Method for determining the position of a moving part along an axis, using an inductive sensor

1. A method using an inductive sensor ( 10 ) for determining a position of a moving part, called a “target” (T), along an axis (X), where said inductive sensor ( 10 ) includes each of

a primary winding (B 1 ) generating an electromagnetic field,

a first secondary winding (R 1 ), generating a first voltage signal (V 1 ) of a sine function type, representing a current induced in said first secondary winding (R 1 ) when the target (T) moves in front of the first secondary winding (R 1 ),

a second secondary winding (R 2 ), generating a second voltage signal (V 2 ) of a cosine function type, representing a current induced in said second secondary winding (R 2 ) when the target moves in front of the second secondary winding (R 2 ), and

a calculation unit ( 20 ′) in communication with the first and second secondary windings (R 1 , R 2 ),

where the first and second secondary windings (R 1 , R 2 ) generate said first and second voltage signals (V 1 , V 2 ) as a function of a spatial angle, representing the position of the target (T) along the axis (X),

said method, carried out by the calculation unit, comprising:

receiving the first voltage signal (V 1 ) and the second voltage signal (V 2 ) respectively from the first secondary winding (R 1 ) and the second secondary winding (R 2 ); and the steps of:

Step 1: calculating an arctangent function (tan(θ)) on the basis of the first voltage signal (V 1 ) and the second voltage signal (V 2 );

Step 2: calculating an error (ε(θ)) between the calculated arctangent function (tan(θ)) and a predetermined straight line (D L ); and

Step 3: calculating positions of linearization points (θ i ) of the arctangent function (tan(θ)) according to the formula

θ

i

=

(

i

-

1

)

×

C

u

(

n

-

1

)

-

[

sin

⁡

(

(

i

-

1

)

×

2

×

π

(

n

-

1

)

)

×

F

×

C

u

]

where:

i is an index of the linearization points, varying from 1 to n,

(θ i ) is the position of the linearization point i as a spatial angle,

F is a spacing factor of the linearization points, where F>0 and the maximum of F, F MAX , is such that:

F

MAX

<

(

i

-

1

)

×

C

u

(

n

-

1

)

-

[

sin

⁡

(

(

i

-

1

)

×

2

×

π

(

n

-

1

)

)

×

C

u

]

C u is a useful travel of the sensor along the axis as a spatial angle;

Step 4: for each value of the arctangent function (tan(θ)), finding an index (i) of the linearization point such that:

θ i <θ<θ i+1

where:

θ i is the position of the linearization point i as a spatial angle,

θ i+1 is the position of the linearization point (i+1) as a spatial angle,

θ is a spatial angle;

Step 5: calculating a correction to be applied to the arctangent function (tan(θ)) according to the formula

Corr

⁡

(

tan

⁡

(

θ

)

)

=

ɛ

⁡

(

θ

i

)

+

[

ɛ

⁡

(

θ

i

+

1

)

-

ɛ

⁡

(

θ

i

)

]

×

[

tan

⁡

(

θ

)

-

tan

⁡

(

θ

i

)

tan

⁡

(

θ

i

+

1

)

-

tan

⁡

(

θ

i

)

]

where:

Corr(tan(θ)) is the correction on the arctangent function at the spatial angle θ,

ε(θ i ) is the error at the spatial angle θ i ,

ε(θ i+1 ) is the error at the spatial angle θ i+1 ,

tan(θ i ) is the value of the arctangent function at the spatial angle θ i ,

tan(θ i+1 ) is the value of the arctangent function at the spatial angle θ i+1 ,

tan(θ) is the value of the arctangent function at the spatial angle θ;

Step 6: calculating a corrected arctangent function (tan corr (θ)):

tan corr (θ)=tan(θ)+Corr(tan(θ))

where:

tan corr (θ) is the corrected arctangent function,

tan(θ) is the arctangent function,

Corr(tan(θ)) is the correction on the arctangent function at the spatial angle θ; and

Step 7: determining the position (θ) of the target (T) along the axis (X) on the basis of the corrected arctangent function in accordance with (tan corr (θ)), where (tan corr (θ)) corrects for an imprecision of the position of the target (T) at opposite ends (E 1 , E 2 ) of the useful travel, and thereby extend the useful travel (Cu) of the target (T).

2. The determination method as claimed in claim 1 , wherein in step 2, the predetermined straight line (D L ) is a linear regression (y DL ) of the arctangent function (tan(θ)).

3. An inductive sensor ( 10 ) for sensing a position of a target (T) along an axis (X) of the sensor, comprising:

a primary winding (B 1 ) generating an electromagnetic field;

a first secondary winding (R 1 ), generating a first voltage signal (V 1 ) of a sine function type, representing a current induced in said first secondary winding (R 1 ) when the target (T) moves in front of the first secondary winding (R 1 );

a second secondary winding (R 2 ), generating a second voltage signal (V 2 ) of a cosine function type, representing a current induced in said second secondary winding (R 2 ) when the target moves in front of the second secondary winding (R 2 ); and

a calculation unit ( 20 ′) in communication with the first and second secondary windings (R 1 , R 2 ), and configured to receive the first voltage signal (V 1 ) and the second voltage signal (V 2 ) respectively from the first secondary winding (R 1 ) and the second secondary winding (R 2 ), and further to operate as

first means (M 1 ) for calculating an arctangent function (tan(θ)) on the basis of the first voltage signal (V 1 ) and the second voltage signal (V 2 );

second means (M 2 ) for calculating an error (ε(θ)) between the calculated arctangent function (tan(θ)) and a predetermined straight line (D L );

third means (M 3 ) for calculating positions of linearization points (θ i ) of the arctangent function (tan(θ)) according to the formula

θ

i

=

(

i

-

1

)

×

C

u

(

n

-

1

)

-

[

sin

⁡

(

(

i

-

1

)

×

2

×

π

(

n

-

1

)

)

×

F

×

C

u

]

where:

i is an index of the linearization points, varying from 1 to n,

(θ i ) is the position of the linearization point i as a spatial angle,

F is a spacing factor of the linearization points, where F>0 and the maximum of F, F MAX , is such that:

F

MAX

<

(

i

-

1

)

×

C

u

(

n

-

1

)

-

[

sin

⁡

(

(

i

-

1

)

×

2

×

π

(

n

-

1

)

)

×

C

u

]

C u is a useful travel of the sensor along the axis as a spatial angle,

means (M R ) for finding an index (i) of the linearization point such that, for each value of the arctangent function:

θ i <θ<θ i+1

where:

θ i is the position of the linearization point i as a spatial angle,

θ i+1 is the position of the linearization point (i+1) as a spatial angle,

θ is a spatial angle;

fourth means (M 4 ) for calculating a correction to be applied to the arctangent function according to the formula:

Corr

⁡

(

tan

⁡

(

θ

)

)

=

ɛ

⁡

(

i

)

+

[

ɛ

⁡

(

i

+

1

)

-

ɛ

⁡

(

i

)

]

×

[

tan

⁡

(

θ

)

-

tan

⁡

(

i

)

tan

⁡

(

i

+

1

)

-

tan

⁡

(

i

)

]

where:

Corr(tan(θ)) is the correction on the arctangent function at the spatial angle θ,

ε(i) is the error at the linearization point i,

ε(i+1) is the error at the linearization point (i+1),

tan(i) is the value of the arctangent function at the point i,

tan(i+1) is the value of the arctangent function at the point (i+1),

tan(θ) is the value of the arctangent function at the spatial angle θ;

fifth means (M 5 ) for calculating a corrected arctangent function:

tan corr (θ)=tan(θ)+Corr(tan(θ))

where:

tan corr (θ) is the corrected arctangent function,

tan(θ) is the arctangent function,

Corr(tan(θ)) is the correction on the arctangent function at the spatial angle θ; and

means (M D ) for determining the position (θ) of the target (T) along the axis (X) on the basis of the corrected arctangent function (tan corr (θ)),

where (tan corr (θ)) corrects for an imprecision of the position of the target (T) at opposite ends (E 1 , E 2 ) of the travel, and thereby extend the useful travel (Cu) of the target (T).

4. A motor vehicle, comprising an inductive sensor ( 10 ) as claimed in claim 3 .