JPH0524441B2 - - Google Patents

Description

(46b) Δφ _0,K = Δφ _J,K +x _J +x _J-1 +…+x1 (from formula (42a)) (46b) −Δφ _J,K =y1+y2+…+y _K −Δφ _J,K (formula (44a) )from)

[0154] If we solve for Δφ _J,K and simplify it, the result is (47) Δφ _J,0 =y1+y2+…+y _K −x1−x2−…x _J
+Δφ _0,0

[0155] Equation (47) can also be obtained by inspecting a diagram (not shown) similar to FIG. 9C representing the following situation. That is, the angular displacement between the reference sensor and the input sensor is determined by rotating the reference sensor and input sensor as one unit around the rotor's axis of rotation until the reference sensor is exactly opposite the pole P1 when addition begins. It remains constant even when
The angle at which pole Q1 rotates from when T _P [ ₁ ] occurs until T _Q [ ₁ ] occurs is φ _0,0 .

[0156] Equation (47) is a "killer"-like permutation that combines everything into one. This equation relates Δφ _J,K to Δφ _0,0 for any value of P#, Q#. Let's now substitute equation (47) for Δφ _J,K in equation (39).

【0157】

[Math. 23] (48a) _yk-1 〓 〓〓 ^J,K T _Q [ _i ]−Q/P _XJ-1 〓 ^XJ+1 T _p [ _i ] =Q [y1+y2+…+y _k −x1−x2−… −x _J +Δφ _0,0
]+(Q-1)y _k+1 +(Q-2) _k+2 +...+Ky _Q +(k-1)y1+...+ _k-
1 −Q/P [(P-1)x _J+1 +(P-2)x _J+2 +…+
Jx _p (48b) =QΔφ _0,0 + (Q-1)y _k+1 + (Q-2)Y _k+
2 +...+Ky _Q +(Q+k-1)y1+(Q+k-2)y2+...+(Q
+1)y _k-1 +Qy _k -Q/P [(P-1)x _J+1 +(P-2)x _J+2 +...+
Jx _p + (P+J-1)x1〕

[0158] Let's "subtract R" from the y and x terms as we did for the equations related to FIGS. 6-8. R is from x1 to x _P (including x1 and x _P )
equal to the sum of all time intervals and also from y1 to y _Q
Recall that it is also equal to the sum of all time intervals up to (including y1 and y _Q ). Consider the y term in equation (48b). Note that all y _i exist and the smallest 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】

[Table 2]

【table】

[0160] Therefore obviously

[0161]

[Math. 24] (48c) _yk-1 〓 〓〓 ^J,K T _Q [ _i ]−Q/P _yk+1 〓 ^XJ+1 T _p [ _i ]=QΔφ _0,0 +KR + _yQ-1 〓 ^y1 T _Q [ _i ]−QJR/P−Q/P _yp+1 〓 ^X1 T _p [ _i ]

[0162] Recalling that J=P# and K=Q#, and solving for φ _0,0 , we get

【0163】

[Number 25]

[0164] The term in the parentheses on the left side of the right side of equation (48e) is exactly the term in the parentheses in equation (1), if only the difference in the type of symbol is ignored. The product of 2π and the term in parentheses on the right side of equation (48e) defines the constant Ψ in equation (1).

[0165] 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

【0165】

[Math. 26] (49a) Ψ=2π/QR{ _i 〓 ^a T _Q [ _i ]−Q/P _y 〓 ^l T _p [ _i ] However, (49b) _j 〓 ^a T _Q [ _i ]= _yQ-1 〓 ^y1 T _Q [ _i ] and (49c) _y 〓 ^l T _p [ _i ]＝ _XP-1 〓 ^X1 T _P [ _i ]

[0167] Therefore, the symbol of formula (49a) is replaced by formula (49b)
Or you can substitute the symbol of formula (49c). By doing this and rearranging, we get the following formula.

【0168】

[Number 27]

[0169] Equation (49d) shows that the right part of the right side of Equation (48e) is actually correct and equivalent to Equation (1).

[0170] 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 φ _0,0 , which is simply the angle obtained when we never start adding unless the associated P# and Q# are zero. Of course,
In that case, stricter rules would be required compared to the fact that P# and Q# (j and K) can be given arbitrary values. Equation (1) and Equation (48e)
The advantage of this is that such strict rules are not necessary. The definition of Ψ is essentially the residual offset obtained when φ _0,0 equal to 0 is the input angle. The necessary sums to obtain Ψ are ΣT _P [ _i ] when P# ₌ 0 and exactly ΣT _P [ i ] when Q#=0 (ie, no Δθ remains).
In other words, the fact that Δθ is equal to 0 at 0 degree input means that T _P [ ₁ ] matches T _Q [ ₁ ]. However, both equation (1) and equation (48e) are "0 degrees"
It is not required that T _P [ ₁ ] match T _Q [ ₁ ] upon input. This is because Ψ is the user's ``0''
T _P [ ₁ ] and the input value that we want to be
This is because it is possible to accurately provide a reference no matter what arbitrary state is obtained between T _Q [ ₁ ].
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 this was one of the simplifying assumptions made at the beginning of the proof of the correspondence between T _P [ ₁ ] and T _Q [ ₁ ]. It can now be shown that this special assumption is unnecessary.
To see why this is so, consider that there is one mechanical input value at which T _P [ ₁ ] and T _Q [ ₁ ] coincide, regardless of the "0" position of the stator or the orientation of P ₁ with respect to Q ₁ . Observe that it exists. 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 option is selected, the only effect is that an offset of α is introduced into the measured results. The amount of offset α can certainly be found by observing the points at which T _P [ ₁ ] and T _Q [ ₁ ] occur simultaneously as the mechanical input changes, but it does not need to be known exactly. There isn't. The difference between the mechanical input angle that causes such simultaneity of T _P [ 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 θ _ref such as "0", "10", etc. Therefore, to find the fundamental value of θ _ref by measurement, we use a modified equation (1) that does not include the −Ψ term. However, its value is expressed as follows. (50) θ _ref = α−Ψ _ideal

[0171] Of course, the actual values of α and Ψ _ideal are unknown, and only the difference θ _ref (measured and modified equation (1)
) is known.

[0172] Next, consider the result of increasing the mechanical input angle by the amount γ from its original value of θ _ref to θ _oew . What we want to do here is find γ. However, θ _oew is a measurable quantity whose value can be obtained. (51) θ _oew = α + γ + Ψ _ideal If we solve for γ, (52) γ = θ _oew − (α − Ψ _ideal )

[0173] Applying equation (50) to the right side of the above equation, the following equation is obtained. (53) γ＝θ _oew −θ _ref

[0174] That is, γ is an input value measured with θ _ref as a reference, and the value of θ _ref is arbitrary. Note that the actual values of α and Ψ _ideal 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] (1′) θ=2π{θ _o+1 ′−θ _o ′] Here, (1)″θ _o ′=ΣT _Q [ _i ]/Q−ΣT _P [ _i ]/P/R+P #/P
-Q#/Q

[0176] θ in equation (1') does not necessarily have to be equal to φ _0,0 as explained in relation to equation (48e), and may differ from φ _0,0 by a certain constant. Whether the two are equal or not depends on the conditions chosen to represent "0 degrees". If the condition is that T _Q [ ₁ ] and T _P [ ₁ ] match at "0 degree", θ is actually equal to φ _0,0 . 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 equation (1″), the value obtained as θ _o ′ at “0 degrees” is also Ψ, so equation (1′) works exactly the same as equation (1) where Ψ is known. but,
“θ is equal to 0 degrees” means that T _P [ ₁ ] is
If the condition does not match T _Q [ ₁ ], θ becomes φ _0,0 plus or minus a constant offset, which is the difference between the two “zero conditions”. However, in any case, the change in θ is equal to the change in φ _0,0 .

[0177] If you are familiar with the field,
It will be appreciated that several ways of exploiting the properties described above are possible. The method consists of actually finding α and Ψ _ideal (either only once for a given fixed configuration, or by finding them on demand, such as at power-up). Sometimes this ranges from initially finding only θ _ref and measuring each angle as a displacement from the new θ _ref to a different θ _oew , choosing the one that makes the most sense for a given application. This is a design issue that should be determined by standards.

[0178] 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 sometimes give a negative answer. Even if such a negative answer is obtained, it is easy to obtain a positive value by simply adding each positive round to the negative value. I can do it, so it's not a problem.

[0179] Let us now return to equation (1) and consider again the other simplifying assumption made at the beginning of the previous proof. Referring to FIGS. 4 to 8, in equations (2) and (3), "time is equal to 0"
Recall that we assumed that we start from point in time. When applied to FIGS. 9A to 9C, this is equivalent to assuming that T _P [ ₁ ] is equal to 0. Next, let's assume that T _P [ ₁ ] is not 0 and consider what kind of results can be obtained. Let T _P [ 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 time intervals (a, b, c... and l, m, n,... or y ₁ ,
y ₂ , y ₃ , ... and x ₁ , x ₂ , x ₃ ...). Equations (2) and (3) refer to summing the ending times of these time intervals (as in equation (1)) and summing the time intervals (which is more explanatory). It shows the relationship between β is not an increment over any of the time intervals (i.e. the values of these time intervals remain unchanged), whether for the sum of T _Q [ _i ] or the sum of T _P [ _i ] , is the common increment of the measurements at the end of each time interval. As done in equation (1), the sum of Q such terms is taken for T _Q [ _i ], and T _P [ _i ]
For , the sum of P terms is taken. Q number of
Since each T _Q [ _i ] increases by β, the total is
Increment by Qβ. Similarly, the sum of T _P [ _i ] is incremented by Pβ. It does not matter what order the various T _P [ _i ] are in;
It does not matter in what order T _Q [ _i ] are added. That is, whether the sum is in the left-hand bracket of the right-hand side of equation (48e) for some Δφ or in the right-hand bracket as Ψ, ΣT _Q [ _i ] increases by each Qβ and ΣT _P [ _i ] are each increased by Pβ. Within each pair of parentheses,

[0181]

[Math. 29] (54) ΣT _Q [ _i ]+Qβ/Q−ΣT _P [ _i ]+Pβ/P = ΣT _Q [ _i ]/Q+β−ΣT _P [ _i ]/P−β = ΣT _Q [ _i ]/Q −ΣT _P [ _i ]／P

[0182] Therefore, it is clear that β≠0 is a self-cancellation condition.

[0183] Finally, in view of equations (2) and (3) and in light of the previous caution regarding simplifying assumptions,
I would like to emphasize the meaning of equation (1). 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 I have given many paragraphs of explanations centered on time intervals, the unwary reader may sometimes find himself having to perform a series of many subtractions to arrive at the answer. You may be under the mistaken impression that you need to actually find each time interval. 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, equations (2) and (3) relate the time interval to the sum required by equation (1). These sums simply add up Q consecutive T _Q [ _i ], and then simply add up consecutive P
It can be obtained exactly by adding the T _P [ _i ]. No subtraction is necessary to make these sums. The first addition of T _P [ _i ] does not have to be 0, nor does T _P [ _i ] and T _Q [ _i ] 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.

[0184] It seems useful here to consider the "meaning" of formula (1) and formula (48e). Although there is no doubt that we have arrived at this point, 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.

[0185] Consider the rotating four-pole roller shown in FIG. During exactly one revolution of the rotor at time R, each time sensor from T ₁ to T ₄ generates a signal. As in the first example, let the time interval between the poles be a,
Let 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) T ₁ = T ₁ (This T ₁ is zero or is measured starting from a certain preceding time T ₀ = 0) (B) T ₂ = T ₁ + a (C) T ₃ = T ₁ + a + b (d) T ₄ =T ₁ +a+b+c (e) R=a+b+c+d

[0186] 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】

[Number 30]

[0188] This averaging or equivalent time is pole number 1
It is important to understand that this refers to starting the addition at . Now “pole number 2”
starts with (delay of 'a' in starting average) 4
If we average two consecutive times, what change will there be in the average time or the new equivalent unipole? ”. Having read the above explanation, it is only natural to expect that the onset time of the new equivalent unipole will be delayed by a time interval "a". However, this is precisely the average time interval between the poles. The following formula (g)
Indicates a new value for the expression (nu).

【0189】

[Math. 31] (G) 〓 ^i=2,3,4,1 _i = (T ₁ +a) + (T ₁ +a+b) + (T ₁ +a+b+c) + (T ₁ +a+b+c+
d) =4T ₁ +4a+3b+2c+d (li) =4T ₁ +3a+2b+c+R

[0190] As shown in equation (l), the difference between these two values (that is, equation (f) and equation (l)) is exactly 1/4 of one rotation time, that is, R/4. You will see that if it were skipped, the difference would be 2/4 of a revolution.Furthermore, it would be 5 times instead of 4 times.
If there were two poles, the corresponding differences in this case would be 1/5 and 2/5 of a revolution, respectively. It is clear that what we have here is a summary of the laws for what we call P#/P and Q#/Q.
The important point of this law is that Q arbitrary time intervals a, b, c, ...k between Q poles are not individually known except that their sum is R. Also, the average time increases by exactly R/Q for each pole skipped before starting the addition that determines the average time of pole occurrence. This is an interesting and perhaps unexpected result, as it relates an arbitrary and unknown magnitude (the skipped amount) to one whose magnitude is both bookmarked and known in advance (the magnitude of the correction). .

[0191] The principle of this correction is equally applied to the case where consecutive occurrence times are averaged over the time for one revolution. Now let me explain the possibilities. The average shall be taken over n rotations,
And let us assume that the number of skipped poles is less than the number of poles on the rotor. In this case, equation (g) and equation (n) can be expressed as follows.

【0192】

[Number 32]

[0193] 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 relates to the preferred embodiment
Consistent with the rules given for determining # and Q#. 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 revolution at most.

[0194] Originally, other matters in equation (1) change for the measurement of n rotations. The sum ΣT _Q [ _i ] will be divided by nQ and the sum ΣT _P [ _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.

[0195] Other possibilities for multiple rotations are worth briefly considering. Consider that the rotor must make n revolutions 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, for one rotor, n
It is possible that the n rotations have little in common (time overlap) with the 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, only nP instead of P, nQ instead of Q, and nR instead of R.
Measurements are easily made using any of the equations already mentioned, except using . A slight extra effort is to recognize every nth mark of the actual one-turn mark as a "super-one-turn mark."

[0196] Any of the multiple rotation methods described above has certain benefits when it is desired to average two or more overall measurements. Instead of making n measurements of one revolution each, one measurement of n revolutions can be made once.
This will require more memory, but will probably measure faster and can be used for 0° or 360°.
The difficulty in combining answers that are very close to is considerably reduced.

[0197] For simplicity of explanation, a formal explanation of the principles of FIG. 10 will not be presented here. However, it must be noted that this proof is not very difficult and that FIG. 6, FIG. 9A, or FIG. 9B and the text related thereto can be interpreted as the basis of the proof. No doubt many variations of this principle have been demonstrated. Recalling that the goal of this discussion is to explain why the phase angle formula, i.e., equation (1), "really works," the purpose of illustrating FIG. 10 and its associated principles is to It is simply a matter of creating some kind of clearly visible and useful principle. Having said this, I will now proceed to its interpretation.

[0198] Perhaps the easiest place to start the interpretation is equation (48d). In this formula, time Δφ _0,0
is based on four other times and two correction terms (JR/P
and KR/Q, i.e. P#/P and Q#/Q)
was considered to be equal to the difference between 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. It is also precisely because it is posted without any ``simplifying'' rearrangement that obscures or absorbs it. Equation (48d) can be rewritten as Equation (55) shown below.

【0199】

[Number 33]

[0200] In Equation (55), first, the term (A) is the second average time of the Q pole reflecting the input angle, and the average starts after skipping J and K poles. It is. Term (B) corrects the change brought about in the average time by skipping K poles. The term (C) is the second average time of the P poles, the angle is zero, and the average starts after J poles have been 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.

[0201] The term is the result of correcting the second average time of the equivalent single pole of the P pole that reflects the input angle to that from the beginning of the Q pole. Note that skipping J poles essentially has no effect on 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 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 true zero angle. However, as stated elsewhere, if the term cancels out by taking the difference, there is no need to find the actual value of this term.
Normally, the value of this term cannot be determined.

[0202] Term (a) is the changed 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 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 simply the result of a previous measurement (such as this difference measurement).

[0203] That is, the measurements of terms (A) to (D) are performed during the same rotation period, but the measurement of Ψ, that is, the term, is often performed during a different rotation period. Also, the term represents Ψ, but if this measurement were actually performed, the term in this section would be
Measurements in sections (E) and (F) are made during the same rotation period.

[0204] The conclusion that can be drawn from the above explanation is that the difference between the two brackets on the left 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 about Ψ and equation (1), Ψ _idefl , α, and equation (50)
to equation (53), and especially equations (1′) and (1″)
Please refer to the related explanation.

[0205] The above measured difference is the average time of occurrence of the Q pole with respect 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 for average times during the rotation of the input rotor. Note that the value given to J essentially defines the value of K, depending on the shape of the respective rotor and the position of the input rotor. Once Δφ _J,K
Once Δφ _{M,N and Δφ M,N} are adjusted to the value of Q#=0, Δφ _J,K and Δφ _M,N are in a sense proportional.
That is, the times Δφ _J,0 and Δφ _M,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 the rotation, which may have different speeds.

[0206] If we ignore the terms in parentheses on the right side of equation (55) (these correspond to Ψ), then equation (1′)
If we remember that Ψ is canceled by subtraction, then equation (1″)
It is not difficult to interpret in light of equation (55). The only difference is that by dividing the equation by R and then making some modifications, we find Δθ to θ
It is to convert it into finding out. Dividing by R is particularly desirable. This is because it normalizes the rotational speed that can vary in various ways.
This is because, unlike a specific time, P#/P and Q#/Q, which represent a certain percentage of one rotation, are obtained. Also, this allows us to
When multiplied by 2π, 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 associated with an arbitrary starting pole. Since the sum of T _P [ _i ] as a subtraction is too large to be adjusted back to the original starting point, P
#/P is added back. Also, Q#/Q is subtracted because the reduced sum of T _Q [ _i ] started out too large by that amount and has not yet been adjusted back to the original starting point.

[0207] The reference rotor and its total are "0 reference"
Further insight into how it works can be gained by considering equation (56).

【0208】

[Number 34]

[0209] In equation (56), the term (G) is the second average time of the Q pole that reflects the input angle, and the average starts after skipping J and K poles. This value is based on the hot second _TO . 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 when the angle is zero. This average is a value based on a certain first T _O starting from the beginning of the Q pole. The (K) term is the second average time of the P pole when the angle is zero. This average is a value that starts after skipping one pole and is based on a certain second _TO . The (L) term corrects the change brought about in the averaging by skipping J poles. The Σ term is the first average time of the P pole when the angle is zero, and is a value starting from the beginning of the P pole and based on a certain first _TO .

[0210] The term is a 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 this difference with the effect of skipping J P poles (here, the effect of skipping J is only to cause K skips). This average time is the second
It is based on T _O. term is the second mean time of the P pole for angle zero. This value is corrected based on the beginning of the P pole, but the second
It is based on T _O. Note that the Σ term and the term generally have different values. It was different for each total
This is due to the timer reset done to provide _TO , and also due to motor speed fluctuations.

[0211] 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 _TOs . Term (c) is the offset between the first and second _TO . 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 the terms related to T _P [ _i ] are grouped together to create the difference. According to the above principle, the quantities in parentheses on the right side of equation (56) are zero if each sum is referenced to the same T _O . i.e. "new but adjusted"
The sum of T _P [ _i ] is equal to the sum of "old" T _Pi . Obviously, in this equation, only T _Q [ _i ] is "angular information"
This information is what we would expect if the reference sensor did not move.

[0213] Then why do we conduct a detailed study on T _P [ _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 even if the two sums are obtained with respect to the same T _O =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 (This also applies to what is in parentheses on the left.) However, the difference between the terms in the right parentheses can ``happen'' to be zero, because at any given time T _O =
This is because it is not possible to keep track of time that increases monotonically from 0 forever. 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 with respect to the same T _O =0 of the clock. It will probably disappear if it is removed. 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. This is because the two sets of parentheses each contain the same difference between arbitrary separate T _O , and as a result, as can be seen from equation (56), the difference between the "same difference" This is because you will have to take . Creating this difference between the two is the main reason for finding the two ΣT _P [ _i ]. This allows us to find the offset of the difference between the two ΣT _Q [ _i ] and remove it. 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 is a measurable offset in the left bracket that must be removed, but this offset also commonly occurs in the right bracket.

[0214] It turns out that none of these events (measurements at different times, clock resets, changes in 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 due to steady state bias due to these effects are canceled. Of course, care may be taken not to reset the clock in the middle of rotation while phase measurement is being performed.

[0215] 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】

[Number 35]

[0217] In equation (1) expressed in the above form, first
The term (M) is the average time when one Q pole appears due to the input angle and skipping Q# poles (Q
The skipping of # poles 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.
(N) term is P due to skipping P# P poles.
This is the average time at which one pole appears. 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 T _P [ 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 T _P [ _i ] but had no corresponding change in the total of T _Q [ _i ]. (Q) is
It is a value based on T _P [ ₁ ], which is 1 of the increase in the equivalent pole spacing due to skipping Q# poles.
It is the ratio to rotation. After all, this skip increased the total average of T _Q [ ₁ ], but
This is because it did not bring about a corresponding change in the sum of T _P [ ₁ ]. The (R) term is the residual spacing at the original reference angle of the equivalent pole spacing. 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 is due to the time interval that existed before giving the input angle (that is, T _P [ ₁ ]≠T _Q [ ₁ ]), and also due to the time interval that existed before the input angle was given (that is, T (delaying) and also by skipping poles (i.e., starting the sum without waiting for T _P [ ₁ ] and T _Q [ ₁ ]).

[0219] The term (d) is a time interval expressed as a percentage of the rotation of the rotor.

【0220】

[Number 36]

[0221] In formula (1) expressed in the above form, (S)
The term reflects the initial time interval, the input angle and the skipping of Q# Q poles, and also the P# P
This is the ratio to one revolution obtained by correcting for skipped poles.

[0222] The term is a percentage of one revolution due to the initial time interval and input angle only. That is, if the first pole appears, T _P [ ₁ ] and T _Q [ ₁ ]
The correction was made to obtain the value that would have been measured if the summation of each had been started.

[0223] The term (E) is the ratio of only the input angle to one rotation, based on starting the respective sums at T _P [ ₁ ] and T _Q [ ₁ ]. Here Ψ is the expression
You can calculate the value and subtract it, as in (1), or cancel it by subtracting the measured values for two different values of the input angle, as in equation (1′) and equation (1″). It's okay.

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

[0225] Now Equation (1), Equation (1′), and Equation (1″)
turns out to be actually correct. It can also be seen that it is not necessary that the number of poles on each rotor be equal to each other, nor is it necessary that the poles 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, which will optimize the sensor response to suppress transient conditions and reduce crosstalk if present. This is desirable in order to make it useful. This uniformity helps indicate absolute position on the rotor,
It also allows reliable detection of missing poles, which serves as a basis for keeping track of P# and Q#. However, the absolute position of the rotor can be detected by other means (e.g., an indicator permanently attached to each gear and associated with a particular pole;
This can also be achieved by providing a separate once-per-rotation sensor to detect this. With such measures, in principle the positioning on the rotor can be completely arbitrary (in a crosstalk-free system). In short, it is not particularly recommended to deliberately place poles haphazardly unless there is a good reason to do so, but the phase measurement technique of the present invention allows for phase measurements whose accuracy is not limited by the precision of the pole placement. be. Depending on other factors,
In any case, it may be necessary to have an essentially regular pole arrangement.

[0226] The only condition is that we are dealing with the device-dependent constant Ψ, then equations (1), (1′) and (1″)
gives an absolute answer that is neither "coarse" nor "fine," but is an integrated, high-resolution solution with precision that is probably as high as the precision and stability of time measurements. 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. There are mechanical factors that can affect the accuracy of the angle conversion device as a whole, some of which will be discussed in separate sections below. However, these factors generally do not adversely affect accuracy by interfering with the principle of equation (1) or equation (1'').

[0227] The integrated answer given by Equation (1) and Equation (1″) is the “averaging” of the large number of poles attached to each rotor, i.e. the high The answer is resolution. 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 them with great confidence.

[0228] To this end, slightly varying the polar range and motor speed may actually help increase the 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.

[0229] The integrated answers in equations (1) and (1″) have easily discernible “coarse” and “fine” differences 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 erroneously conclude that since regularity appears to give modulus properties to the difference in quotients with respect to the sum, with regularly arranged poles it does not matter at which pole the sum begins. It is.

[0230] 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 in principle not just an essential part of the answer, but on the other hand P
It must be clear that #/P and Q#/Q are not just rough parts 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#/ for a small part of the “input circle”
There is a considerable change in P and 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 exists between the behavior of addition and the "essence part."

[0232] Furthermore, if we consider the principle and why fractional adjustment is performed in the first place, we can see that the average value is adjusted relative to the place where the averaging process started. I understand. 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? Equations (1), (1′) and (1″)
As far as this is concerned, it seems best to abandon the concepts of coarse and fine in favor of the idea of integrated results, as explained above.

[0233] However, equation (1) is the basis for another equation (57) below, which yields only the "element" part of the answer. The answer given by equation (57) can be supplemented with another coarse measurement, or it can be completely incremental, accumulating the coarse part when the fine part of the answer corresponds to one complete revolution. Can be used within the system. Equation (57) is the basis of Equations (57') and (57''), and has a similar relationship to the relationship of Equations (1') and (1'') to Equation (1).

【0234】

[Math. 37] (57) θ _fioe = 2πθ/RΔθ = 2π{ΣT _Q [ _i ]−Q/P
ΣT _P [ _i ]/R+P#(Q-P)/P}−QΨ (57′) θ _fioe =2π{θ _o+1 ′−θ _o ′} where (57″) θ _o ′=ΣT _Q [ _i ]−Q/PΣT _P [ _i ]/R+P#(
Q-P)/P Value of "Sei"

[0235] 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. Then in the answer
It turns out that the multiple of 2π simply adds an integral number of rotations (expressed in radians) to the coarse part of the answer. This makes it possible to understand that the obtained θ _fioe is now a modulo quantity and remove a certain term from the multiplied elements on the right side of equation (1).

[0236] The resulting equation contains the following terms:

【0237】

[Number 38] (58a) ...+(P#/P-Q#/Q)Q...

[0238] However, (58a) is simplified as follows.

【0239】

[Number 39] (58b) =QP#/P-Q# (58c) = (Q-P+P)P#/P-Q# (58d) = (Q-P)P#/P+P#-Q# (58e) =P#(Q-P)/P

[0240] In the above derivation process, note that the difference P# - Q# in equation (58d) contributes only to the coarse answer of counting integer rotations (each expressed in the amount of 2π radians). We obtain equation (58e).

[0241] Equation (57) can be used in two ways. First, it provides an easy way to configure incremental systems. 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 coefficient "turns around." be done. In such a system, the input or Q rotor need not have an absolute reference pole. In equation (57), Q
Note that the # does not appear. Nor is it necessary for this purpose, since no coarse measurements are taken. Therefore, the missing pole on the input rotor may be eliminated.

[0242] Second, equation (57) can be used in a system that performs separate measurements to obtain a "coarse" answer 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 event, 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 phase coarse measurements. The reason is to increase the insensitivity of the measurement to changes in the angular velocity of the rotor.
Generally speaking, such a system has equations (1), (1′)
and (1″), but with extra overhead. Systems of this type have been built in practice, however, and work quite well.

[0243] 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, if you arbitrarily set one i value and measure the time from one T _p [ _i ] to the next T _p [ _i ] (or the time between T _Q [ _i ]), you can determine that it is R. Become. If the motor speed fluctuates considerably, it is desirable to obtain the value of R by averaging the two.

[0244] Angle measurement Next, return to the angle conversion device shown in FIGS. 3A to 3C and create a value indicating the input angle in FIG. 3A
Consider how the phase measurement technique is applied to the signals A, B, X and Y produced by the rotor and sensors of .

[0245] 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. On the other hand, B
The phase difference between A "coupled" with Y on the other hand and X "coupled" with Y on the other hand is what we are looking for. Averaging is done by “combining” A and B and X and Y,
Not only eccentricity errors but also certain other errors can be reduced. 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.

[0246] The type of eccentricity considered here is one in which the center of rotation of the input stator is not on the rotation axis 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. That is,
Instead of averaging the signal and then measuring the phase, we need a method that first measures the phase and then averages it.

[0247] Let's imagine that there is only one input sensor A. The phase measurement techniques described earlier can be used for phase AX and
It can be used to measure AY. The angle to the AX phase is ideally different from the angle to the AY phase by exactly half a circle (π radians or 180 degrees). Taking this difference into account (e.g., 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, so they can be averaged taking into account the difference in semicircle between sensors X and Y. This difference is the offset from reference X for AX and BX to reference Y for AY and BY. That is, if the angles for various phases from AX to BY are first corrected for the difference in half of the circumference, the following equation is obtained.

【0248】

[Number 40] (59a)∠AX+∠AY/2+∠BX+∠BY/2/2 =∠AX+∠AY+∠BX+∠BY/4

[0249] That is, the average values can be averaged or all four measurements can be directly averaged.

[0250] Similarly, if there are more sensors, the following will occur.

【0251】

[Math. 41] (59b) ∠AX+∠AY/2+∠BX+∠BY/2+∠CX+∠C
Y/2/3 =∠AX+∠AY+∠BX+∠BY+∠CX+∠CY/6 (59c) ∠AX+∠AY+∠AZ/3+∠BX+∠BY+∠BZ/
3/2 =∠AX+∠AY+∠AZ+∠BX+∠BY+∠BZ/6

[0252] Averaging of the above form can be performed on the combined answers from equation (1) or (1″) or on the fine angles from equation (57) or (57″). . If fine angles are used, they must be averaged before combining with coarse angles. This is itself a similar average. In the preferred embodiment for the configurations of FIGS. 3A-3C, averaging is performed as shown on the right side of equation (59a).

[0253] Now it may 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 such a placement error of 1° to 2° to produce a significant error. However, if the offset between the sensors is known, multiple independent sensors, whether or not they are placed on exact diametrically opposite sides, can be considered for the averaging described in connection with equations (59a)-(59c). can be used.

[0254] For systems that give 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 diametrically opposite sides will not be accurate. They are not separated by a half circumference. Referring to FIG. 3A, the phase
When determining the result of AX and then determining the phase BX, this is equivalent to moving the input stator before the second measurement to bring the A sensor exactly where the B sensor was. 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, and the offset due to the sensor placement between AY and BY is removed from BY, for example.
The sensor placement offset between AX and AY is AY
and once removed from the already adjusted BY,
All four phases can be averaged as explained above. The correction just described ends up using AX as a reference for each other phase.
The sensor placement offset is different for each new BX,
AY and BY can be excluded exactly, or Ψ
can be incorporated into the value of 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.

[0255] A convenient method for the integrated answer is to base measurements on equations (1') and (1''). Using this approach, the offset of the sensor placement can be There is no need to know exactly what the offset is, as long as it is close enough to 180 degrees to satisfy the eccentricity correction.
The particular phase value A _i X in question is a certain reference value A _p
is actually measured as the change from X, while B _i
B _p is measured in terms of X. Then, measurements are made in the same manner. The original offset between A _p X and B _p X remains, but due to the differential nature of the measurement, A _{i X} − _{A p} Can be averaged. (In principle, it can be averaged, but in practice it is not possible. See the next section.) Similarly, A _i Y−A _p Y and
B _i Y−B _p Y can also be averaged. Furthermore, since they each represent the same change in input angle, the two average values can be averaged. Essentially,
For the same reasons that there is no need to know the specific values of Ψ, there is no need to know the specific values of the sensor placement offsets. These are canceled by subtraction.

[0256] However, the situation is somewhat more complex than what has been described so far. Both the combined answer and the fine angle are modulo numbers, and special care must be taken when averaging numbers near the known modulus. Here, the value of the modulus is a value corresponding to 360 electrical degrees. In some systems of the prior art, the angular value to be averaged is
We solved this problem by adding or subtracting a value corresponding to 180 degrees, averaging, and then removing the added value. The problem with the method in this example is that 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. be. If you insist on adding 180 degrees, you can add 180 degrees to some selected value and remove the appropriate fraction of 180 degrees from the result. For example, if only one of the four values changes, subtract 1/4 of 180 degrees, or 45 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.

[0257] Other, simpler methods work at least as well. This method has various phases.
Observe the offset between AX, AY, BY and BY. This is one of the phases, e.g.
This is done by taking AX as the basis and creating the following "averageability offset": (60a) O ₁ =AX−AX (60b) O ₂ =AY−AX (60c) O ₃ =BX−AX (60d) O ₄ =BY−AX

[0258] These average possible 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.

[0259] By using the averageable offset, the measured phase can be modified as follows. (61a) AX′=(AX−O ₁ )mod360°(61b) AY′=(AY−O ₂ )mod360°(61c) BX′=(BX−O ₃ )mod360°(61d) BY′=(BY −O ₄ ) mod360° These modified phases can be adjusted in the usual way (that is, you can add 180 degrees first in the usual way), adjusting all terms or none at all. It can be averaged.

[0260] 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 variations are caused by changes 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.

[0261] Reducing crosstalk Now let's 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. Also, although the origins of individual crosstalks may differ in various embodiments, the net result is generally the same, and thus FIGS. 3A to 3
It is useful to examine the nature of the crosstalk for the specific example shown in connection with C.

[0262] The final result of crosstalk is a configuration similar to that shown in FIGS. 3A-3C, but each gear has the same number of teeth. The answer seen by the instrument had a periodic error of 120 seconds in degrees.
The magnitude of the error is a function of the input stator position. The error value was maximum 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 showed that the cause of this error was entirely the magnetic stroke. 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.

[0263] 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 magnetic devices 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.

[0264] 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. Another return path is through air from rotor 5 to rotor 6 , thence through input sensor 10 to the case and then back to 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 is determined by the fact that the rotor pole is the reference sensor 8.
how close it is to depends on something generally unrelated. 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. The poles of the reference rotor 5 are ideally arranged and the gears are completely round.
etc., the effect is always 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 . However, 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 focus will primarily be on the effects of rotor-to-rotor crosstalk rather than crosstalk between sensors on the same rotor. . 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 the given signals A to Things happen earlier than they are supposed to happen, and other things happen later than they are supposed to happen. However, even with this phase distortion, the number of zero crossings does not change. This is because the level of crosstalk is quite small, for example around -40dB. 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'' with respect to one rotation,
If it is, or almost so,
An apparent change in a given pole position will be offset by a corresponding opposite change in the other apparent pole positions, and the net effect of crosstalk will be very small.
For all practical purposes, cancellation of such crosstalk effects takes place in the case of the described embodiment.

[0265] Since the above assertion alone may be too superficial, a more detailed explanation will be provided below. First, it was explained that the various ψ and Ψ in equations (1) through (57) are (arbitrary) constants related to the particular pole placement on the particular rotor at hand. 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 inter-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 limit situation is continuous as opposed to the finite sampling of zero crossings in the presented example. However, the latter constitutes a good approximation of the former.

[0267] 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] (62a) l=T _p [ _z ]−T _p [ ₁ ]l′=T _p [ _z ]+
δ ₂ (T _p [ ₁ ] + δ ₁ ) (62b) m=T _p [ ₃ ]−T _P [ ₂ ]m′=T _P [ ₃ ]
+δ ₃ (T _p [ ₂ ] + δ ₂ ) (62c) y=T _p [ _P ]−T _P [ _P-1 ]y′=T _P [ _P ]
+δ _P − (T _P [ _P-1 ] + δ _P-1

[0269] In these equations, δ _i to δ _p are changes in zero-crossing time caused by phase distortion caused by crosstalk. The quantities 1', m', . . . y' are the new angular displacements between the poles on the rotor (expressed in incremental time).

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

【0271】

[Math. 43] (63a) _y ′ 〓 ^l ′T _P [ _i ]=T _P [ ₁ ]+δ ₁ +T _P [ ₂ ]+δ ₂ +…… +T _P [ _P-1 ]+δ _P-1 +T _P [ _P ]+δ _P (63b) = _P 〓 ⁱ⁼¹ δ _i + _P 〓 ⁱ⁼¹ T _P [ _i ]

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

【0273】

[Math. 44] (63c) _P 〓 ⁱ⁼¹ T _P [ _i ]= _y 〓 ^l T _P [ _i ]

[0274] Since it can be expressed as, the following formula is obtained.

【0275】

[Math. 45] (64) _y ′ 〓 ^l ′T _P [ _i ]＝ _P 〓 ⁱ⁼¹ δ _i + _y 〓 ^l T _P [ _i ]

[0276] In other words, the two sums in question (i.e., the sum for T _p [ _i ] and the sum for T′ _p [ _i ]
) are equal if the sum of various δ _i is 0. A similar argument holds for T′ _Q [ _i ]. The condition that the sum over one revolution of the various δ _i must be small is that if the phase measurement technique must be insensitive to crosstalk,
Crosstalk is an essential criterion that must be met. Such insensitivity is guaranteed if this criterion is met. That is, T _p [ _i ] and
This is because the sum with respect to T _Q [ _i ] does not change significantly from its pre-crosstalk value 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 δ _i becomes almost zero when the numbers of poles in two rotors are different from each other. The following discussion considers the effect of crosstalk from the input rotor/stator on the reference rotor/stator. For this purpose, the interference signal, after being attenuated through the crosstalk path, has an amplitude of magnitude 1 at the reference sensor, while the amplitude of the signal that was originally to be measured at the reference sensor is less than 1. It is convenient to think of it as being twice as large. Correspondingly, there are also explanations that consider reference rotor/stator crosstalk at the input sensor. However, since the explanation for both is the same,
For the sake of brevity, the second explanation will be omitted.

[0277] Let the interference signal from the input rotor/stator be:

【0278】

[Math. 46] (65) y=sin(2π radian/rotation/rotation/second/pole/
number of times / seconds) = sin (2πωQt) (“Q signal”)

[0279] Similarly, the main signal from the reference rotor/stator is (67) y = Asin (2πωPt) (“P signal”)

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

[0281] It is convenient to think of the ratio of P and Q in the form of an irreducible fraction. (69) P/Q=P'/Q'

[0282] Let P′/Q′ be an irreducible fraction and an integer
Assume that neither P' nor Q' is equal to 1.

[0283] Now, there are certain situations in which various δ _i actually become zero. Imagine that the P and Q signals have at least one common zero crossing.
The coincidence of zero crossings is when both go positive,
This can occur 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 immediately follows from the contrastive nature of the algebraic sum of two symmetrical waveforms whose equal but opposite symmetries experience a common zero crossing. The periods of such common zero crossings are m and n
It is 1/2 of the smaller of . 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.

[0284] However, generally the main signal and the crosstalk signal do not have a common zero crossing. Without such common zero-crossings, the sum of the two signals would no longer be symmetrical about the midpoint of their periods, and the predominance of zero-crossings would not be able to be combined with pairs of equal magnitude but opposite direction. . In these cases, the sum of δ _i is actually non-zero. Therefore, an explanation of this situation is given below.

[0285] In order to proceed with the explanation, it is convenient to rewrite equation (65) as follows. (70) y=sin(2πωQt+φ) where φ is the Q of the point where there is no common zero crossing with the P signal
Represents the phase of the signal.

[0286] 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 makes a positive zero crossing at time t _i (such a difference in the Q signal for 1/4 cycle is a certain value). In some sense this 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 values of φ are different from δ _i and δ _i It may be a case of maximizing the absolute value of the difference with another quantity ε _i that will become an approximation value below.) Since the Q signal has a positive peak value of 1 of t _i , some time before t _i Let t i −δ _i be a reasonable approximation at the time t _i −δ i . 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 t _i -δ _i , ε _i is sometimes larger than the associated δ _i and sometimes smaller.

[0287] ε _i is determined as follows. Figure 1
As shown in Fig. 1, the P signal near t _i is regarded as a substantially straight line, and its slope is determined by two methods. The first method obtains the slope as the derivative of the P signal at t _i . The second method is to consider the line from the point where both P and Q signals become zero to the point where the P signal alone becomes zero (from t _i −δ _i to t _i on the time axis) and calculate the slope of the line. The slope of the P signal is determined as the slope. In addition,
Here, since δ _i is sufficiently small, the Q signal can be regarded as almost constant in the vicinity of t _i - δ _i (the Q signal is
Since the maximum value is obtained at t _i ), the value of the Q signal at t _i −δ _i is approximated by the value at t _i . By assuming that the two slope values thus obtained are equal and solving this using δ _i , an approximate value of δ _i , ε _i , can be obtained as follows.

[0288] In other words, the slope according to the first method is sin(2πωQt _i +φ)/(−ε _i ) The slope according to the second method is

【0289】

[Formula 47] dy／dtAcos(2πωPt _i )・2πωPt _i =A2πωP

(If anything, Asin(2πωPt) is t
Because the positive slope crosses zero at =2πPt _i )

[0291] Therefore, (71) ε _i = sin(2πωQt _i +φ)/(A2πωP) = δ _i

[0292] Let us approximate the sum of δ _i by the sum of ε _i .

【0293】

[Math. 48] (72) Σ〓ε _i Σδ _i

[0294] This is all not as bad as it seems. The denominator of the middle equation in equation (71) 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′ values are the resulting total Q′/Q
of the continuous Q signal that constitutes the part of
They are equally spaced in time during the Q′ cycle. That is, the various P' t _i that are zero crossings of the P signal are P' samples sampled during Q' consecutive cycles of the Q signal. Each review 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. From this, the unit sine wave
The idea is, what is obtained from adding the amplitudes sampled at every P' equally spaced time intervals during Q' successive cycles?

[0295] 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, each time the rotor rotates, 24 such corresponding events occur.
Appears twice. 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 detail, first, the set S of sampling times in the time interval 0 to P'・m=Q'・n is clearly S={0, m, 2m, . . .
(P′-1)・m} Since this is the point that divides the above time interval into P′ equal parts, S can be expressed as follows. S={α/P'×Q'・n | α is an integer from 0 to P'-1 If these sampling points are considered on the Q signal, the period of the Q signal is n, so each sampling point By moving (α×P′)×Q′×n in parallel for a time that is an appropriate integer multiple of n, the time interval 0 to
The result of sampling at n will be the same. In this sense, the set S' of sampling points equivalent to S can be expressed as follows.

【0297】

[Formula 49] S′={x mod n|x∈S}={n×β/P′|β∈
N _p ′} where N={(Q′×0mod P′, (Q′×1)mod P′, (Q′×
2) modP′, ..., Q′×(P′×1) modP′}

[0298] However, since P' and Q' are relatively prime, N _P ' 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′}

[0299] The time interval between the samples compressed by this mapping into a single cycle is also uniform, as seen from S' above. Therefore, P′×
A sine function sampled at an interval of 1/P' is obtained. It is known that the sum of such samples is always 0. Therefore, the following formula is immediately obtained.

【0300】

[Math. 50] (73) Σε _i = 0 and Σδ _i 0

[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 ε _i and the sum of δ _i 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 provide an overview of the rigorous examination of this idea.

[0302] 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)2πωt+φ)
]

[0303] The two terms in the sine function argument 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.

[0305] Substitute these into (67) and (70) and get 2
Adding the two expressions, we get

【0306】

[Math. 51] (77) AsinX+Bsin(X+Z)=Bsin(X+σ) However, (78) B=√(+) ² 8 and (79) σ=tan ^-1 [sinZ/cosZ+A]

[0307] The right side of equation (77) is a signal with a distorted phase 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] (80) σ=tan ^-1
[sin((Q-P)2πωt+φ)/cos((Q-P)2π
ωt＋φ)＋A〕

[0309] Equation (80) indicates 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 during the same time interval during which P poles and Q poles pass in front of their respective associated sensors, one of the signals corresponding to (Q-P) poles
This means that a cycle exists. However, this time interval is just one revolution or an integer fraction of one revolution. Therefore, since there are an integral number of periods in equation (80) during one rotation,
The integral over one rotation of equation (80) also becomes 0.

[0311] The value of σ in equation (80), however, is
Sampled a finite number of times. Moreover, furthermore,
In principle, the sampling is performed at the zero crossing point of the phase-distorted signal.
Not exactly evenly spaced. However, as the number of samples increases, only if the "sampling density" is substantially constant throughout the entire time interval, regardless of whether sampling occurs at equal intervals.
It is clear that the sampling is well approximated by the integral in the continuous case.

[0312] The crosstalk reduction techniques described herein work better for low levels of crosstalk for two reasons. First, under low-level crosstalk, the sampling intervals tend 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. Figure 13A shows the time change of σ at the talk level (A=2) and the low crosstalk level (A
FIG. 13C, which shows the time change of σ when =10), compares the waveforms. Although FIG. 13A 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. 13c is almost sinusoidal, although the amplitude is much smaller. Therefore, if sampling is performed at approximately equal intervals, the total will be almost zero. Figure 13
The difference between A and FIG. 13C reflects the different values chosen for A in equation (67). Note how this affects the shape of the function representing σ (Equation (80)).

[0313] In summary, if the magnitude of crosstalk is low to medium, approximation by sampling is very effective. 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. The first method is to perform sampling not only at positive zero crossing points of the P signal but 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 P' and Q' are made large enough), you can still get low to moderate levels of crosstalk. You can avoid losing the benefits gained from crosstalk. For example, the phase distortion α and amplitude of a signal mixed with crosstalk when A=2, P′=6, and Q′=5
Please refer to FIGS. 13A and 13B, which respectively show Bsin(2πω×Pt+α). Here, the ratio of the main signal to the interference signal is only 2:1, and the shape of the σ function is a rounded sawtooth shape. However, the integral over one revolution of the rounded sawtooth wave in FIG. 13A is still 0, and even with finite sampling, this integral can be approximated as many times as the number of sampling points is sufficiently increased.

Once-Per-Revolution Sensing for P# and Q# There are many ways in which an absolute reference mark can be placed on the waveform from the sensor. For example, there can be detectable non-uniformity in the spacing of gears or rotors. In this way, each rotation causes one corresponding periodic variation in the signal from the sensor. Such non-uniformity can be achieved by a variety of means, including monotonically increasing the pole spacing, having poles wider than normal poles, and increasing the normal spacing between two poles. This can be achieved by making the spacing slightly narrower or wider than the spacing, and by providing a missing pole as described above. 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 non-uniformities provided for once-per-revolution marks from others. For example, consider optically detecting both transparent and opaque regions alternately provided on a rotor. If the beams are very well collimated, as is probably 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. This "fidelity" in detection is
Although it requires more effort to reach that point, it is possible with magnetic and capacitive sensing mechanisms. For example, a magnetic sensor whose magnetic poles extend from the north and south poles of the magnet can have its space above and below the tip of the edge line along the tooth crests of a gear, with the nearest tooth The change in magnetic flux caused by the passage can be maximized and the extent to which adjacent teeth and alternating flux paths influence the output signal of the sensor can be minimized. 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. This means that certain complications in estimating or "smoothing out" non-uniformities for data processing convenience are 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 certain magnetic application embodiments described above, the magnetic sensor does not have a "narrow field of view." Referring again to FIG. 3A, for example, as soon as the magnetic field lines leave the magnetic pole 25 at the end closest to the gear 5, the magnetic field lines spread out in all directions towards the gear. 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, but some other cycles have their transitions shifted from where they should be.

[0317] To further summarize the situation, it may be inconvenient to assume that all sensors are constructed and installed 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 though the polarities may 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, an apparent misalignment will occur between the sensors of different polarities at positions near the missing tooth, and the procedure for "filling" the missing tooth will change accordingly. 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 depends on "when the information becomes available" and "what it is".
It's not a difference. Even if such a sensor is used to make coarse phase measurements (i.e., measuring the percentage of a revolution between the absolute reference marks of two rotors), the apparent deviation is It only introduces a certain offset in the resulting answer. Such offsets are easily removed once their constant 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, it is not difficult to recognize long periods in each of the signals A-X and to ascertain the case or the polarity of the case 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, Figures 14A and 14B
It is easy to correct the positions of transition points containing errors and to approximate missing transitions according to the constant relationship shown in .

[0319] Of course, all sensors may have the same selected polarity and always use one of the two situations shown in FIGS. 14A and 14B. However, some believe that conditions such as having the same selected polarity are conditions that may no longer hold due to 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.

[0320] 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. The microprocessor arbitrarily selects the cycles of each waveform that serve as pseudo-absolute reference marks to which the various p# and Q# are referenced. The selected cycles are repeatedly recognized by counting cycles modulo P and cycles modulo Q. Thus,
P# and Q# are determined by noting what the modulus count is when the measurement request is received.

[0321] Generalized phase measurement By using a pseudo-absolute reference mark, Eq.
(1), 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 (such as distance) that result in corresponding phase shifts due to propagation delays.

[0322] 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 this need not occur at the same time, but rather that one may occur immediately after the other or after some delay, quite separately. Similarly, they may partially overlap each other.

Angle Measurement Techniques 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 around a common rotational axis.
An orbital motion is possible 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.

[0324] The information contained in the input and reference signals may be configured to be retrieved after at least one revolution of transition time data has been captured and stored in a storage device. In order to identify an index pole, it is convenient to physically remove the pole and place in memory the estimated transition flagged by this missing pole.

[0325] During at least one revolution of each rotor, calculate the average of successive times when a pole occurs to determine the average time when 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 single poles, at which point the time interval suddenly drops to zero.
and then 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 revolution 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 the 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. If both summations are always initiated by (or wait until) the detection or occurrence of the respective index pole, then the difference in the average times of occurrence is in fact a measure of the above-mentioned time interval. This is certainly possible, but
This goes against the requirement that rotations related to each sum 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 maximum. 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.

[0327] In return for this flexibility in when to start the summation, we must ensure that we do 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 measured values of the average values of the occurrences of both equivalent single poles. Similarly, the average time interval between input rotor poles must be subtracted from the above difference for each pole skip on the input rotor side. 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 includes all the extra confidence products given by the 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.

[0329] 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, or "turning point."

[0330] The measurement or corrected measurement of the time interval between the equivalent monopoles is a direct indication of the input angle (of course
(appropriate scaling) or may be compared to a residual time interval related to some arbitrary input condition. This arbitrary input condition may be "0 degrees" 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 may be due to the initial difference between the two mean times for the equivalent single pole when the index pole coincidence occurs, or may simply be corrected for another measurement or after the measurement for purely arbitrary input conditions. can represent a value.

[0331] The measurement technique described above also applies when the ratio of frequencies is a rational number (i.e. an integer number of cycles of one signal occurs in 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. If the method described above is used to measure the phase between two signals, for example, where P cycles of one are within an equal length of time to Q cycles of the other, then as the index cycle: It is convenient to use any cycle of each waveform and then use each Pth and Qth cycle as an index cycle. The Pth and Qth cycles are respectively
They can be easily distinguished by counting the cycles of the signals involved by modP and modQ.

[0332] The phase measurement technique described above may have a pair of sensors placed on diametrically opposite sides. 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 corrected for a unique offset relative to one of the four. 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 poles are selected for one rotor and Q poles are selected for the other rotor. The irreducible type of fraction P/Q is a fraction
Let P′/Q′. However, it is assumed that both P' and Q' are not equal to 1. Of course, P and Q may be selected such that P/Q is already irreducible in a state where both P and Q are not 1.

[0334] 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.

[0335] The phase measurement techniques described above are preferred in this regard. This is because this technique measures the average over an integer number of times and allows P and Q to be set to arbitrary values.

[0336] Method of 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, a "one-round" error requires one pair of diameter-opposed sensors, a "two-round" error requires two pairs separated by 90 degrees, and so on. If phase measurements are performed using separate sensors before such averaging, when the two signals are analogously averaged before phase measurement, the phase information in the smaller amplitude signal will be replaced by the larger amplitude signal. There will be no more distortion. 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 drawings]

1 is a perspective view of the mechanical part of a device according to an embodiment of the invention; FIG.

FIG. 2 is an exploded view of the components of FIG. 1;

FIG. 3A is a block diagram of an apparatus according to one embodiment of the invention.

FIG. 3B is a block diagram of an apparatus according to one embodiment of the invention.

FIG. 3C is a block diagram of an apparatus according to 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: Magnet 29, 30, 31, 32: Amplifier 33, 34, 35, 36: Zero crossing detector 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.