Electrical angle-detecting apparatus and driving system of synchronous motor using the same

Claims

What is claimed is:

1. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

first memory means for previously storing a relationship between electrical angles and values of electric current flowing in response to a predetermined voltage applied to a first interphase combination,

second memory means for previously storing a relationship between electrical angles and values of electric current flowing in response to said predetermined voltage applied to a second interphase combination, which is different from said first interphase combination;

first measurement means for applying said predetermined voltage to said first interphase combination and measuring a value of a first electric current flowing in response to said predetermined voltage;

second measurement means for applying said predetermined voltage to said second interphase combination and measuring a value of a second electric current flowing in response to said predetermined voltage; and

electrical angle calculation means for determining an electrical angle of said synchronous motor in a range of through 2.pi. based on said values of said first and second electric currents measured by said first measurement means and said second measurement means with reference to said relationships stored in said first memory means and said second memory means.

2. An electrical angle-detecting apparatus in accordance with claim 1, wherein said first memory means and said second memory means respectively store relationships between values of electric current and inductances corresponding to an electrical angles.

3. An electrical angle-detecting apparatus in accordance with claim 1, wherein a pair of poles of said synchronous motor comprise a north pole and a south pole having different magnetic properties, so that a values of electric current with respect to an electrical angle of a first .pi. is made different from that with respect to an electrical angle of a second .pi..

4. An electrical angle-detecting apparatus in accordance with claim 1, wherein at least one of said first measurement means and said second measurement means comprises voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and said first or second interphase combination, to said first or second interphase combination.

5. An electrical angle-detecting apparatus in accordance with claim 1, wherein at least one of said first measurement means and said second measurement means measuring a respective one of said first and second electric currents as a time period elapsing before said respective one of said first and second electric currents reaches a predetermined level.

6. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 to .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified.

7. An electrical angle-detecting apparatus in accordance with claim 6, said range specification means further comprises:

voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination;

detection means for detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied; and

electrical angle range specification means for specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected by said detection means.

8. An electrical angle-detecting apparatus in accordance with claim 7, wherein said electrical angle range specification means further comprises means for specifying said range of said electrical angle based on comparison between an intensity of said electric current and a predetermined threshold value.

9. An electrical angle-detecting apparatus in accordance with any one of claims 1, 6, or 7, said apparatus further comprising means for abruptly reducing said applied voltage after application of said voltage to said interphase combination and detection of a value of electric current in response to said applied voltage.

10. An electrical angle-detecting apparatus in accordance with any one of claims 1, 6, or 7, said apparatus further comprising means for regulating a frequency of said applied voltage to be higher than a frequency of a driving ac voltage applied to said winding.

11. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

wherein said electrical angle calculation means further comprises:

current detection means for successively applying said fixed voltage to each of N interphase combinations in a three-phase synchronous motor so as to detect a value of electric current flowing in response to said fixed voltage, where N represents 3 or a greater integer;

selection means for selecting a value having a least error in linear approximation out of said N values of electric current detected by said current detection means; and

approximation means for calculating an electrical angle of said synchronous motor by linear approximation of said value of electric current thus selected by said selection means.

12. An electrical angle-detecting apparatus in accordance with claim 11, wherein said current detection means further comprises:

means for actually measuring values of electric current for (N-1) interphase combinations out of said N interphase combinations; and

means for calculating a value of electric current for a last interphase combination based on values measured for said (N-1) interphase combinations.

13. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

wherein said synchronous motor comprises a three-phase synchronous motor using three-phase alternating current;

said electrical angle calculation means further comprising:

electric current detection means for detecting an electric current flowing in response to said fixed voltage applied into each interphase combination of said three phases;

area specification means for specifying one of six areas, which are defined by equally dividing an electrical angle of .pi., according to an intensity and a mean of the three electric currents detected by said electric current detection means;

phase calculation means for determining a phase of said electrical angle in said specified area by an approximate equation of .theta..congruent.(tan2.theta.)/2 for an interphase where said electric current has an extreme value; and

angle calculation means for calculating said electrical angle in said range of 0 through .pi. or in said range of .pi. through 2.pi. based on said specified area and said phase determined by said phase calculation means.

14. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

wherein said range specification means further comprises,

voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination,

detection means for detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied, and

electrical angle range specification means for specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected by said detection means;

wherein said electrical angle range specification means further comprises means for specifying said range of said electrical angle based on comparison between an intensity of said electric current and a predetermined threshold value;

wherein said electrical angle range specification means further comprises means for selecting one of plural threshold values according to an area to which an electrical angle calculated by said electrical angle calculation means belong to.

15. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means-for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

wherein said range specification means further comprises,

voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination,

detection means for detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied, and

electrical angle range specification means for specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected by said detection means;

wherein said voltage application means comprises voltage determination means for determining said voltage to be applied according to an area to which an electrical angle calculated by said electrical angle calculation means belong to;

said electrical angle range specification means further comprising means for specifying said range of said electrical angle based on comparison between a predetermined threshold value and an intensity of electric current flowing through said specific interphase combination in response to said voltage applied.

16. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.; and

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

wherein said range specification means further comprises:

first voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination;

second voltage application means for applying a reverse voltage having an opposite polarity to that of said applied voltage to another interphase combination, which is different from said specific interphase combination; and

electrical angle range specification means for specifying a range of said electrical angle by a unit of .pi. based on comparison between intensities of electric currents flowing in response to said applied voltage and said reverse voltage.

17. An electrical angle-detecting apparatus in accordance with claim 16, said apparatus further comprising interphase determination means for determining said specific interphase combination and said another interphase combination, to which said first voltage application means and said second voltage application means apply said voltage and said reverse voltage, based on said range specified by said range specification means;

said voltage and said reverse voltage applied by said first voltage application means and said second voltage application means being defined as a lower limit of said non-linear region.

18. An electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

angle detection means for applying a fixed voltage to a specific interphase combination within an elapse of a time period required for each electrical angle .theta., which is determined by an upper limit of rotating speed of said synchronous motor, and detecting an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. based on a value of electric current flowing in response to said fixed voltage;

range specification means for determining, at least once, whether said electrical angle detected is in said range of 0 through .pi. or in said range of .pi. through 2.pi.; and

electrical angle updating means for determining an initial value of said electrical angle according to said electrical angle detected by said angle detection means and said range specified by said range specification means and updating a current electrical angle by said electrical angle most recently detected by said angle detection means.

19. A driving system of a synchronous motor comprising:

an electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising,

first memory means for previously storing a relationship between electrical angles and values of electric current flowing in response to a predetermined voltage applied to a first interphase combination,

second memory means for previously storing a relationship between electrical angles and values of electric current flowing in response to said predetermined voltage applied to a second interphase combination, which is different from said first interphase combination,

first detection means for applying said predetermined voltage to said first interphase combination to detect value of a first electric current flowing in response to said predetermined voltage,

second detection means for applying said predetermined voltage to said second interphase combination to detect value of a second electric current flowing in response to said predetermined voltage, and

electrical angle calculation means for determining an electrical angle of said synchronous motor in a range of 0 through 2.pi. based on said values of said first and second electric currents detected by said first detection means and said second detection means with reference to said relationships stored in said first memory means and said second memory means;

reverse electromotive voltage detection means for detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor;

second electrical angle detection means for detecting an electrical angle based on said reverse electromotive voltage detected by said reverse electromotive voltage detection means; and

driving voltage application means for applying a driving voltage to said winding according to results of detection by said electrical angle-detecting apparatus in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said second electrical angle detection means in a second range where said rotor rotates at a speed of not less than said predetermined level.

20. A driving system of a synchronous motor comprising:

an electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising:

first electrical angle calculation means for calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation based on a value of electric current flowing in response to a fixed voltage applied to each interphase combination;

range specification means for determining whether said electrical angle calculated is in a range of 0 through .pi. or in a range of .pi. through 2.pi.;

electrical angle determination means for determining an unequivocal electrical angle according to said electrical angle calculated and said range specified;

reverse electromotive voltage detection means for detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor;

second electrical angle detection means for detecting an electrical angle based on said reverse electromotive voltage detected by said reverse electromotive voltage detection means; and

driving voltage application means for applying a driving voltage to said winding according to results of detection by said electrical angle-detecting apparatus in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said second electrical angle detection means in a second range where said rotor rotates at a speed of not less than said predetermined level.

21. A driving system of claim 20, wherein said range specification means further comprises:

voltage application means for applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination;

detection means for detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied, and

electrical angle range specification means for specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected by said detection means.

22. A driving system of a synchronous motor comprising:

an electrical angle-detecting apparatus of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said apparatus comprising,

angle detection means for applying a fixed voltage to a specific interphase combination within an elapse of a time period required for each electrical angle .theta., which is determined by an upper limit of rotating speed of said synchronous motor, and detecting an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. based on a value of electric current flowing in response to said fixed voltage;

range specification means for determining, at least once, whether said electrical angle detected is in said range of 0 through .pi. or in said range of .pi. through 2.pi., and

electrical angle updating means for determining an initial value of said electrical angle according to said electrical angle detected by said angle detection means and said range specified by said range specification means and updating a current electrical angle by said electrical angle most recently detected by said angle detection means;

reverse electromotive voltage detection means for detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor;

second electrical angle detection means for detecting an electrical angle based on said reverse electromotive voltage detected by said reverse electromotive voltage detection means; and

driving voltage application means for applying a driving voltage to said winding according to results of detection by said electrical angle-detecting apparatus in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said second electrical angle detection means in a second range where said rotor rotates at a speed of not less than said predetermined level.

23. A method of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said method comprising the steps of:

(a) previously storing a relationship between electrical angles and values of electric current flowing in response to a predetermined voltage applied to a first interphase combination;

(b) previously storing a relationship between electrical angles and values of electric current flowing in response to said predetermined voltage applied to a second interphase combination, which is different from said first interphase combination;

(c) applying said predetermined voltage to said first interphase combination to detect a value of a first electric current flowing in response to said predetermined voltage;

(d) applying said predetermined voltage to said second interphase combination to detect a value of a second electric current flowing in response to said predetermined voltage; and

(e) determining an electrical angle of said synchronous motor in a range of 0 through 2.pi. based on said values of said first and second electric currents detected in said step (c) and step (d) with reference to said relationships stored in said step (a) and step (b).

24. A method of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said method comprising the steps of:

(a) previously storing values of electric current flowing in response to a fixed voltage applied to each interphase combination;

(b) applying said fixed voltage to each interphase combination and detecting electric currents flowing in response to said fixed voltage;

(c) calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation of said electric currents detected in said step (b) based on said values stored in said step (a); and

(d) determining whether said electrical angle calculated is in said range of 0 to .pi. or in said range of .pi. through 2.pi. so as to determine an unequivocal electrical angle based on said electrical angle calculated.

25. A method in accordance with claim 24, wherein said step (d) further comprises the steps of:

(d-1) applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination;

(d-2) detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied; and

(d-3) specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected in said step (d-2).

26. A method in accordance with any one of claims 23, 24, or 25, said method further comprising the step of: making a voltage abruptly discharged after application of said voltage to said interphase combination and detection of a value of electric current in response to said applied voltage.

27. A method of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said method comprising the steps of:

(a) applying a fixed voltage to a specific interphase combination within an elapse of a time period required for each electrical angle .theta., which is determined by an upper limit of rotating speed of said synchronous motor, and detecting an electrical angle in a range of 0 to .pi. or in a range of .pi. through 2.pi. based on a value of electric current flowing in response to said fixed voltage;

(b) determining, at least once, whether said electrical angle detected is in said range of 0 to .pi. or in said range of .pi. through 2.pi.; and

(c) determining an initial value of said electrical angle according to said electrical angle detected in said step (a) and said range specified in said step (b) and updating a current electrical angle by said electrical angle most recently detected in said step (a).

28. A method of driving a synchronous motor comprising the steps of:

(a) first electrical angle detection process of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said process comprising the steps of,

(a') previously storing a relationship between electrical angles and values of electric current flowing in response to a predetermined voltage applied to a first interphase combination,

(b') previously storing a relationship between electrical angles and values of electric current flowing in response to said predetermined voltage applied to a second interphase combination, which is different from said first interphase combination,

(c') applying said predetermined voltage to said first interphase combination to detect value of a first electric current flowing in response to said predetermined voltage,

(d') applying said predetermined voltage to said second interphase combination to detect value of a second electric current flowing in response to said predetermined voltage, and

(e') determining an electrical angle of said synchronous motor in a range of 0 through 2.pi. based on said values of said first and second electric currents detected in said step (c') and step (d') with reference to said relationships stored in said step (a') and step (b');

(b) second electrical angle detection process of detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor and detecting an electrical angle based on said reverse electromotive voltage thus detected; and

(c) application process of applying a driving voltage to said winding according to results of detection by said process (a) in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said process (b) in a second range where said rotor rotates at a speed of not less than said predetermined level.

29. A method of driving a synchronous motor comprising the steps of:

(a) first electrical angle detection process of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said process comprising the steps of,

(a') previously storing values of electric current flowing in response to a fixed voltage applied to each interphase combination,

(b') applying said fixed voltage to each interphase combination and detecting electric currents flowing in response to said fixed voltage,

(c') calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation of said electric currents detected in said step (b') based on said values stored in said step (a'), and

(d') determining whether said electrical angle calculated is in said range of 0 through .pi. or in said range of .pi. through 2.pi. so as to determine an unequivocal electrical angle based on said electrical angle calculated,

(b) second electrical angle detection process of detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor and detecting an electrical angle based on said reverse electromotive voltage thus detected; and

(c) application process of applying a driving voltage to said winding according to results of detection by said process (a) in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said process (b) in a second range where said rotor rotates at a speed of not less than said predetermined level.

30. A method of driving a synchronous motor comprising the steps of:

(a) first electrical angle detection process of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, comprising the steps of,

(a') previously storing values of electric current flowing in response to a fixed voltage applied to each interphase combination,

(b') applying said fixed voltage to each interphase combination and detecting electric currents flowing in response to said fixed voltage,

(c') calculating an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. by approximation of said electric currents detected in said step (b') based on said values stored in said step (a'), and

(d') determining whether said electrical angle calculated is in said range of 0 through .pi. or in said range of .pi. through 2.pi. so as to determine an unequivocal electrical angle based on said electrical angle calculated,

wherein said step (d') further comprises the steps of,

(d'-1) applying a voltage corresponding to a non-linear region of magnetic properties of a magnetic circuit, which consists of said rotor and a specific interphase combination, to said specific interphase combination,

(d'-2) detecting a value of electric current flowing through said specific interphase combination in response to said voltage applied, and

(d'-3) specifying a range of said electrical angle by a unit of .pi. based on said value of said electric current thus detected in said step (d'-2);

(b) second electrical angle detection process of detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor and detecting an electrical angle based on said reverse electromotive voltage thus detected; and

(c) application process of applying a driving voltage to said winding according to results of detection by said process (a) in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said process (b) in a second range where said rotor rotates at a speed of not less than said predetermined level.

31. A method of driving a synchronous motor comprising the steps of:

(a) first electrical angle detection process of detecting an electrical angle of a synchronous motor which makes a multi-phase alternating current flow through a winding to rotate a rotor by means of an interaction between a magnetic field formed by said winding and a magnetic field formed by a permanent magnet, said process comprising the steps of,

(a') applying a fixed voltage to a specific interphase combination within an elapse of a time period required for each electrical angle .theta., which is determined by an upper limit of rotating speed of said synchronous motor, and detecting an electrical angle in a range of 0 through .pi. or in a range of .pi. through 2.pi. based on a value of electric current flowing in response to said fixed voltage,

(b') determining, at least once, whether said electrical angle detected is in said range of 0 through .pi. or in said range of .pi. through 2.pi., and

(c') determining an initial value of said electrical angle according to said electrical angle detected in said step (a) and said range specified in said step (b') and updating a current electrical angle by said electrical angle most recently detected in said step (a');

(b) second electrical angle detection process of detecting a reverse electromotive voltage generated in said winding accompanied with rotation of said rotor and detecting an electrical angle based on said reverse electromotive voltage thus detected; and

(c) application process of applying a driving voltage to said winding according to results of detection by said process (a) in a first range where said rotor is at a stop or rotates at a speed of less than a predetermined level and according to results of detection by said process (b) in a second range where said rotor rotates at a speed of not less than said predetermined level.