Angle sensor, a bearing unit, electrical motor, a control system and error-check system

Abstract

An angle sensor is provided for determining an absolute angle signal of a first part rotated with respect to a second part. The angle sensor comprises a first grating ring for generating a first signal representative of a relative position of a first sensor along a corresponding ring segment of the first grating ring. The angle sensor further comprises a second grating ring for generating a second signal representative of a relative position of a second sensor along the corresponding ring segment of the second grating ring. The first plurality and the second plurality are co-prime numbers and a difference between the first plurality and the second plurality being larger than 1. The angle sensor also comprises a calculator configured for calculating the absolute angle signal using a first linear combination of the first signal and the second signal.

Claims

1. An angle sensor for determining an absolute angle signal of a first part rotated with respect to a second part, the angle sensor comprising: a first grating ring being constituted of a first plurality of first grating elements being arranged adjacent to each other constituting ring segments, each first grating element interacting with a first sensor for generating a first signal representative of a relative position of the first sensor along the corresponding ring segment of the first grating ring; a second grating ring being constituted of a second plurality of second grating elements being arranged adjacent to each other constituting ring segments, each second grating element interacting with a second sensor for generating a second signal representative of a relative position of the second sensor along the corresponding ring segment of the second grating ring, the first grating ring and the second grating ring being configured to rotate the same rotation angle as the first part is rotated with respect to the second part, the first plurality and the second plurality being co-prime numbers and a difference between the first plurality and the second plurality being larger than one; and a calculator configured for determining the absolute angle signal using a first linear combination of the first signal and the second signal and an electrical angle signal of an electrical motor using the first grating ring and the second grating ring, wherein the calculator comprises a corrector configured for reducing a noise in the electrical angle signal by refining the absolute angle signal a first time by using the electrical angle signal to produce a refined absolute angle signal and refining the absolute angle signal a second time using the refined electrical angle signal that contains less noise than the electrical angle signal.

2. The angle sensor according to claim 1, wherein a difference between the first plurality and the second plurality being equal to a number of magnetic pole pairs of the electrical motor, wherein the calculator is configured for calculating the electrical angle signal by calculating the difference between the first signal and the second signal.

3. The angle sensor according to claim 2, wherein the corrector is configured for generating a virtual correction signal being a repetitive signal having a repetition frequency fitting a further integer times the electrical angle signal, the virtual correction signal comprising a sum of signal one and signal two, wherein signal one is chosen from a list comprising: the first signal, the second signal, an improved first signal and an improved second signal, wherein signal two is chosen from a list comprising: the absolute angle signal and an improved absolute rotation angle signal.

4. The angle sensor according to claim 2, the first plurality and the second plurality being co-prime number pairs indicated as pairs and the difference between the first plurality and the second plurality being equal to the number of magnetic pole pairs of the electrical motor, wherein: for the electrical motor comprising 2 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (15,17), (17,19), (19,21), (21,23), (23,25), (25,27), (27,29), (29,31), (31,33), (33,35), (35,37), (37,39), (39,41), (41,43), (43,45), for the electrical motor comprising 3 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (16,19), (17,20), (19,22), (20,23), (22,25), (23,26), (25,28), (26,29), (28,31), (29,32), (31,34), (32,35), (34,37), (35,38), (37,40), for the electrical motor comprising 4 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (15,19), (17,21), (19,23), (21,25), (23,27), (25,29), (27,31), (29,33), (31,35), (33,37), (35,39), (37,41), (39,43), (41,45), (43,47), for the electrical motor comprising 5 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (16,21), (19,24), (21,26), (24,29), (26,31), (29,34), (31,36), (34,39), (36,41), (17,22), (18,23), (39,44), (41,46), (44,49), (46,51), for the electrical motor comprising 6 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (17,23), (19,25), (23,29), (25,31), (29,35), (31,37), (35,41), (37,43), (41,47), (43,49), (47,53), (49,55), (53,59), (55,61), (59,65), for the electrical motor comprising 7 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (15,22), (20,27), (22,29), (27,34), (29,36), (34,41), (36,43), (17,24), (18,25), (41,48), (43,50), (48,55), (50,57), (24,31), (25,32), for the electrical motor comprising 8 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (15,23), (17,25), (23,31), (25,33), (31,39), (33,41), (39,47), (41,49), (47,55), (49,57), (55,63), (57,65), (63,71), (65,73), (19,27), for the electrical motor comprising 9 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (17,26), (19,28), (26,35), (28,37), (35,44), (37,46), (44,53), (46,55), (22,31), (23,32), (53,62), (55,64), (62,71), (64,73), (31,40), for the electrical motor comprising 10 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (19,29), (21,31), (29,39), (31,41), (39,49), (41,51), (49,59), (51,61), (59,69), (61,71), (17,27), (69,79), (71,81), (79,89), (81,91), for the electrical motor comprising 11 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (21,32), (23,34), (32,43), (34,45), (16,27), (17,28), (43,54), (45,56), (54,65), (56,67), (15,26), (27,38), (28,39), (65,76), (67,78), for the electrical motor comprising 12 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (23,35), (25,37), (35,47), (37,49), (47,59), (49,61), (59,71), (61,73), (71,83), (73,85), (83,95), (85,97), (95,107), (97,109), (107,119), for the electrical motor comprising 13 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (25,38), (27,40), (38,51), (40,53), (19,32), (20,33), (51,64), (53,66), (64,77), (66,79), (17,30), (32,45), (33,46), (77,90), (79,92), for the electrical motor comprising 14 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (15,29), (27,41), (29,43), (41,55), (43,57), (55,69), (57,71), (69,83), (71,85), (19,33), (83,97), (85,99), (23,37), (97,111), (99,113), for the electrical motor comprising 15 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (16,31), (29,44), (31,46), (44,59), (46,61), (22,37), (23,38), (59,74), (61,76), (74,89), (76,91), (37,52), (38,53), (89,104), (91,106), for the electrical motor comprising 16 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (17,33), (31,47), (33,49), (47,63), (49,65), (63,79), (65,81), (79,95), (81,97), (21,37), (95,111), (97,113), (27,43), (111,127), (113,129), for the electrical motor comprising 17 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (18,35), (33,50), (35,52), (50,67), (52,69), (25,42), (26,43), (67,84), (69,86), (84,101), (86,103), (23,40), (42,59), (43,60), (101,118), for the electrical motor comprising 18 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (19,37), (35,53), (37,55), (53,71), (55,73), (71,89), (73,91), (89,107), (91,109), (107,125), (109,127), (125,143), (127,145), (143,161), (145,163), for the electrical motor comprising 19 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (20,39), (37,56), (39,58), (56,75), (58,77), (28,47), (29,48), (75,94), (77,96), (94,113), (96,115), (25,44), (47,66), (48,67), (113,132), for the electrical motor comprising 20 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (21,41), (39,59), (41,61), (59,79), (61,81), (79,99), (81,101), (99,119), (101,121), (27,47), (119,139), (121,141), (33,53), (139,159), (141,161), for the electrical motor comprising 21 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (22,43), (41,62), (43,64), (62,83), (64,85), (31,52), (32,53), (83,104), (85,106), (104,125), (106,127), (52,73), (53,74), (125,146), (127,148), for the electrical motor comprising 22 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (23,45), (43,65), (45,67), (65,87), (67,89), (87,109), (89,111), (109,131), (111,133), (29,51), (131,153), (133,155), (37,59), (153,175), (155,177), for the electrical motor comprising 23 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (24,47), (45,68), (47,70), (68,91), (70,93), (34,57), (35,58), (91,114), (93,116), (114,137), (116,139), (31,54), (57,80), (58,81), (137,160), for the electrical motor comprising 24 motor pole pairs, the co-prime number pairs being selected from the list of co-prime pairs comprising: (25,49), (47,71), (49,73), (71,95), (73,97), (95,119), (97,121), (119,143), (121,145), (143,167), (145,169), (167,191), (169,193), (191,215), (193,217).

5. The angle sensor according to claim 1, wherein the first grating ring is a magnetic encoder having the first plurality of grating elements being the first plurality of magnetic poles, and the second grating ring is a magnetic encoder having the second plurality of grating elements being the second plurality of magnetic poles.

6. The angle sensor according to claim 1, wherein at least one of the first sensor and the second sensor is selected from a list comprising: a hall-sensor and a fiber Bragg grating coated with a magnetostrictive material.

7. The angle sensor according to claim 1, wherein at least one of the first sensor and the second sensor is selected from a list comprising: a resistive sensor, an inductive sensor, a reluctive sensor, an eddy-current sensor, a magnetoresistive sensor, a capacitive sensor, and an optical sensor.

8. The angle sensor according to claim 1, wherein the first grating ring and the second grating ring are connected to the first part being a rotating part, while the first sensor and the second sensor being connected to the second part being a static part.

9. The angle sensor according to claim 1, the first plurality and the second plurality being co-prime number pairs indicated as pairs, wherein the co-prime number pairs are selected from the list of co-prime pairs comprising: (15,29), (15,31), (16,31), (16,33), (17,33), (17,35), (18,35), (18,37), (19,37), (19,39), (20,39), (20,41), (21,41), (21,43), (22,43), (22,45), (23,45), (23,47), (24,47), (24,49), (25,49), (25,51), (26,51), (26,53), (27,53), (27,55), (28,55), (28,57), (29,57), (29,59), (30,59), (30,61), (31,61), (31,63), (32,63), (32,65), (33,65), (33,67), (34,67), (34,69), (35,69), (35,71), (36,71), (36,73), (37,73), (37,75), (38,75), (38,77), (39,77), (39,79), (40,79), (40,81), (41,81), (41,83), (42,83), (42,85), (43,85), (43,87), (44,87), (44,89), (45,89), (45,91), (46,91), (46,93), (47,93), (47,95), (48,95), (48,97), (49,97), (49,99), (50,99), (50,101), (51,101), (51,103), (52,103), (52,105), (53,105), (53,107), (54,107), (54,109), (55,109), (55,111), (56,111), (56,113), (57,113), (57,115), (58,115), (58,117), (59,117), (59,119), (60,119), (60,121), (61,121), (61,123), (62,123), (62,125), (63,125), (63,127), (64,127), (64,129), (65,129), (65,131), (66,131), (66,133), (67,133), (67,135), (68,135), (68,137), (69,137), (69,139), (70,139), (70,141), (71,141), (71,143), (72,143), (72,145), (73,145), (73,147), (74,147), (74,149), (75,149), (75,151), (76,151), (76,153), (77,153), (77,155), (78,155), (78,157), (79,157), (79,159), (80,159), (80,161), (81,161), (81,163), (82,163), (82,165), (83,165), (83,167), (84,167), (84,169), (85,169), (85,171), (86,171), (86,173), (87,173), (87,175), (88,175), (88,177), (89,177), (89,179), (90,179), (90,181), (91,181), (91,183), (92,183), (92,185), (93,185), (93,187), (94,187), (94,189), (95,189), (95,191), (96,191), (96,193), (97,193), (97,195), (98,195), (98,197), (99,197), (99,199), (100,199), (100,201), (101,201), (101,203), (102,203), (102,205), (103,205), (103,207), (104,207), (104,209), (105,209), (105,211), (106,211), (106,213), (107,213), (107,215), (108,215), (108,217), (109,217), (109,219), and (110,219).

10. The angle sensor according to claim 1, wherein the angle sensor is integrated into a bearing unit.

11. The angle sensor according to claim 1, wherein the angle sensor is integrated into an electric motor.

12. The angle sensor according to claim 1, wherein the angle sensor is integrated into a control system, wherein the control system is adapted to control the electric motor.

13. An error-check system for checking a determined electrical angle signal of an electrical motor using a determined absolute angle signal, the error-check system comprising an angle sensor, the angle sensor includes: a first grating ring being constituted of a first plurality of first grating elements being arranged adjacent to each other constituting ring segments, each first grating element interacting with a first sensor for generating a first signal representative of a relative position of the first sensor along the corresponding ring segment of the first grating ring, a second grating ring being constituted of a second plurality of second grating elements being arranged adjacent to each other constituting ring segments, each second grating element interacting with a second sensor for generating a second signal representative of a relative position of the second sensor along the corresponding ring segment of the second grating ring, the first grating ring and the second grating ring being configured to rotate the same rotation angle as the first part is rotated with respect to the second part, the first plurality and the second plurality being co-prime numbers and a difference between the first plurality and the second plurality being larger than 1, and a calculator configured for determining the absolute angle signal using a first linear combination of the first signal and the second signal and an electrical angle signal of an electrical motor using the first grating ring and the second grating ring, wherein the calculator comprises a corrector configured for reducing a noise in the electrical angle signal by refining the absolute angle signal a first time by using the electrical angle signal to produce a refined absolute angle signal and refining the absolute angle signal a second time using the refined electrical angle signal that contains less noise than the electrical angle signal, wherein a difference between the first plurality and the second plurality being equal to a number of magnetic pole pairs of the electrical motor, and wherein the calculator is configured for calculating the electrical angle signal by calculating the difference between the first signal and the second signal, wherein the angle sensor is adapted to determine both the electrical angle signal and the absolute angle signal, the error-check system being configured for determining whether the electrical angle signal is coherent with the absolute angle signal.

14. The error-check system according to claim 13, wherein the calculator further comprises a low-pass filter for eliminating high-frequency noise from the absolute angle signal.

15. A method of determining an absolute angle signal of a first part rotated with respect to a second part using an angle sensor, the angle sensor comprising: a first grating ring being constituted of a first plurality of first grating elements being arranged adjacent to each other constituting ring segments, each first grating element interacting with a first sensor for generating a first signal representative of a relative position of the first sensor along the corresponding ring segment of the first grating ring, a second grating ring being constituted of a second plurality of second grating elements being arranged adjacent to each other constituting ring segments, each second grating element interacting with a second sensor for generating a second signal representative of a relative position of the second sensor along the corresponding ring segment of the second grating ring, the first grating ring and the second grating ring being configured to rotate the same rotation angle as the first part is rotated with respect to the second part, the first plurality and the second plurality being co-prime numbers and a difference between the first plurality and the second plurality being larger than 1, and a computing device configured for determining the absolute angle signal and an electrical angle signal, the computing device comprising a corrector configured for reducing a noise in the electrical angle signal by refining the absolute angle signal a first time by using the electrical angle signal to produce a refined absolute angle signal and refining the absolute angle signal a second time using the refined electrical angle signal that contains less noise than the electrical angle signal, wherein the computing device performs the method comprises the steps of: capturing the first signal of the first sensor, capturing the second signal of the second sensor, determining a set of integer numbers C and D such that C*n1+D*n2=1, wherein n1 is the first plurality and n2 is the second plurality, and where n1 and n2 are coprime, and determining the absolute angle signal using a linear combination of the first signal and the second signal using the set of integer number C and D such that C*A1+D*A2=AA, wherein A1 is the first signal, A2 is the second signal, and AA is the absolute rotational angle signal, and determining the electrical angle signal of an electrical motor using the first grating ring and the second grating ring, wherein the absolute angle signal is twice refined, with a second time using a refined electrical angle signal that contains less noise than the electrical angle signal.

16. The method of claim 15, wherein the method comprises determining a difference between the first plurality and the second plurality being equal to a number of magnetic pole pairs of the electrical motor and determining the electrical angle signal by calculating a difference between the first signal and the second signal such that (A1A2)=EA, wherein A1 is the first signal, A2 is the second signal and EA is the electrical rotational angle.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the drawings:

(2) FIG. 1 illustrates a typical control system application of the invention;

(3) FIG. 2 illustrates a graphical illustration of the angle sensor according to the invention;

(4) FIG. 3 illustrates a side view of the angle sensor in which the magnet rings are arranged at radially different distances;

(5) FIG. 4 illustrates a side view of an alternative angle sensor setup according to the invention, in which the encoder magnet rings are arranged along an axle at axially different locations, preferably at the same radial distance from the axle;

(6) FIG. 5 illustrates an Absolute angle signal together with a first signal from a first grating ring 345 having n1=7 and a second signal from a second grating ring 340 having n2=3;

(7) FIGS. 6a, 6b, and 6c illustrate different steps in a known angle refinement technique; and

(8) FIGS. 7a and 7b illustrate the absolute angle signal and the electrical angle signal, respectively, containing a significant amount of noise.

DETAILED DESCRIPTION OF THE INVENTION

(9) FIG. 1 illustrates a typical application of the invention, where an electrical motor 100, for example, a brushless DC motor 100, is driven/controlled by a motor controller 120 with the help of an angle encoder 110. The angle encoder 110 is coupled to the motor axle 102 of the electrical motor 100. When the motor axle 102 turns the angle encoder 110 provides the motor controller 120 with a first signal A1 and a second signal A2 that represent the rotary position of the motor axle 102 and thus the positional relationship between a stator and a rotor of the motor 100. The motor controller 120 can convert the first signal A1 and the second signal A2 into an absolute angle signal AA and/or an electrical angle signal AE, and depending on the absolute angle signal AA and/or electrical angle signal AE convert a supplied power 125 into correct power signals 105 to feed to the motor 100. It is very important for an electronic controller 120 of a brushless DC motor 100 to know the rotational relationship between rotor and stator to enable the motor to be driven as efficiently as possible.

(10) FIG. 2 illustrates a graphical illustration of the angle sensor 110 according to the invention having a first grating ring 345 and a second grating ring 340. Each of the first grating ring 345 and the second grating ring 340 comprise a plurality of grating elements 225, 220 in which each of the grating elements 225, 220 is constituted by a magnetic pole pair (each magnetic pole-pair is indicated with N of North-pole and S of South-pole in FIG. 2). The first grating ring 345 comprises a first plurality n1 of grating elements 225, and the second grating ring 340 comprises a second plurality n2 of grating elements 220. The number of grating elements 225, 220 between the first grating ring 345 and the second grating ring 340 are different. When rotating the angle sensor 110 around an axle 302, a first sensor 355 (not shown in FIG. 2 as it is located behind or in front of the grating elements 225see FIG. 3) will generate a first signal A1, and a second sensor 350 (again not shown in FIG. 2 as it is located behind or in front of the grating elements 220see FIG. 3) will generate a second signal A2. Because the number of grating elements 225, 220 between the first grating ring 345 and the second grating ring 340 are different rotational angle information can be calculated from these first signal A1 and second signal A2.

(11) FIG. 3 illustrates a side view of an angle sensor 110 setup according to the invention, where encoder magnet rings 340, 345 are arranged at radially different distances and preferably on a same plane. The encoder magnet rings 340, 345 are typically mounted on a same plane about a rotatable 303 axle 302. Each encoder magnet ring 340, 345 will comprise a plurality of magnetic pole-pairs. With a sufficient number of magnetic pole-pairs around an encoder magnet ring 340, 345 a corresponding sensor unit 350, 355 will produce a sine wave output. In the known angle sensors the difference in number of pole-pairs on the inner ring 340 in relation to the outer ring 345 is one, for example n1=6 and n2=5, the phase difference is unambiguous for a full turn, thus creating a full turn absolute position encoder. In the angle sensor according to the invention, the difference between the number of pole-pairs on the inner ring 340 and the outer ring 345 is larger than one. To still ensure that the phase difference is unambiguous for a full turn, the first plurality n1 and the second plurality n2 are co-prime number. This will be further elucidated below.

(12) FIG. 4 illustrates a side view of an alternative position encoder setup according to the invention, where encoder magnet rings 440, 445 are arranged along an axle at axially different locations, preferably at a same radial distance from a rotating 403 axle 402. This embodiment also comprises corresponding sensor units 450, 455 mounted on a carrier 459.

(13) A first embodiment of this invention is about obtaining the absolute angle signal AA of a rotating shaft. The number of first grating elements n1 and the number of second grating elements n2 denote the number of magnetic pairs on the first grating ring 345 (outer ring) and the second grating ring 340 (inner ring) attached to this shaft 302 or axle 302, respectively. In our computations we will assume that magnetic pairs on each ring are identical. Note that in the example in FIG. 5, for deriving the absolute angle signal AA from the first signal A1 of the first grating elements 225 and the second signal A2 of the second grating elements 220, n1=7, and n2=3.

(14) Throughout the rest of the section, the following convention is used: AA, A1, A2[0, 2). Starting with the following equivalences.
A.sub.1n.sub.1AA(mod 2)
A.sub.2n.sub.2AA(mod 2)

(15) These equivalences may be written as:
n.sub.1AA=2k+A.sub.1
n.sub.2AA=2l+A.sub.2

(16) for some integers k and l. Multiplying the first equality by n.sub.2/2 and the second by n.sub.1/2 to obtain

(17) $\frac{n_{1} n_{2}}{2} AA = n_{2} k + \frac{n_{2}}{2} A_{1}$ $\frac{n_{1} n_{2}}{2} AA = n_{1} l + \frac{n_{1}}{2} A_{2}$

(18) Let us denote

(19) $\frac{n_{1} n_{2}}{2} AA by x, \frac{n_{2}}{2} A_{1}$
by a.sub.1 and

(20) $\frac{n_{1}}{2} A_{2}$
by a.sub.2. Now, we can write these equalities as equivalences as follows.
xa.sub.1(mod n.sub.2)(1)
xa.sub.2(mod n.sub.2)(2)

(21) If n.sub.1 and n.sub.2 are chosen to be coprime, then one can find a unique x between 0 and n.sub.1n.sub.2 that solves the above set of congruences by invoking the well-known Chinese remainder theorem. One may immediately recall the definition of x and deduce that a unique x between 0 and n.sub.1n.sub.2 corresponds to a unique A between 0 and 2.

(22) Thus, it can be concluded that if n.sub.1 and n.sub.2 are coprime, it is possible to recover the absolute angle signal AA of the shaft 302 by using the angles of the outer 345 and the inner ring 340.

(23) Now it will be shown how to derive the absolute angle AA numerically from A.sub.1 and A.sub.2. First, we give the solution to the congruences (1) and (2). We claim that x given by
x=n.sub.1Ca.sub.1+n.sub.2Da.sub.2(3)

(24) where C and D are solutions to Bezout's identity,
n.sub.1C+n.sub.2D=1(4)

(25) satisfies the congruences (1) and (2). To see this, first note that a.sub.2a.sub.1 is an integer. Multiplying (4) by a.sub.1, one gets:
n.sub.1a.sub.1C=a.sub.1n.sub.2a.sub.1D

(26) Substituting this into (3), we obtain
x=a.sub.1+n.sub.2D(a.sub.2a.sub.1)

(27) This shows that indeed xa.sub.1(mod n.sub.2). Using a similar reasoning one can show that x as given in (3) satisfies xa.sub.2(mod n.sub.1). Now, we need to show that x as given in (3) is the unique solution to (1) and (2) between 0 and n.sub.1n.sub.2. For this purpose suppose that there is another solution x satisfying (1) and (2). That means xx is divisible by both n.sub.1 and n.sub.2 and hence by n.sub.1n.sub.2. That means x=x+n.sub.1n.sub.2q for some integer q. Therefore, x given in (3) is the unique solution to (1) and (2) between 0 and n.sub.1n.sub.2.

(28) Now substituting the definitions of x, a.sub.1 and a.sub.2 into (3) to arrive at

(29) AA=CA.sub.1+DA.sub.2 This formulation shows how to obtain the absolute rotation angle signal AA directly from the angle of the first signal A1 of the first grating ring 345 (outer ring in FIG. 2) and the second signal A2 of the second grating ring 340 (inner ring).

(30) As a side note we would like to remark that AA is known modulo 2 only. If the sum CA.sub.1+DA.sub.2 is equal to, say 10, this does not mean the shaft has rotated 5 times. It only means the shaft is at its reference position, i.e. 100 (mod 2).

EXAMPLE

(31) Assume n.sub.1=143 and n.sub.2=119. The Bezout numbers are then 5 and 6. (1435+119(6)=1)

(32) After measuring the first signal A1 (angle of the outer ring), and the second signal A2 (angle of the inner ring), the absolute angle signal AA of the shaft is simply given as 5A.sub.16A.sub.2.

(33) The second embodiment of this invention is about making the absolute angle signal AA more accurate and preserving the accuracy of the electrical angle signal EA. In a design example, n.sub.1=144 and n.sub.2=120. Electrical angle signal EA, which is required to have a frequency 24 times the mechanical frequency is immediately obtained by subtracting A.sub.2 from A.sub.1.
EA=A.sub.1A.sub.2

(34) What is noteworthy about this design is that exactly 6 revolutions of A.sub.1 fit in each revolution of the electrical angle signal EA (144/24=6). This allows for a refinement procedure which increases the accuracy of EA by a factor of 6{square root over (2)}. Details of this refinement procedure can be found with respect to FIGS. 6a to 6c. To explain this refinement procedure two angle signals are needed: coarse angle signal and refiner angle signal. We will refine the coarse angle signal using the refiner angle signal. In FIG. 6a, coarse angle is represented by the solid line and the refiner angle signal is represented by the dashed line. It is assumed that an exact integer number of revolutions of the refiner angle signal fit in a single revolution of the coarse angle signal. This integer number is k in FIG. 6a. There is assumed to be a zero-mean noise with standard deviation .sub.c in the coarse angle signal and a zero-mean noise with standard deviation .sub.1, in the refiner angle signal. Typically, .sub.c>.sub.r. For ease of exposition, the noise is not shown in the FIGS. 6a to 6c.

(35) Once the coarse angle signal and refiner angle signal are retrieved, the following calculations can be done to pertaining to the refinement procedure. First, the range of the coarse angle signal is changed from [0,2) to [0, k) by multiplying it by k/2 and subsequently also changing the range of the refiner angle signal from [0,2,) to [0,1) by dividing it by 2. The resulting angles are shown in FIG. 6b. Next, the decimal part of each scaled coarse angle signal is truncated, i.e. we rounded towards zero, to get the FIG. 6c.

(36) Finally, the scaled and truncated coarse angle signal and the scaled refiner angle signal are added to obtain the scaled and refined coarse angle, which has a range [0, k). Multiplying it by 2/k gives us the refined coarse angle signal in the range [0,2). Hence, we exchanged a noise of standard deviation .sub.c with a noise of standard deviation .sub.r/k.

(37) Now we return to a different design where n.sub.1=143 and n.sub.2=119. The electrical angle signal EA is still given by A.sub.1A.sub.2. However, there is no longer a whole number of revolutions of either the first signal A1 or the second signal A2 that fit in an electrical revolution of the electrical angle signal EA. Thus, the electrical angle cannot be refined using the know method of refining as shown in FIGS. 6a to 6c. To overcome this issue, the following algorithm is presented. First, the absolute angle signal AA is calculated using AA=5A.sub.16A.sub.2 and the electrical angle signal by EA=A.sub.1A.sub.2. Since a whole number (24) of electrical revolutions fit in each mechanical revolution, we refine the absolute angle signal AA using the electrical angle signal EA. Then, we sum the refined absolute angle signal AA.sub.refined, and the first signal A.sub.1 to get an angle that has a frequency 144 times the mechanical frequency.
A.sub.1*=A.sub.1+AA.sub.refined

(38) A.sub.1* is the angle we would get instead of A.sub.1 if n.sub.1 were 144 instead of 143. Since 6 revolutions of A.sub.1* fit in each electrical angle, we can refine the electrical angle by using A.sub.1*. Thus, in comparison with the current design, the new design offers the absolute angle signal AA with very little loss in the accuracy of the electrical angle signal EA.

(39) Furthermore, the absolute angle signal AA can be refined a second time by using the refined electrical angle signal EA.sub.refined. Since the refined electrical angle signal EA.sub.refined contains less noise than the electrical angle signal EA, this second refinement will result in a more accurate absolute angle signal. Denoting this refined absolute angle signal by AA.sub.refined*, we can calculate
A.sub.1**=A.sub.1+AA.sub.refined*

(40) A.sub.1** is the same as A.sub.1* except that it is more accurate. Using A.sub.1** we can refine the electrical angle signal EA a second time and using this doubly refined electrical angle, we can refine the absolute angle a third time and so on. As the number of these refinement iterations increases, the accuracy of the artificial angle (of the frequency 144 times the mechanical frequency) approaches the accuracy of A.sub.1. In this process, the accuracies of the electrical angle and the absolute angle approach their limit values.

(41) The error-check system according to the invention also used the absolute angle signal AA or the refined absolute angle signal AA.sub.refined together with the electrical angle signal EA or the refined electrical angle signal EA.sub.refined to perform a error-check procedure. Considering, for example, the absolute angle signal AA shown in FIG. 7a and the electrical angle signal EA in FIG. 7b. One can see that they contain a significant amount of noise. As such, the refinement process may give wrong estimates of these angles. For this purpose, the following check in the algorithm may be used. The refined absolute angle signal is indicated by FAA and the refined electrical angle signal by FEA. We have that

(42) $[\begin{matrix} FAA \\ FEA \end{matrix}] = [\begin{matrix} 5 & - 6 \\ 1 & - 1 \end{matrix}] [\begin{matrix} A_{1} \\ A_{2} \end{matrix}]$

(43) Therefore, FAA and FEA need to be checked whether they satisfy the equation above. Put in another way,

(44) $[\begin{matrix} A_{1} \\ A_{2} \end{matrix}] = [\begin{matrix} - 1 & 6 \\ - 1 & 5 \end{matrix}] [\begin{matrix} FAA \\ FEA \end{matrix}]$

(45) It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. Use of the verb comprise and its conjugations does not exclude the presence of elements or steps other than those stated in a claim. The article a or an preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Angle sensor, a bearing unit, electrical motor, a control system and error-check system

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G01D5/2454

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G01D5/24428

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G01D5/36

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G01D5/245

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G01D5/245

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G01D5/36

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G01D5/244

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