not just a rough part in principle. As an extreme example,
Imagine that all of the poles on each rotor are clustered into a small portion of the rotor's circumference. Under such conditions, when the input angle is increased equally, P#/P and Q#/Q do not change equally. P#/P for a small part of the "input circle"
There is a considerable change in Q#/Q, but the remaining large parts remain unchanged. However, the "coarse part" must change regularly in accordance with the regularly changing input. A similar discrepancy is the behavior of addition and the “element”
It also exists between.

[0232] Furthermore, if we carefully consider the principle and why fractional adjustment is performed from the beginning, we can see that the average value is corrected relative to the point where the averaging process started. . However, where on the rotor the addition begins is also a function of when during rotation the measurement is taken, and not just where the input stator is due to the input angle. But "coarse" and "fine" are certainly a function only of where the input stator is. How can "what time" change its angle? As far as equations (1), (1') and (1'') are concerned, it seems best to abandon the concepts of coarse and fine, as explained above, in favor of the idea of an integrated result. It will be done.

However, equation (1) is the basis for another equation (57) below which yields only the "essential" part of the answer. Formula (57
) can be supplemented with another coarse measurement, or in a completely incremental system in which the coarse part of the answer is accumulated when the fine part of the answer corresponds to one complete revolution. It can be used in Equation (57) is Equation (57')
and (57"), which is the basis of equations (1') and (1"
) is similar to the relationship for equation (1).

[0234]

[Math. 37]

Equation (57) can be obtained from Equation (1) as follows. First, multiply equation (1) by Q to get the answer that the rotor "turns" Q times per revolution. Next, it can be seen that the multiple of 2π in the answer simply adds an integral number of rotation calculations (expressed in radians) to the coarse part of the answer. This makes it possible to understand that the obtained θfine is now a modulo quantity and remove a certain term from the multiplied elements on the right side of equation (1).

The resulting equation contains the following terms:

[0237]

[Math. 38]

However, (58a) is simplified as follows.

[0239]

[Math. 39]

In the above derivation process, the difference P#-Q# in equation (58d) is the rough answer (2π
Equation (58e) is obtained by noting that the contribution is only in the amount of radians).

Equation (57) can be used in two ways. First, an incremental system
This is a simple method to configure the system. In such systems, no coarse measurements are taken, and the actual final value is maintained by adjusting the answer up or down by the value of the "fine" modulus (2π) as the fine count "turns around." . In such a system, the input or Q rotor need not have an absolute reference pole. Formula (57
Note that Q# does not appear in ). Nor is it necessary for this purpose, since no coarse measurements are taken. Therefore, the missing polarity on the input rotor may be eliminated.

Second, equation (57) is a system that performs separate measurements to obtain a "coarse" answer, and can be used in the part that produces a "fine" answer. Such a system would still not require a Q#, but some type of once-per-revolution marking on the input rotor would be necessary. This mark may take the form of a missing pole or a combination of a separate mark and its associated sensor. In any case, it is advantageous to use the passage of a pole on the input rotor through a sensor on the input stator as a clock signal for the coarse phase measurement. The reason is to increase the insensitivity of the measurement to changes in the angular velocity of the rotor. In general, such a system is substantially equivalent to one based on equations (1), (1') and (1''), but with extra overhead. It's actually made and works extremely well.

Finally, R in equations (1) and (57) requires that the value of R remains constant even if the measurement changes, as long as the actually occurring value of R for each measurement is used for the measurement. There isn't. This is easily ensured by measuring the time required for each exactly one revolution used in taking the sum. In other words, by arbitrarily determining one i value and measuring the time from one Tp[i] to the next Tp[i] (or the time between TQ[i]), it becomes R. If the motor speed fluctuates considerably, it is desirable to obtain the value of R by averaging the two.

Angle Measurement Returning now to the angle converter shown in FIGS. 3A-3C, the signals A, B, and X produced by the rotor and sensor of FIG. 3A produce a value indicative of the input angle.
, and how the phase measurement technique is applied to Y.

First, there are four sensors and four signals, instead of two sensors and two signals in the case of the basic phase measurement technique description. Nevertheless, the desired end result is the same. What we are looking for is the phase difference between A "coupled" with B on the one hand, and X "coupled" with Y on the other hand. The "combining" of A and B and X and Y provides averaging that can reduce not only eccentricity errors but also certain other errors. However, the word "averaging" here refers to determining the average phase, which is not necessarily the same as what is obtained when the instantaneous values of the signal are averaged by analog summation.

The type of eccentricity considered here is one in which the center of rotation of the input stator is not on the axis of rotation 22 of the rotor. Among other things, such eccentricity causes variations in the degree of coupling between each of the input sensors and the input rotor. In this case this variation is a function of the input angle. As a result, differences appear in the signal amplitudes originating from the sensors themselves. This difference in signal amplitude prevents direct analog averaging from producing a signal with an average phase. This can be summarized as follows. In other words, instead of averaging the signal and measuring the next phase, a method is needed that first measures the phase and then averages it.

Let us imagine that there is only one input sensor A. The phase measurement techniques described above can be used to measure the phases AX and AY. The angle with respect to the AX phase is ideally different from the angle with respect to the AY phase by exactly half a circle (π radians or 180 degrees). Taking this difference into account (eg, corrected according to the 180 degree offset), these two angles can be averaged. Results corresponding to phases BX and BY are obtained when B is the only input sensor. However, the averaged answers obtained in each case correspond to the same input angle, and they can therefore be averaged taking into account the difference in semicircle between sensors X and Y. This difference is from the reference X for AX and BX to AY and BY
This is the offset to the reference Y for . That is, A
If the angles for the various phases from X to BY are first corrected for the difference in half of the circumference, the following equation is obtained.

[0248]

[Math. 40]

That is, either average the average values or
All measurements can be directly averaged.

Similarly, if there are more sensors, the following will occur.

[0251]

[Math. 41]

[0252] The above form of averaging is expressed by equation (1) or (1'')
or for the fine angles from equations (57) or (57''). If fine angles are used, average them before combining them with the coarse angles. This itself results in a similar average. In the preferred embodiment for the configurations of FIGS. 3A-3C, the averaging is performed as shown on the right hand side of equation (59a).

[0253] It may now happen that the independent sensors placed on diametrically opposite sides are not exactly diametrically opposite. The degree of influence this has on the desired eccentricity correction is not particularly severe. There must be a 1° to 2° such placement error to result in a significant error. However, if the offset between the sensors is known, then equations (59a) to (59c)
Multiple independent sensors can be used for the averaging described in connection with ).

In a system that gives an average integrated solution based on a strict interpretation of equation (1), that is, if Ψ is determined explicitly, the results obtained from sensors that are not placed on opposite sides of the diameter will not be accurate. They are not separated by a half circumference. Referring to Figure 3A, when determining the result of phase AX and then determining phase BX, this is done by moving the input stator before the second measurement, bringing the A sensor exactly where the B sensor was. It is the same as coming. Apart from the influence of eccentricity, these two measurement methods are completely equivalent. Another way of thinking is that both AX and BX are measured from the same reference state determined by the reference rotor and the X sensor. The same caution applies to AY and BY. The offset due to the sensor placement between AX and BX is removed from BX, the offset due to the sensor placement between AY and BY is removed from BY, and the offset between AX and AY is removed from, for example, BY. The sensor placement offset is A
Once removed from Y and BY already adjusted, all four phases can be averaged as described above. The correction just described ends up using AX as a reference for each other phase. The sensor placement offset can be precisely removed for each new BX, AY, and BY, or can be incorporated into the value of Ψ for those measurements. . Each of the four phase measurements has its own constant Ψ, and the offset of the sensor placement is also constant. Therefore, they can be combined.

A more convenient method for an integrated answer is to base measurements on equations (1') and (1''). Using this approach, the offset of the sensor placement It is not necessary to know exactly what the offset is, as long as it is close enough to 180 degrees to satisfy the correction.The particular phase value Ai in question
X is actually measured as a change from some reference value AoX, while BiX is measured with respect to BoX. Then, measurements are made in the same manner. Although the original offset between AoX and BoX remains, AiX-AoX can in principle be directly averaged with BiX-BoX due to the differential nature of the measurements. (In principle, it can be averaged, but in practice it is not possible. See the next section.) Similarly, AiY-AoY and BiY-Bo
Y can also be averaged. Furthermore, since they each represent the same change in input angle, the two average values can be averaged. Essentially, there is no need to know the specific values of the sensor placement offsets for the same reasons that there is no need to know the specific values of Ψ. These are canceled by subtraction.

However, the situation is somewhat more complex than has been described so far. Both the combined answer and the precise angle are modulo numbers, and as is well known, special care must be taken when averaging numbers near the modulus value. Here, the value of the modulus is a value corresponding to 360 electrical degrees. Some prior art systems add or subtract a value corresponding to 180 electrical degrees to the angular value to be averaged;
We solved this problem by averaging and then removing the added values. The problem with the method in this example is:
If you change a pair of values near the modulus value by 180 degrees, you can move that pair out of the troublesome region, but other pairs will enter the troublesome region. If we insist on adding 180 degrees, we can add 180 degrees to some selected values and remove the appropriate fraction of 180 degrees from the result. For example, if only one of the four values changes, 1/4 of 180 degrees, or 4
Subtract 5 degrees from the average. This method is quite labor intensive and requires a considerable degree of judgment and flag setting each time an average is performed.

Other, simpler methods work at least as well. This method uses various phases AX, AY, B.
Observe the offset between X and BY. This takes one of the phases, e.g.
This is done by creating a ``lity offset''. (60a) O1=AX-AX (60b) O2=AY-AX (60c) O3=BX-AX (60d) O4=BY-AX

These averageable offsets may be measured with the transducer rotated to any position similar to that described above in connection with sensor placement. This is because these are relative measurements. Furthermore, since these are constants, it is only necessary to measure them once.

By using the averageable offset, the measured phase can be modified as follows. (61a) AX'=(AX-O1) mod 36
0° (61b) AY'=(AY-O2) mod
360° (61c) BX'=(BX-O3) mod
360° (61d) BY'=(BY-O4)m
od 360° These modified phases can then be averaged in the usual way (that is, the 180 degree addition can be done first in the usual way), adjusting all terms or no adjustment at all. can do.

The term "eccentricity" used above suggests other types of related sources of error. That is, it is an error related to an eccentrically mounted rotor. This error appears to the sensor as a rotor with imperfectly placed poles, even though the signal amplitude variation is caused by a change in the spacing between the rotor poles and the sensor. Changes in amplitude do not themselves cause errors since the nature of the measurement is limited to phase only. Additionally, phase measurement techniques are, in principle, immune to pole placement errors, so eccentrically mounted rotors do not introduce errors into the measurement.

Reducing Crosstalk Now let us explain the problem of crosstalk. Eliminating this effect is the first reason why the input rotor and reference rotor must have different numbers of poles. Furthermore, although the origins of individual crosstalks may differ in various embodiments, the net result is generally the same, so Figure 3
It is useful to examine the nature of crosstalk for the specific embodiments shown in connection with FIGS. 3A-3C.

The final result of the crosstalk is a configuration similar to that shown in FIGS. 3A-3C, but with the gears each having the same number of teeth. The answer there seen on the device is 12 in degrees.
There was a periodic error of 0 seconds. The magnitude of the error is a function of the input stator position. The error value was highest when the input and reference stator sensors were aligned. Between these extreme values the error resulted in a waveform with many cycles of varying amplitude as a function of input stator position. Subsequent experiments revealed that this error was entirely due to magnetic crosstalk. This is because the inclusion of a high permeability metal shield between the reference magnetic circuit and the input magnetic circuit eliminated almost all observable errors in the transducer.

Shielding is often easier said than done. In addition to requiring additional thought and weight, shields can present undesirable complications during alignment and repair. Here we show that the phase measurement technique described above, when using a rotor with a different number of poles spaced approximately equidistantly, is free from errors introduced by crosstalk for all practical purposes. yes. Preferred embodiments of the invention omit the rotor-to-rotor or stator-to-stator shields with no discernible adverse effects, yet still achieve angular second accuracy and resolution. Similar insensitivity to crosstalk can be obtained if the crosstalk effects are similar to some phase distortion of the signal from the sensor, and if such phase distortion meets certain criteria described below. Just being there is enough. That is, there are no magnetic-specific circumstances that would prevent a magnetic device from achieving the same insensitivity to crosstalk as in electrostatic and optical devices. Nor does the crosstalk mechanism need to be limited to actual rotor-to-rotor or stator-to-stator interference. The physical location of the crosstalk can be anywhere where sensitive components or conductors are sufficiently close to each other.

Note that it is useful to more briefly consider the mechanism of crosstalk in the device using magnetism under consideration. Consider reference sensor 8, which is the magnetic sensor of FIG. 3A. The main magnetic circuit for the magnet 23 passes through the pole piece 25 to the gear 5 and then back through the air to the other end of the magnet 23. The other return path passes air from rotor 5 to rotor 6.
and from there through the input sensor 10 to the case and then back to the reference sensor 8. A similar return path is input sensor 1
1 exists along with that passing through the reference sensor 9. Obviously these other return paths are affected by the proximity of the remote rotor pole to the associated remote sensor. That is, the individual influence of each other return path depends on something that is generally independent of how close the rotor pole is to the reference sensor 8. In the case of input sensors 10, 11, "what" is the position of the input stator (as far as the reference sensor and rotor are concerned) in conjunction with any located pole on the input rotor. Even in the case of the reference sensor 9, the influence of other return paths on the sensor 8 is not necessarily strongly related to what state is on the reference sensor 8 side. If the poles of the reference rotor 5 are ideally placed and the gears are perfectly round, etc., the effect will always be the same and can be ignored. Any difference in the spacing of the poles around the circumference of the rotor will have a corresponding arbitrary influence on the reference sensor 8 by the reference sensor 9 . but,
Even in this case, the effect of such crosstalk over one revolution is constant and never changes. The effect is simply some constant offset. Therefore, even though each sensor is influenced essentially arbitrarily by each of the other sensors, the crosstalk between sensors on the same rotor is
The main focus will be on the effects of inter-rotor crosstalk. It is not possible to rely on the individual effects of these various types to simply cancel each other out with the effects of other return paths. That is, they do not "sum up to zero," at least momentarily, and crosstalk exists. At the level of observation regarding a given signal A to Things happen earlier than they are supposed to happen, and other things happen later than they are supposed to happen. However, this phase distortion does not change the number of zero crossings. This is because the magnitude of crosstalk is quite small, for example, about -40 dB. Due to the influence of such crosstalk between the rotors, it appears as if a dynamically changing pole placement error is introduced. That is, the apparent pole position on the rotor appears to be a function of the input angle. If the rotor-to-rotor crosstalk is "symmetrical" or nearly so with respect to one revolution, then an apparent change in one pole position will be offset by a corresponding opposite change in the other apparent pole position. , the net effect of crosstalk will be very small. For all practical purposes, cancellation of such crosstalk effects occurs in the case of the described embodiment.

Since the above assertion may be too superficial, a more detailed explanation will be given below. 1st
The various ψ, Ψ in equations (1) to (57) are related to the particular pole arrangement on the particular rotor at hand (
(arbitrary) constant. It is not possible to determine one value of Ψ for the first measurement of θ and a significantly different value for the second measurement, and the difference between the two θ is exactly the difference between the two measurements. You can't expect it to be the angle you experienced in between. Further, unless Ψ is substantially constant, it is not possible to always subtract the constant Ψ to obtain each θ independently.

[0266] The various φ and Ψ in equations (1) to (57) indicate that even though the rotor-to-rotor crosstalk appears apparently as a dynamic misplacement of the poles on the rotor, it is essentially as assumed. is constant. Within limits they are actually truly constant. The nature of this marginal situation is
Continuous as opposed to finite sampling of zero crossings in the presented embodiment. However, the latter constitutes a good approximation of the former.

To see why this is so, consider again the properties of the sum created by equation (2). Let us consider that each of the terms in parentheses in equation (2) is correctly expressed for the case where there is no crosstalk. If there is crosstalk, it can be written as:

0268

[Math. 42]

In these equations, δi to δp are changes in zero-crossing time caused by phase distortion caused by crosstalk. Quantities l', m', . ．． ．． y' is the new angular displacement between the poles on the rotor (expressed in incremental time).

[0270] Therefore, it can be written as follows.

0271]

[Math. 43]

[0272] However, the term on the right side of the above equation is simply

0273

[Math. 44]

[0274] Therefore, the following formula is obtained.

0275]

[Math. 45]

[0276] That is, the sum of the two in question (
That is, the sum of Tp[i] and the sum of T'p[i] are equal if the sum of various δi is 0. A similar argument holds for T'Q[i]. The condition that the sum over one revolution of the various δi must be small is an essential criterion that the crosstalk must satisfy if the phase measurement technique is to be insensitive to crosstalk. Such insensitivity is guaranteed if this criterion is met. That is, Tp[i
] and TQ[i] do not change significantly from their pre-crosstalk values when crosstalk is introduced. Thus, the value of Ψ remains the same and we get the correct answer. Now, let us consider why the sum of various δi becomes almost zero when the two rotors have different numbers of poles. The following discussion considers the effect of crosstalk from the input rotor/stator on the reference rotor/stator. For this purpose, the interference signal is attenuated through a crosstalk path and then attenuated by a magnitude of 1 at the reference sensor.
It is convenient to consider that it has an amplitude of , whereas the amplitude of the signal that is actually to be measured produced at the reference sensor is A times greater than 1. Correspondingly, there are also explanations that consider reference rotor/stator crosstalk at the input sensor. However, since the explanation for both is the same, the second explanation will be omitted for the sake of brevity.

Let the interference signal from the input rotor/stator be:

[0278]

[Math. 46]

Similarly, the main signal from the reference rotor/stator is (67) y=A sin (2πωPt) (“P signal”
)

[0280] When the Q signal experiences a cycle of a certain average period n Q times, the P signal experiences a cycle of a certain average period m P times during the same length of time R. Therefore, (68
)Pm=Qn=R

It is convenient to think of the ratio of P and Q in the form of an irreducible fraction. (69) P/Q=P'/Q'

Let P'/Q' be an irreducible fraction and an integer P
Assume that neither ' nor Q' is equal to 1.

Now, there are certain situations in which various δi actually become zero. Imagine that the P and Q signals have at least one common zero crossing. Zero-crossing coincidences occur when both go positive, when both go negative, or a mixture of both. Show (e.g. by inspection of superimposed waveforms) that the sum (or difference) between the signals obtained in such a case, i.e. the composite signal, is symmetrical about the midpoint of its period R in the following form: I can do it. That is, any change in the position of a zero crossing on one side of the midpoint has a corresponding change of equal magnitude in the opposite direction in comparison to the associated zero crossing on the other side of the midpoint. (It is assumed here that the poles on the rotor are approximately equally spaced.) When both signals are combined, the above-mentioned changes in opposite directions cancel each other out. It follows immediately from the symmetrical nature of the algebraic sum of two symmetrical waveforms that equal but opposite symmetries experience a common zero crossing. The period of such common zero crossings is 1/2 of the smaller of m and n. In the case of transducer magnetic crosstalk here, this periodicity is experienced as the input stator changes position, contributing to the oscillatory nature of the crosstalk error.

However, the main signal and the crosstalk signal generally do not have a common zero crossing. Without such a common zero-crossing, the sum of the two signals would no longer be symmetrical about the midpoint of their period, and perturbations to the zero-crossings would not be able to be combined with pairs of equal magnitude but opposite directions. In these cases, the sum of δi is actually non-zero. Therefore, an explanation of this situation is given below.

In order to proceed with the explanation, it is convenient to rewrite equation (65) as follows. (70) y=sin(2πωQt+φ) where φ represents the phase of the Q signal at a point where there is no common zero crossing with the P signal.

An example of such φ is shown in FIG. As shown in the figure, φ is a value such that the Q signal becomes maximum when the P signal crosses zero toward the positive at time ti (such a difference in the Q signal for 1/4 cycle means that This situation seems to be the worst case at hand. This situation is the "furthest" from the case where their zero crossings coincide. However, in other senses it means that some different value of φ is equal to δi and an approximation of δi. It may be a case of maximizing the absolute value of the difference with another quantity εi that will become clear below.) Since the Q signal has a positive peak value of 1 of ti, at a certain time before ti, ti−δi be a reasonable approximation of The relationship shown in equation (71) below is valid if the slope of the P signal is substantially constant near the zero crossing obtained as a result of combining both signals. The condition for this validity is that the maximum slope of the Q signal is smaller than the maximum slope of the P signal, but this comes from the condition that the amplitude of the P signal is much larger than the Q signal. It is. Depending on whether the peak value of the Q signal occurs before or after the actual ti-δi, εi is sometimes larger than the associated δi, and sometimes smaller.

[0287] εi is determined as follows. Figure 11
As shown in , the P signal in the vicinity of ti is regarded as a substantially straight line, and its slope is determined by two methods. The first method is
Obtain the slope as the derivative of the P signal at ti. The second method is from the point where both the P and Q signals become zero to the point where the P signal alone becomes zero (from ti-δi to t on the time axis).
(up to i) is regarded as a straight line, and the slope of the P signal is determined as the slope of the line. Note that here δi is sufficiently small, so ti
The value of the Q signal at ti-δi is approximated by the value at ti using the fact that the Q signal can be regarded as almost constant near -δi (because the Q signal takes the maximum value at ti). By assuming that the two slope values thus obtained are equal and solving this using δi, an approximate expression for δi, εi, is obtained as follows.

That is, the slope according to the first method is sin
(2πωQti+φ)/(-εi) The slope according to the second method is

0289]

[Math. 47]

[0290] (If anything, Asin(2πωPt)
Because the positive slope crosses zero at t = 2πPti)

02
91] Therefore, (71) εi=sin(2πωQti
+φ)/(A2πωP)=δi

The sum of δi will be approximated by the sum of εi.

0293

[Math. 48]

[0294] This is all not as bad as it seems. Formula (7
The denominator of the central equation in 1) is a certain constant. When the numerator sine function argument is used in the summation of equation (72), there are only P' different values. These P'
The values are equally spaced in time during the Q' cycles of successive Q signals that constitute the Q'/Q portion of the resulting total. That is, the various P'ti's that are zero crossings of the P signal are P' samples sampled during Q' consecutive cycles of the Q signal. Each sample yields an ε that approximates the corresponding δ. However, each ε is some constant that is divided into the value of the Q signal at the zero crossing point of the P signal. This gives us the idea of what can be obtained by adding the amplitudes sampled at P' equally spaced time intervals during Q' consecutive cycles of a unit sine wave. It's coming.

The situation is depicted in FIG. For convenience,
It is drawn to represent the case of P=144 and Q=120. This results in P'=6 and Q'=5. That is, there are 6 cycles of the reference sensor signal for every 5 cycles of the input sensor signal. Furthermore, such a corresponding event occurs 24 times for each rotation of the rotor. Since each event is the same (assuming a regular array of poles on the rotor), we need to consider what happens during only one such event.

FIG. 12 shows how P' consecutive and equally spaced samples of the amplitude of the Q signal can be mapped into a single cycle of the Q signal. To explain this in more detail, first, the time interval 0~P'・m=Q'・n
The set S of sampling times in is clearly S={0
,m,2m,,. ．． ．． , (P'-1)·m} Since this is a point that divides the above time interval into equal parts P', S can be expressed as follows. S={α/P'×Q'・n|α is an integer from 0 to P'-1 Considering these sampling points on the Q signal, Q
Since the signal has a period n, each sampling point (α×
By translating P') x Q' x n by a time that is an appropriate integer multiple of n, the sampling results in time intervals 0 to n become the same. In this sense, a set S' of sampling time points equivalent to S can be expressed as follows.

0297]

[Math. 49]

However, since P' and Q' are relatively prime, Np' is a set of integers from 0 to P'-1, as is well known. Therefore, the following formula is obtained. S'={0, n/P', 2n/P', . ．． ．． , (P'-
1) n/P'}

The time interval between samples compressed by this mapping into a single cycle is also uniform, as seen from S' above. Therefore, a sine function sampled at intervals of P'×1/P' is obtained. It is known that the sum of such samples is always 0. Therefore, the following formula is immediately obtained.

0300]

[Number 50]

[0301] The proofs so far suggest more than the tautology of "to eliminate the effects of crosstalk, reduce the amplitude of crosstalk." The difference between the sum of εi and the sum of δi is related to the amplitude ratio of the main signal and the interference signal, but the ratio of the difference between these sums becomes smaller as the number of samples increases. In other words, if we consider the phase distortion caused by crosstalk as continuous, the phase disturbance is not necessarily symmetrical, but it is periodic (repeat once per rotation), and is averaged to 0 at each period. Become. Next, I will outline a more rigorous examination of this idea.

It is difficult to connect equations (67) and (70) as long as the arguments of each sine function are expressed by different parameters. However, equation (70) can be rewritten as follows. (74) y=sin[2πωPt+((Q-P)2
πωt+φ)]

The two terms in the argument of the sine function are set as follows. (75) X=2πωPt (76) Z=(Q-P)2πωPt+φ

0304
]X can be thought of as t multiplied by a certain frequency, and Z as a phase that changes with time.

Substituting these into (67) and (70), we get 2
Adding the two expressions, we get

0306]

[Math. 51]

The right side of equation (77) is a signal whose phase is distorted due to crosstalk. Here, the continuous change in the value of σ is distortion due to the movement of the device. Equation (79) shows this change. Substituting Z into equation (79) yields the following equation.

0308

[Math. 52]

Equation (80) shows a periodic odd function with half-wave symmetry, and its period is 1/(Q-P)ω. Therefore, if equation (80) is integrated over one period, the result becomes 0.

[0310] Now, the period of equation (80) is 1/(Q-P)
ω means that (Q−
This means that there is one period of the signal corresponding to P) poles. However, this time interval is just one revolution or an integer fraction of one revolution. Therefore, since the period of equation (80) is an integral number of times in one rotation, the integral of equation (80) over one rotation is also zero.

The value of σ in equation (80), however, is sampled a finite number of times. Furthermore, the sampling is performed at zero crossing points of the phase-distorted signal, so in principle it is not exactly equidistant. However, as the number of samples increases, the sampling becomes integral for the continuous case, regardless of whether the sampling occurs at regular intervals, only if the "sampling density" is substantially constant over the entire time interval. It is clear that a better approximation is possible.

The crosstalk reduction techniques described herein work better for low levels of crosstalk for two reasons. First, under low-level crosstalk, the sampling interval tends to be equal (there is less phase distortion at the zero-crossing position), and the shape of the function representing σ (Equation (80)) approaches a sine function. Crosstalk level (A=2)
Figure 13 (A) showing the time change of σ at time and Figure 13 (A) showing the time change of σ at low crosstalk level (A = 10)
(C) compares waveforms. Although Figure 13(A) shows waveform half-wave symmetry, the half-cycle itself is not symmetric about its midpoint, so even equally spaced samples cannot be expected to sum to zero. . This can be most easily understood by extracting various arbitrary pairs from values sampled at equal intervals. In contrast, the waveform in FIG. 13(c) is almost sinusoidal, although the amplitude is much smaller. Therefore, if sampling is performed at approximately equal intervals, the total will be almost zero. The difference between FIG. 13(A) and FIG. 13(C) reflects the difference in the value chosen for A in equation (67). Note how this affects the shape of the function representing σ (Equation (80)).

In summary, sampling approximation is very effective when the magnitude of crosstalk is low or moderate. The accuracy of the sampling approximation can be further increased by increasing the number of pulling points. There are at least two ways this can be easily done. 1st
The method is to perform sampling not only at positive zero crossing points of the P signal but also at all zero crossing points. A second method is to increase each of P' and Q' while keeping P'-Q' the same. And if you think about it, even if the basic level of crosstalk is abnormally high, if you make the sampling density high enough (for example, if you make P' and Q' large enough)
The benefits gained from low to moderate levels of crosstalk can be preserved. For example, A=2,P'
Please refer to FIG. 13(A) and FIG. 13(B), which respectively show the phase distortion α and amplitude Bsin(2πω×Pt+α) of a signal mixed with crosstalk when Q′=6 and Q′=5. Here, the ratio between the main signal and the interference signal is only 2:1, and σ
The shape of the function is rounded and serrated. However, Fig. 13 (A
) is still 0 for the rounded sawtooth wave over one rotation.
Even with finite sampling, this integral can be approximated as many times as you like by increasing the number of sampling points sufficiently.

There are many ways in which a once-per-revolution sensing absolute reference mark for P# and Q# can be placed on the waveform from the sensor. For example, the spacing of gears or rotors can have detectable non-uniformity. In this way, each rotation causes one corresponding periodic variation in the signal from the sensor. Such non-uniformity can be achieved by various means, such as monotonically increasing the pole spacing, having poles wider than the normal pole, or increasing the spacing between two poles from the normal spacing. slightly narrower or wider, and as already explained,
This can be realized by providing a missing pole. As far as the phase measurement technique is concerned and as long as crosstalk effects are ignored, these non-uniformities need not be particularly accurate in their implementation. The phase measurement technique itself is ultimately insensitive to pole placement errors.

[0315] The nature of the pole and its associated sensing mechanism may influence the technique used to distinguish one non-uniformity provided for a once-per-revolution mark from another. For example, consider optically detecting both transparent and opaque regions alternately provided on a rotor. If the beams are very well collimated, as is likely the case, or if the field of view of the sensor is sufficiently narrow, then the output waveform from the sensor should be a pattern image that is the same as the area distribution on the rotor. For example, when detecting a missing polarity, the normal waveform portion that would have appeared if the polarity existed would only be removed and appear. Such "fidelity" in sensing is possible with magnetic and capacitive sensing mechanisms, although it requires more effort to achieve. For example, a magnetic sensor whose magnetic poles extend from the north and south poles of the magnet can have its air gap above and below the tip of the edge line that follows the tooth ridges of a gear, allowing the nearest tooth to pass through. It is possible to maximize the change in magnetic flux caused by the change in magnetic flux, and to minimize the extent to which adjacent teeth and alternating flux paths influence the output signal of the sensor. Regardless of how it is done, the point is that, in contrast to the situation described in the next section, such fidelity in detection allows for the recognition of non-uniformity and (if necessary) the location of missing poles. Estimating or "smoothing out" non-uniformity for data processing convenience
This means that certain complications in the process can be avoided. For example, if a pole is missing, the cycles from the zero-crossing detector will simply disappear without any side effects. You will notice that the period between successive zero crossings in the same direction becomes longer, and you will probably insert a ``replacement'' in the middle.

[0316] In the particular magnetic application embodiment described, the magnetic sensor does not have a "narrow field of view." Figure 3A again
For example, as soon as the magnetic field lines leave the magnetic pole 25 at the end closest to the gearwheel 5, these magnetic field lines spread out in all directions towards the gearwheel. Also influencing the flux path reluctance to a significant extent are the other teeth on the gear on either side of the tooth closest to the pole 25. In other words, if a tooth is missing, the detection of teeth passing before and after the sensor will be affected. This effect is symmetrical with respect to where the missing tooth should be, and due to the dφ/dt nature of magnetic sensing, the sensor generates one long cycle in a time that would normally have been two cycles. . In this way, not only are cycles missing;
Some other cycles cause their transitions to shift from where they should be.

To further summarize the situation, it may be inconvenient to assume that all sensors are constructed and mounted in such a way that they always produce the same polarity transition when they meet the leading edge of a pole. Therefore, what is a positive transition for one sensor may correspond exactly to another sensor. However, even if the polarities differ between the sensors, it is desirable for the system to operate on zero crossings in only one direction. If the polarities of the sensors are mixed in this way, there will be an apparent misalignment between the sensors of different polarities near the missing tooth, and this will cause the sensor to "fill in" the missing tooth.
Procedures change. The apparent deviation can be ignored. First, the representations by such sensors for the rest of the associated rotor are offset by the same amount. Second, a P# or Q# value is never compared to other P# or Q# values for that same rotor. This value is only used in conjunction with Q# or P# for another rotor. The magnitude of this discrepancy is a difference in ``when the information becomes available,'' not a difference in ``what the information is.'' Even if such a sensor is used for coarse phase measurements (i.e. 2
(Measuring the time in percent of a revolution between the absolute reference marks of two rotors), the apparent deviation only causes a constant offset in the resulting answer. Such offsets are easily removed once their permanent value is known.

[0318] The long period and the difference in polarity give rise to two different situations regarding depolarization. These situations can be handled as shown in FIGS. 14A and 14B. With a microprocessor, signals A to X
It is not difficult to recognize the long periods in each of the cases and to ascertain the polarity of case I or case II based on the given non-uniformity. This information can be verified repeatedly as the rotor moves, or it can be determined only once for each sensor and permanently encoded. Once these polarities are known, the positions of the erroneous transition points are corrected according to the fixed relationships shown in FIGS. 14A and 14B;
It is also easy to approximate missing transitions.

Of course, all sensors should have the same polarity of some choice, always FIGS. 14A and 14
Either one of the two situations shown in B may be used. However, some believe that a condition such as having the same selected polarity is a condition that may be broken upon assembly or repair. This view is based on the consideration that if the polarity does not matter from the beginning, things will not go well, and that it would be better not to rely on polarity in a particular direction. There is.

A second general method is to eliminate any discernible periodic disturbances in the waveform caused by non-uniformities on the rotor. Instead, the microprocessor expects the signal from the input rotor to repeat P cycles while the signal from the reference rotor repeats Q cycles. Microprocessors come in various P# and Q
A cycle of each waveform is arbitrarily selected to serve as a pseudo-absolute reference mark that serves as a reference for #. The selected cycles are repeatedly recognized by counting the cycles modulo P and the cycles modulo Q. Thus, P# and Q# are determined by noting what the modulo count is when the measurement request is received.

By using the generalized phase measurement pseudo-absolute reference mark, Equation (1),
The applicability of Equation (57) and the equations derived therefrom can be generalized to situations where P cycles of one signal occur within the same time as Q cycles of the other signal. This certainly includes the case where P=Q, ie, where the signal is subjected to some phenomenon that causes a phase lag before being compared with itself. Such schemes are often used to transform physical properties (eg, distance) that result in corresponding phase shifts due to propagation delays.

An advantage of the phase measurement technique described above in such applications is that the accuracy of the phase measurement does not depend on the accuracy or stability of the signal being measured out of phase. All that is required for phase measurements is the stability of accurately measuring the various time intervals separated by zero crossings and the times of P or Q cycles. If we are willing to trust that these latter two times are equal, we will also see that they need not occur at the same time, but may occur quite separately, one immediately after the other or after some delay. . Similarly, they may partially overlap each other.

Angle Measurement Technique A multi-pole input rotor and a multi-pole reference rotor mounted on a common axis of rotation generate input and reference signals, respectively, as the poles pass the associated input and reference sensors. The input sensors are journalled for orbital rotation about a common axis of rotation and are capable of orbital movement around the periphery of the input rotor. The reference sensor is fixed at a position adjacent to the periphery of the reference rotor. A once per revolution mark on each rotor may be arranged to identify one pole on each rotor as a reference or index pole. Each pole passing through its associated sensor causes a cycle in the associated input signal and reference signal. The rotor does not need to have its poles placed with any particular precision. If crosstalk is a problem, the number of poles on one rotor may be different from the number of poles on the other rotor.

The information contained in the input and reference signals may be configured to be retrieved after at least one rotation of transition time data has been captured and stored in a storage device. To identify the indicator pole, physically remove the pole and
It is also convenient to put the estimated transitions flagged by this depolarization into storage.

During at least one revolution of each rotor, calculate the average of successive times at which a pole occurs to determine the average time at which the associated equivalent single pole occurs. The average times of occurrence of these equivalent monopoles are then compared as if they actually originated from a rotor with only one pole. As the input stator sensor advances in the direction of rotation of the rotor, the equivalent unipolar time interval increases until the time interval reaches one revolution. As the input stator sensor advances further, it passes the point of coincidence between the equivalent monopoles, at which point the time interval suddenly drops to zero and begins to increase again. The measured time interval is proportional to the angle between the input and reference sensors, which is equal to or only differs from the input angle by a constant amount. The measured time interval is scaled to represent the input angle in any desired units. In the example described, the measured time interval is first normalized as a percentage of one rotation by dividing the measured time interval by the measured rotation time of the rotor. The result of this normalization can then be increased or decreased by an appropriate constant offset.

[0326] The equivalent single-pole average occurrence time is measured for each rotor by dividing the sum of the occurrence times of consecutive poles that occur at intervals of at least one rotor rotation (or an integral number of rotations) by the number of poles. It is done with attention. In other words, the above-mentioned summation is not performed for fractions of one rotation. Both summations are also performed with respect to a common time reference point. Assuming that both summations always begin with (i.e. wait until) the detection or occurrence of their corresponding indicator poles, then
The difference in the average time of occurrence is in fact a measure of the time interval mentioned above. Although this is certainly possible, it violates the requirement that the rotations whose respective sums are related should overlap as much as possible. In other words, if the totals are taken for different rotations, the variations in rotation speed from one rotation to the next will cause the rotation times to have a different average value, making them incomparable unless they are normalized separately. It is from. To avoid such complications, preferably the overlap of rotations for both sums is maximal. For this purpose, instead of an index pole, the summation is started as soon as any pole passes. However, the common point of reference time is preserved. This common point can, for example, conveniently be the beginning of successive transitions of the reference signal.

In return for this flexibility in when to start the summation, we must not lose track of where the summation starts relative to the index pole. This can be done by counting the number of poles skipped on each rotor since the associated index pole last appeared. According to a useful principle, the average measurement of the time of occurrence of an equivalent monopole can be corrected for each skipped pole by the average time interval between the poles. This average time interval between poles is simply the time for one revolution divided by the number of poles. For each pole skipped on the reference rotor side, the interpole average time interval on the reference rotor must be added to the value of the difference between the measurements of the average values of the occurrences of both equivalent monopoles. Similarly,
For each pole skip on the input rotor side, the average time interval between input rotor poles must be subtracted from the above difference. In this way, by counting the number of skipped poles in the input and reference rotors, and based on that, correcting the measured value of the difference between the occurrence times of both equivalent single poles by the average interpole time interval and the number of skipped poles, Although the summation actually starts from an arbitrary pole, we obtain the value of the difference between the occurrence times when the summation starts from the index pole.

[0328] The result has all the extra reliability given by averaging, and its precision is comparable to the precision of the time measurements used to make the sum. The accuracy of the pole placement on the rotor has no effect on the accuracy of the result, except perhaps through indirect effects such as crosstalk. However, only when the poles are arranged approximately regularly, crosstalk can be effectively canceled if the numbers of poles on both rotors are chosen to be different. Even in this case, it is not necessary to arrange the poles with high precision.

The result obtained is an integrated modulo solution, one cycle of which directly represents exactly one rotation of the input angle, ie 360 degrees, with no coarse or fine components. Therefore, there is no need to add an algorithm that correctly links the coarse and fine components, and there is no need to suspect that noise may introduce errors when the measured value is close to the latter value, ie, the "turning point."

The measurement or corrected measurement of the time interval between equivalent monopoles can be a direct indication (with appropriate scaling, of course) of the input angle, or it can be a residual measurement relative to some arbitrary input condition. (residual) time interval. This arbitrary input condition is “0
degree' or some unknown value. In any case, the measured or post-measurement corrected value of the difference in the mean time of occurrence of the equivalent unipole, when subtracted by this remaining time interval, is the difference between the current input condition and any input condition. represents the sweep angle of This remaining time interval is determined by the initial difference between the two mean times for the equivalent single pole when the index pole coincidence occurs, or simply by another measurement for purely arbitrary input conditions or by correction after the measurement. can represent the value given.

The measurement technique described above also requires that the ratio of frequencies be rational (i.e., an integer number of cycles of one signal occurs within a length of time equal to another integer number of cycles of the other signal). ) may be considered a method of measuring the phase between two signals. The method described above can be applied, for example, to one P
Use any cycle of the respective waveform as an index cycle when used to measure the phase between two signals such that Q cycles lie within a time period equal to Q cycles of the other; It is then convenient to use each Pth and Qth cycle as an index cycle. The Pth and Qth cycles are easily distinguished by counting the cycles of the signals that are related by modP and modQ, respectively.

The phase measurement technique described above may use a pair of diametrically opposed sensors. In a preferred embodiment, both the input stator and the reference stator each include a pair of sensors arranged diametrically opposite from each other. Four phases are measured. That is, each sensor on one stator is taken into separate relationship with two sensors on the other stator, resulting in four possible combinations. The four phase measurements thus obtained are one of the four.
corrected for inherent offsets relative to one. The reference phase and the remaining three corrected phases are then averaged.

Crosstalk Suppression Technique Crosstalk between sensors is suppressed by selecting the number of poles on the rotor to be unequal in a particular way and implementing the phase measurement technique described above. P the pole of one rotor
Q pieces are selected for the other rotor. Fraction P/
Let the irreducible type of Q be the fraction P'/Q'. However, P' and Q'
are not equal to 1. Of course, P and Q may be selected such that P/Q is already irreducible when both P and Q are not 1.

The effect of this is to create a phase measurement error function whose integral over one revolution is zero. Therefore, if the signal with crosstalk is sampled at a sufficiently high density over an integral number of rotations, the influence of crosstalk can be self-cancelled to any desired degree.

The phase measurement technique described above is preferred in this regard. This is because with this technique, the average can be measured over an integer number of times and P and Q can be set to arbitrary values.

[0336] Method for correcting periodic errors Errors that are a function of the input angle (eccentricity errors, etc.) and whose period is 360 input angles (one round error) or 180 input angles (two round errors), etc. The self-cancelling effect of errors with the error function is enhanced by measuring the phases between associated diametrically opposed sensors before averaging these phases. In a preferred method, each sensor generates a separate signal whose phase is measured relative to a reference. Zero-crossing detection and time measurement are preferred because they reduce sensitivity to amplitude variations. The measured phase can then be arithmetic averaged across diametrically opposed sensors, and the result then averaged with similar results from other pairs of diametrically opposed sensors, if such exist. can do. In general, "1 lap 1
A pair of diameter-opposite sensors is required for a ``times''error;
``One round twice'' error requires two pairs separated by 90 degrees, and so on. Performing phase measurements with separate sensors before such averaging can result in the phase information in the smaller amplitude signal being distorted by the larger amplitude signal when the two signals are analogously averaged before phase measurement. It disappears. Such amplitude fluctuations are often introduced by error mechanisms, and distortions appearing in the analog average phase remain as errors despite averaging. Measuring the phase first and then averaging eliminates the deleterious effects caused by such incidental amplitude fluctuations and allows errors to more nearly completely self-cancel.

[Brief explanation of the drawing]

FIG. 1 is a perspective view of a mechanical part of an embodiment of the present invention.

FIG. 2 is an exploded view of the mechanical part of FIG. 1.

FIG. 3A is a block diagram of one embodiment of the invention.

FIG. 3B is a block diagram of one embodiment of the invention.

FIG. 3C is a block diagram of one embodiment of the invention.

FIG. 4 is an explanatory diagram of the basic principle of the present invention.

FIG. 5 is an explanatory diagram of the basic principle of the present invention.

FIG. 6 is an explanatory diagram of the basic principle of the present invention.

FIG. 7 is an explanatory diagram of the basic principle of the present invention.

FIG. 8 is an explanatory diagram of the basic principle of the present invention.

FIG. 9A is an explanatory diagram of the basic principle of the present invention.

FIG. 9B is an explanatory diagram of the basic principle of the present invention.

FIG. 9C is an explanatory diagram of the basic principle of the present invention.

FIG. 10 is an explanatory diagram of the basic principle of the present invention.

FIG. 11 is an explanatory diagram of crosstalk error correction.

FIG. 12 is an explanatory diagram of crosstalk error correction.

FIG. 13 is an explanatory diagram of crosstalk error correction.

FIG. 14A is a diagram illustrating the influence of the difference in polarity of the detectors on detection of the missing tooth position.

FIG. 14B is a diagram illustrating the influence of different polarities of detectors on detecting the position of a missing tooth.

[Explanation of symbols]

1: Mechanical part 2: Reference stator 3: Input stator 4: Rotor shaft 5: Reference rotor 6: Input rotor, 7: Printed circuit board 8, 9: Reference sensor 10, 11: Input sensor 22: Axis, 23, 24: Magnets 29, 30, 31, 32: Amplifiers 33, 34, 35, 36: Zero crossing detectors 37, 38,
39, 40: Delay circuit 45: Clock signal 52: Counter 53: New data counter 54, 62: Decoder/multiplexer 59: Interrupt catch-up counter 60: Comparison circuit 61: Microprocessor 63: Random access storage device

Claims (11)

[Claims] Claim 1: A transducer provided with the following (a) to (k): (a) having P poles and Q poles different from P on the first and second peripheries, and around an axis; first and second rotors pivoted for simultaneous and identical rotations; said first and second rotors each having one first and second index mark per rotation; (b) said first and second rotors having one first and second index mark per revolution; (c) means coupled to the first and second rotors for causing them to rotate about an axis; (d) a first sensor means for generating a first sensor signal of P cycles at a time; (e) second sensor means pivotally supported to produce a second sensor signal of Q cycles per revolution in response to passage of a pole of said second periphery; (e) said first and second sensors, respectively; first and second digital signals coupled to the signal to generate first and second digital signals;
zero crossing means; (f) transition detection means coupled to said first and second digital signals for detecting that at least one of said signals has transitioned; (g) clock means for providing digital time information;
h) coupled to said first digital signal, 1 per revolution;
first index mark identification means for identifying a first index mark per revolution; (i) second index mark identification means coupled to said second digital signal for identifying a second index mark once per revolution; (j ) the first and second digital signals, the transition detection means, the clock means and the first and second index identification means; The sum of P times Σ up to each selected transition during P consecutive cycles of
TP and Q from said zero point to each selected transition during Q consecutive cycles of said first digital signal.
The sum of the times ΣTQ and the number of intervening cycles P between the first index mark and the first cycle of the P consecutive cycles in the first digital signal are taken modulo. The number P# and the second
a first digital process for determining a number Q# obtained by taking the modulo of Q of intervening cycles between the second index mark and the first cycle of the Q consecutive cycles in the digital signal; means and (k
) second digital processing means coupled to said R, said ΣTP, said ΣTQ, P# and Q# for determining the phase θ between said sensor signal and said second sensor signal; 2. The converter according to claim 1, wherein the phase θ is obtained by evaluating an equation including the following terms: (ΣTQ/Q−ΣTP/P)/R+P#/P− Q#/Q
3. The converter according to claim 1, wherein the phase θ is obtained by evaluating an equation including the following terms: (ΣTQ/Q−ΣTP/P)/R+P#/P− Q#/Q
−ψ However, ψ is a constant. 4. The P and Q are not in a relationship such that one is a multiple of the other, and the P poles of the first peripheral portion are actually arranged at (P-1) equal intervals. consists of a pole and one virtual pole, distinguishable by the absence of a real pole,
The Q poles of the second peripheral portion are characterized in that they consist of (Q-1) equally spaced real poles and one virtual pole that is distinguishable by the absence of a real pole. Claim 1
Transducer as described. 5. The once-per-rotation first index mark is the virtual pole of the first periphery, and means for identifying the first index mark is the first index mark at the first periphery. In response to the absence of a pole, the once per rotation second index mark is the virtual pole on the second periphery, and means for identifying the second index mark is the virtual pole on the second periphery. 5. A transducer as claimed in claim 4, characterized in that it is responsive to the absence of an actual pole. [Claim 6] A transducer provided with the following (a) to (k): (a) having P poles and Q poles different from P on the first and second peripheral parts, and around the axis; first and second rotors pivoted for simultaneous and identical rotations; said first and second rotors each having one first and second index mark per revolution; (b) said (c) means coupled to the first and second rotors for causing them to rotate about an axis; (d) a first sensor means for generating a first sensor signal of P cycles at a time; (e) second sensor means pivotally supported to produce a second sensor signal of Q cycles per revolution in response to passage of a pole of said second periphery; (e) said first and second sensors, respectively; first and second digital signals coupled to the signal to generate first and second digital signals;
zero crossing means; (f) transition detection means coupled to said first and second digital signals for detecting that at least one of said signals has transitioned; (g) clock means for providing digital time information;
h) coupled to said first digital signal, 1 per revolution;
first index mark identification means for identifying a first index mark per revolution; (i) second index mark identification means coupled to said second digital signal for identifying a second index mark once per revolution; (j ) the first and second digital signals, the transition detection means, the clock means and the first and second index identification means; The sum of P times Σ up to each selected transition during P consecutive cycles of
TP and Q from said zero point to each selected transition during Q consecutive cycles of said first digital signal.
ΣTQ, the sum of times ΣTQ, and further determine the number P of cycles intervening between the first index mark and the first cycle of the P consecutive cycles in the first digital signal. (k) first digital processing means coupled to said first digital processing means for determining a number P# modulo of said first and second sensor signals; Second processing means for determining the precision part: Q cycles of the precision part of the phase θ correspond to one orbital revolution of the second sensor means about the axis. 7. Converter according to claim 6, characterized in that the high-precision part of the phase θ is obtained by evaluating an equation containing the following terms: (ΣTQ−(Q/P)ΣTP)/ R-P#(Q-P)/
P 8. A converter according to claim 6, characterized in that the highly accurate part of the phase θ is obtained by evaluating an equation containing the following terms: (ΣTQ−(Q/P)ΣTP)/ R-P#(Q-P)/
P−ψ where ψ is a constant. 9. Third digital processing means coupled to means for identifying said first and second index marks once per rotation and generating a coarse phase θ in response to said R; 7. A transducer as claimed in claim 6, characterized in that it is coupled to processing means and said third digital processing means to combine said coarse phase θ and a fine portion of said phase θ. 10. The P and Q are not in a relationship such that one is a multiple of the other, and the P poles of the first peripheral portion are actually (P-1) arranged at equal intervals. and one virtual pole distinguishable by the absence of a real pole, and the Q poles of the second periphery are separated by (Q-1) equally spaced real poles and one virtual pole. 7. A transducer according to claim 6, characterized in that it consists of one virtual pole distinguishable by the absence of a pole. 11. The once-per-rotation first index mark is the virtual pole of the first peripheral edge, and means for identifying the first index mark is one of the virtual poles of the first peripheral edge. In response to the absence of a pole, the once per rotation second index mark is the virtual pole on the second periphery, and means for identifying the second index mark is the virtual pole on the second periphery. 11. A transducer as claimed in claim 10, characterized in that it is responsive to the absence of an actual pole.