Angular inertial sensor with speed variation compensation

Abstract

Angular sensor comprising: a resonator 2() capable of exhibiting a vibration mode, radial with respect to an axis of symmetry of the resonator (2); transducers (5.1, 5.2, 6.1, 6.2) to provide a first measurement signal and a second measurement signal of a deformation of the resonator (2) respectively along a first direction and a second direction orthogonal to each other of a reference frame of the vibration mode and to apply a force on the resonator (2) along these two orthogonal directions; and an electronic processing circuit (7) electrically connected to the transducers (5, 6) and arranged so as to determine from the measurement signals an estimate of an angular velocity applied to the angular sensor and to emit control signals of the transducers (6.1, 6.2).2) to generate and maintain a vibration of the resonator (2) at a frequency corresponding substantially to a theoretical natural frequency and with a substantially constant amplitude a and a substantially zero quadrature component q, by processing an amplitude control error where is an amplitude controlled to an amplitude setpoint, a quadrature control error, an angle estimation error and a phase estimation error, characterized in that the electronic processing circuit (7) is arranged to perform compensation making said errors insensitive to a variable angular velocity of the sensor by taking into account the theoretical natural frequency and the angle estimation of the angular sensor. FIGURE OF THE ABRIDGED: Fig. 1.

Description

Title of the invention: Angular inertial sensor with speed variation compensation The present invention relates to the field of inertial angular sensors such as vibrating resonator gyroscopes and gyroscopes. BACKGROUND OF THE INVENTION A known angular sensor, described in document FR-A-2749394, comprises: a resonator capable of exhibiting a second-order, planar, stationary, and radial vibration mode about an axis of the resonator; detector transducers for measuring a deformation of the resonator in two orthogonal directions relative to a reference frame of the vibration mode; and actuator transducers for applying a force to the resonator along these two orthogonal directions. The resonator and transducers are mounted in a housing, and electronic means are electrically connected to the transducers. The actuator transducers must be powered to excite the resonator in the specified vibration mode at a natural frequency co of the resonator, and the detector transducers will respectively emit a first measurement signal and a second measurement signal of the deformation.The measurement signals each have an in-phase component and a quadrature component which are modulated at the natural frequency co. . The electronic means are arranged to receive measurement signals and emit power signals to the actuator transducers in opposite phase to generate and maintain a vibration of the resonator at its resonance frequency by maintaining the vibration amplitude at a constant value via amplitude control and canceling a quadrature component of the vibration via quadrature control. In operation, if the casing is subjected to a rotation around the axis of the resonator by an angle 0 at a speed Q, the vibration field tends to shift under the effect of Coriolis forces: each vibration node then moves relative to the transducers by an angle 0e (commonly called the electric angle) proportional to the rotation Q, undergone by the casing, integrated over a time interval. The commonly accepted mathematical model for perfect vibrating gyroscopes, i.e., without defects, is: f fî l +cû 2 ri1=2aQri2 (1) [ i)2+ üJ 2 r}2= -2aQfi1 In this model:

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[0026] Q = @ is the angular velocity applied by the carrier to the angular sensor (the electrical angle 0e, corresponding to the angle of the vibration deformation in the modal frame, is ideally equal to ad)); Pi and ip are the coordinates of the vibration in the modal frame of reference; a is a form factor that depends on the shape of the resonator and is determined empirically during a calibration step; co is the natural frequency of the resonator. The estimated vibration state is affected by several errors, including an amplitude control error, an angle estimation error, a phase estimation error, and a quadrature control error. For simplicity, we will refer here to the amplitude control error as Xp- â0 (where Xp is an amplitude controlled by the amplitude setpoint), the angle estimation error as Yp, the phase estimation error as Xq, and the quadrature control error as Yq. These errors are defined as follows: Xp = xlcosθ + x2sinθ Yp = x2cosd - x^inG Xq = x3cos0 + x^sin0 Y q = -x3sind + x4cosÔ In these formulas: g is the estimate of the angle Oe of the deformation in the modal reference frame (the angle 0e is commonly called the electric angle); ^1 is the in-phase component of the first measurement signal and ^3 is the quadrature component of the first measurement signal; x2 is the in-phase component of the second measurement signal and ^4 is the quadrature component of the second measurement signal; ao is an amplitude control setpoint. In order to improve the performance of these angular sensors, enriched models have been proposed, notably that of the document DD Lynch, Vibratory Gyro Analysis by the Method of Averaging, Proceedings 2nd Saint Petersburg Int. Conf. on Gyroscopic Technology and Navigation, pp. 26-34, 1995. This model takes the following form: ' (jû2i]l=2aQ02+1^1^+ aQi]2 f]2+ m2t)2 =- aQr^

[0027] In this model:

[0028] Q is equal to ©;

[0029] r|i and r|2 are the coordinates of the vibration in the modal reference frame;

[0030] a is the traditional form factor

[0031] [3 is a second form factor dependent on the shape of the resonator;

[0032] co is the natural frequency of the resonator.

[0033] For the sake of simplification, it is common to neglect the terms in ctQ.

[0034] The inventors have, however, observed that this term introduces a non-negligible error between the estimated value of the angle applied to the angular sensor and the actual value of the angle applied to the angular sensor when the rotational speed of the housing is not constant. This error leads to an error in the estimation of the angular position of the vibration and therefore in the measurement of the amplitude control errors, quadrature control errors, angle estimation errors, and phase estimation errors.

[0035] SUBJECT OF THE INVENTION

[0036] The invention is notably aimed at improving the performance of inertial angular sensors. Summary of the invention

[0037] For this purpose, the invention provides an angular sensor comprising: a resonator capable of exhibiting a radial vibration mode with respect to an axis of symmetry of the resonator; detector transducers to provide a first measurement signal and a second measurement signal of a deformation of the resonator respectively along a first direction and a second direction orthogonal to each other of a reference frame of the vibration mode; actuator transducers to apply a force on the resonator along these two orthogonal directions;and an electronic processing circuit electrically connected to the transducers and arranged to determine, from the measurement signals, an estimate Q of an angular velocity applied to the angular sensor and to output power signals to the actuator transducers to generate and maintain a vibration of the resonator at a frequency corresponding substantially to a theoretical natural frequency and with a substantially constant amplitude a and a substantially zero quadrature component q, by processing an amplitude control error Xp- a0 where Xp is an amplitude of the vibration controlled to a setpoint of amplitude ^0, a quadrature control error Yq, an angle estimation error Yp and a phase estimation error Xq. The electronic processing circuit is arranged to perform compensation making said errors insensitive at a speed of ;

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[0051] variable rotation of the sensor, taking into account the theoretical natural frequency and the estimation of the angle of the angular sensor. By making the error measurement insensitive to the movements of the angular sensor, the performance of the angular sensor is improved. Using the theoretical natural frequency of the resonator instead of its actual natural frequency provides a sufficient approximation for compensation. According to a first embodiment, the electronic processing circuit is arranged so that the processing includes a phase of calculating compensated errors, yy Xq, used for the rest of the processing and such that: 5?"__1 . ( Y û vz ] ^P~ ,2 [A p -^ï q ) Indeed, from model (2), we can write the vibration in the following form: / / cos(-a0)\ / -sin(-a6)\ \ / / cos(-a0)'i / -sin(-a0)\ \ n~co -a . , sin <wt+(T , coswt +aûj a . . coswt+Q , . smwt l \sin(-a0) / ^\cos(-a3)l / \sm(-a0) / \cos(-a0) / / In this formula, J equals / 0 - 1 \. We then set / CO^0-Ct0)\ ct = (pq> in which is Ae \ sin(0-a0) / the estimation of the angle of vibration (commonly called the electrical angle) and is the estimation of the phase. Using the definition of errors mentioned above and dividing the variables by the theoretical natural frequency ^0, we obtain: ( Ypj =^(a Va0 + sinA <p4-gJVAecosA^ q = 7¾ -a VA9 sin^ + QjVÀ0coszl(p +^J(aVAe cos Acp + qJV^sïnA(p) ql \ / To reduce angle and phase estimation errors, as well as amplitude and quadrature control errors, it appears necessary to compensate for the Q terms. However, Q and w are two unknowns in the problem: is an unknown constant, and D is the angular velocity information from the angular sensor. must measure. To compensate for these terms as much as possible, we use Q, which are known and close to raw and respectively.

[0052] We then define the compensated errors Xp, yq, y, xq:

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[0054] The result is: 'an _ n' a VA0 cosA(p+qJVMSinA(p)--^J ife) -aV^Q smA(p + qJV^cosA(p -a VAe smAcp + qJV^cosA(p)+ aV^ cGsA(p+qJV&esinA(p\

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[0060] Finally, assuming that Q — qq and ~, we obtain: = a V A0 cosA(p + qJV^QsinA(p g = -a VA0 sinzl^+QjVAecoszl(p > ql

[0061] It is noted that the compensation carried out made it possible to cancel the terms in 12.

[0062] According to a second embodiment, each measurement signal has a phase component x1, x2 and a quadrature component x3, x4, and the electronic processing circuit is arranged to perform compensation on the components x1, x2, x3, x4 of the measurement signals. Preferably:

[0063] 1 idli x / fy _ XL y 1 w0a4 /

[0064] w)

[0065] = ■ ifé) (^3 + ¾¾)

[0066] 1¼)

[0067] According to optional features, used individually or in whole or in part in any technically feasible combination: - the electronic processing circuit is arranged to filter compensated errors in order to obtain vibration control signals and / or estimation signals. - The amplitude Xp is obtained using the following formula:

[0068] x p = x1cos&+ x2siiïO

[0069] in which a 0 is an amplitude control setpoint, is a phase component of the first measurement signal and x2 is a phase component of the second measurement signal. - The quadrature control error Yq is obtained using the following formula:

[0070] -x3sine+ x4cos0

[0071] in which $ is an estimate of an angle of the deformation in the modal reference frame, -^3 is a quadrature component of the first measurement signal and ^4 is a quadrature component of the second measurement signal. - The error in estimating angle Yp is obtained using the following formula:

[0072] x2cos0- x^ind

[0073] in which is an estimate of an angle of the deformation in the modal reference frame, 1 is a phase component of the first measurement signal and x2 is a phase component of the second measurement signal. - The phase estimation error Xq is obtained using the following formula:

[0074] x3cos0+ x4sin0

[0075] in which g is an estimate of an angle of the deformation in the modal reference frame, x3 is a quadrature component of the first measurement signal and x4 is a quadrature component of the second measurement signal. - the electronic processing circuit is arranged to determine a precession command by difference between an angle setpoint and an estimate 0 of a deformation angle in the modal reference frame.

[0076] Other features and advantages of the invention will become apparent from the following description of a particular and non-limiting embodiment of the invention. Brief description of the drawings

[0077] Reference will be made to the attached drawings, among which:

[0078] [Fig-1] is a schematic top view of an angular sensor according to the invention;

[0079] [Fig.2] is a representation of the vibration of the resonator of [Fig.1], in a reference frame linked to the vibratory mode;

[0080] [Fig.3] is a functional diagram of the angular sensor according to a first version of the invention;

[0081] [Fig.4] is a functional diagram of the angular sensor according to a second version of the invention. DETAILED DESCRIPTION OF THE INVENTION

[0082] With reference to [Fig. 1], the angular sensor according to the invention comprises a housing or support 1 and a hemispherical resonator 2 rigidly connected to the support 1 by a central foot 3 extending along a central axis of symmetry of the resonator 2 between the support 1 and a pole of the resonator 2 such that the resonator 2 has a flat annular edge 4 extending parallel to the support 1. The resonator 2 is, for example, made of quartz. Of course, other resonator shapes are usable; this is only one example of an embodiment.

[0083] Resonator 2 exhibits a second-order, stationary, radial vibration mode with respect to the axis of symmetry of resonator 2, at a frequency corresponding to a natural frequency co of resonator 2. The annular plane edge 4 of resonator 2 is circular when resonator 2 is at rest and deforms to take on an elliptical shape when resonator 2 vibrates according to this vibration mode. An elliptical standing wave array of this vibration mode is represented by a dashed line in [Fig. 1] and a wave is represented by a thin line in [Fig. 2]. It should be noted that the "actual" natural frequency co of resonator 2 is not known but is close to the theoretical natural frequency co0, taking into account manufacturing defects and dispersions of resonator 2.

[0084] The angular sensor also includes transducers 5 and 6, namely: a first detector transducer 5.1, a second detector transducer 5.2, a first actuator transducer 6.1 and a second actuator transducer 6.2. The first transducers 5.1, 6.1 are placed on either side of the resonator 2 on a first axis Al intersecting the central axis of symmetry of the resonator 2 and the second transducers 5.2, 6.2 are placed on either side of the resonator 2 on a second axis A2 intersecting the central axis of symmetry of the resonator 2. The axes Al, A2 extend in a plane perpendicular to the central axis of symmetry of the resonator 2 and constitute the axes of a reference frame of the second-order vibration mode mentioned above. Transducers 5.1 to 6.2, known in themselves, can for example be of piezoelectric or electrostatic type and include electrodes fixed to support 1 and / or resonator 2 and connected to an electronic processing circuit 7.

[0085] The physical arrangement and operating principle of the angular sensor are identical here to those described in document FR-A-2749394. Model 2 indicated above is applicable to the angular sensor of the invention.

[0086] When the actuator transducers 6.1, 6.2 are powered in opposite phase by the electronic processing circuit 7 to excite the resonator 2 at the frequency corresponding to the natural frequency co, the resonator 2 vibrates and its annular edge 4 takes the elliptical shape shown in [Fig. 2] with an amplitude component a along the major axis of the ellipse and an amplitude component b, or spatial quadrature, along the minor axis of the ellipse. The detector transducers 5.1, 5.2 provide the electronic processing circuit 7 respectively with a first measurement signal and a second measurement signal, both having an in-phase component x1, x2 respectively and a quadrature component x3, x4 respectively, which are modulated at the said frequency corresponding to the natural frequency co.

[0087] Thus, when a rotation of a determined angle is imparted to the support 1 around the central axis of the resonator 2, the vibration field tends to rotate relative to the support 1, around the central axis of the resonator 2, by an angle Qe (commonly called the electric angle) proportional to the angle of rotation of the support 1 (provided that the electronic processing circuit 7 allows this rotation to occur freely by operating in gyroscope mode).

[0088] The measurement signals provided by the detector transducers 5.1, 5.2 to the electronic processing circuit 7 allow an estimation @ of the electric angle 0e to be made and an estimate of the angular velocity Q to be deduced.

[0089] We will now focus more specifically on the exploitation of these signals by the electronic processing circuit 7.

[0090] The treatment performed includes (with reference to [Fig.3]): - a phase estimation branch of 100, - a servo control branch with an amplitude of 200, - a quadrature servo branch 300, and - a branch for estimating angle 400.

[0091] The frequency control branch 100 is arranged to provide a CF signal from a phase estimation error Xq that has been corrected to obtain a compensated phase estimation error Xq-

[0092] The phase estimation error Xq is obtained from the quadrature components of the measurement signals by a calculation function 101 applying the following formula:

[0093] x q = x3cosQ+ x^sinO

[0094] A correction function 102 then calculates the compensated phase estimation error Xq from the phase estimation error Xq by applying the following formula:

[0095] __1 fy Q y ) JA)2 ' w° 1

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[0106] The compensated phase estimation error Xq is then amplified by means of an amplification function 103 having a gain GF(p) whose output corresponds to the control signal CF. The CF signal feeds a voltage-controlled oscillator 104 (or VCO) to provide an in-phase reference signal <e>and a quadrature reference signal Q. The phase and quadrature reference signals are used in particular to demodulate the measurement signals in order to extract the phase component ^1 and the quadrature component -^3 of the first measurement signal and the phase component and the quadrature component ^4 of the second measurement signal. The phase and quadrature reference signals are also used, as will be seen later, to remodulate the supply signals of the actuator transducers 6.1, 6.2. The amplitude control branch 200 is arranged to provide an AC control signal developed from an amplitude control error that depends on an amplitude Xp controlled to an amplitude control setpoint and which has undergone a correction to provide a compensated amplitude control error x - a. The AC control signal has the function of supplying the actuator transducers 6.1, 6.2 to maintain the vibration amplitude in such a way that this amplitude is constant. The amplitude Xp is obtained from the phase components of the measurement signals by a calculation function 201 applying the following formula: X p = x1cos0 + x2sin0 A correction function 202 then calculates the compensated amplitude x& from the amplitude Xp by applying the following formula: _ 1 . | y G y ] ^p— [Ap-^ïq) 1¼) The compensated amplitude x is then compared to the amplitude control setpoint 3q to provide the compensated amplitude control error Xp-Sq-. The compensated amplitude control error Xp is then amplified. by means of an amplification function 203 having a gain GA(p) whose output corresponds to the control signal AC. The quadrature control branch 300 is arranged to provide a CQ control signal derived from a quadrature control error Yq that has been corrected to obtain a compensated quadrature control error. Ÿq- The CQ control signal has the function of powering the actuator transducers 6.1, 6.2 to cancel the spatial quadrature.

[0107] The quadrature control error Yq is obtained from the quadrature components of the measurement signals by a calculation function 301 applying the following formula: [0i08] Yq=-x3sin6+ x4cos0

[0109] A correction function 302 then calculates the compensated quadrature control error Ÿq from the quadrature control error Yq by applying the following formula:

[0110] _ 1 . ( vv ) Mwo /

[0111] The compensated quadrature control error is then amplified y by means of an amplification function 303 having a gain Gq(p) whose output corresponds to the control signal Cq.

[0112] The angle estimation branch 400 is arranged to provide an output signal CT developed from an angle estimation error Yp which has been corrected to provide a quadrature servo error compensated y p. The output signal CT allows the estimation of the electrical angle to be obtained in the modal frame.

[0113] The angle estimation error Yp is obtained from the phase components of the measurement signals by a calculation function 401 applying the following formula:

[0114] y p = x2cos⁻ x^inO

[0115] A correction function 402 then calculates the compensated error of angle estimation yp from the error of angle estimation Yp by applying the following formula:

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[0118] The compensated error in angle estimation yp is then amplified by means of an amplification function 403 having a gain GT(p) whose output corresponds to the output signal CT. The output signal CT represents the rotational speed of the vibration Qe and, after application of an integration function 404, allows obtaining the estimate 'q of the electric angle 0e. To obtain the rotational speed, called 1 / 7, applied to the angular sensor and the angle, called 1 / 7, in which the angular sensor is located around the central axis of resonator 2, it suffices to multiply, by a correction function 405, the estimated angular speed q and the estimated angle by -1 / a (i.e., the inverse of the coefficient of shape a of resonator 2, this shape coefficient being determined for example during a calibration operation known in itself).

[0119] The process further includes a precession control branch 500 arranged to provide a precession control signal Cp applied to the actuator transducers 6.1, 6.2 to create a force maintaining the vibration orientation (or electrical angle) at a predetermined value. This force, being proportional to the angular velocity applied along the sensor's sensitive axis, constitutes a measure of said velocity. In this mode of operation, the angular measurement method thus comprises the steps of applying a precession control so as to control a vibration orientation at an angular setpoint value and of determining an angular measurement from the precession control.

[0120] The precession control branch 500 includes a subtractor 501 receiving on its positive input an electrical angle setpoint 3C and on its negative input the estimate of the electrical angle to provide at the output the precession error 0C - Q which is then amplified by an amplification function 502 with a gain GP(p) to obtain the precession control signal Cp.

[0121] The CA, CQ and CP control signals applied to the actuator transducers 6.1, 6.2 are then subjected to trigonometric processing 10 and then to remodulation 20.

[0122] More specifically, the quadrature control signal CQ is: - on the one hand, multiplied by _ ginQ by application of the trigonometric function 11 before being remodulated by the phase reference signal <e>and applied to an adder 30.1 supplying the actuator transducer 6.1; - on the other hand, multiplied by applying the trigonometric function 12 before being remodulated by the phase reference signal <e>and applied to an adder 30.2 supplying the actuator transducer 6.2.

[0123] The AC and CP control signals are: - on the one hand multiplied by qqet _ gi^g respectively by application of the trigonometric function 13 (q COS3- C SÏU0) before being remodulated ^4 P by the quadrature reference signal Q and applied to the adder 30.1 supplying the actuator transducer 6.1; - on the other hand, multiplied by gi^g and _|_ QQgg respectively by application of the trigonometric function 14 (q sinQ - Q COSO^ before being j4 P remodulated by the phase-reflective reference signal <e>and applied to an adder 30.2 supplying the actuator transducer 6.2.

[0124] Apart from the calculation of compensated errors, the operation of the angular sensor is identical to that of document FR-A-2749394 and will therefore not be detailed further here.

[0125] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

[0126] In particular, the invention is applicable to any type of inertial angular sensors, regardless of the shape of the axisymmetric resonator and its vibration modes.

[0127] The present invention is described in a particular case where only two detectors and two actuators are used, but the invention applies to the more general case where there are more transducers. Alternatively, the same transducers can successively form detectors and actuators.

[0128] The transducers may be integral with the housing and the resonator, or only with the resonator.

[0129] The sensor can be a pure gyrometer or a pure gyroscope.

[0130] The electronic processing circuit can be implemented by one or more processor(s), microprocessor(s), microcontroller(s), FPGA...

[0131] The functions can be performed digitally or analogically.

[0132] Alternatively, as shown in Figure 4, the electronic processing circuit 7 is arranged to perform compensation on the components %2 ^3 of the measurement signals, via a compensation function 1234 implemented upstream of the calculation functions 101, 201, 301, 401. The compensated errors can then be calculated as follows:< / e> < / e> < / e> < / e>

Claims

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2. Demands Angular sensor comprising: a resonator 2() capable of exhibiting a vibration mode, radial with respect to an axis of symmetry of the resonator (2); transducers (5.1, 5.2, 6.1, 6.2) to provide a first measurement signal and a second measurement signal of a deformation of the resonator (2) respectively along a first direction and a second direction orthogonal to each other of a reference frame of the vibration mode and to apply a force on the resonator (2) along these two orthogonal directions; and an electronic processing circuit (7) electrically connected to the transducers (5, 6) and arranged so as to determine from the measurement signals an estimate Q of an angular velocity applied to the angular sensor and to emit control signals of the transducers (6.1, 6.2).2) to generate and maintain a vibration of the resonator (2) at a frequency corresponding substantially to a theoretical natural frequency and with a substantially constant amplitude a and a substantially zero quadrature component q, by dealing with an amplitude control error Xp- 3q where Xp is an amplitude controlled to an amplitude setpoint &o, a quadrature control error Yq, an angle estimation error Yp and a phase estimation error Xq, characterized in that the electronic processing circuit (7) is arranged to perform a compensation making said errors insensitive to a variable angular velocity of the sensor by taking into account the theoretical natural frequency ^0 and the estimation of the angle of the angular sensor.Sensor according to claim 1, wherein the electronic processing circuit (7) is arranged so that the processing includes a phase of calculation of compensated errors Xp, yy, Xq used for the rest of the processing and such that:. _ 1 [ y Q y I i • 1 Y 4- — Y 1 p~ JM

3. Sensor according to claim 1, wherein each measurement signal has an in-phase component (-^1, ^2) and a quadrature component (-^3, ^4) and the electronic processing circuit (7) is arranged to perform compensation on the components (-^1, ^2 ^4) of the measurement signals.

4. Sensor according to claim 3, wherein: 1 / Q \ X4 = -2 • 1&) ^3=__x__. (x3+^x2) — 1 . 1 V 1 1

5. Sensor according to any one of the preceding claims, wherein the electronic processing circuit (7) is arranged to filter compensated errors in order to obtain vibration control signals (CA, Cq) and / or estimation signals (Cf, Ct).

6. Sensor according to any one of the preceding claims, wherein the amplitude control error Xp is obtained by the following formula: Xp = xlcos0+ x2sinO where $ is an estimate of an angle of the deformation in the modal reference frame, ^1 is a phase component of the first measurement signal and is a phase component of the second measurement signal.

7. Sensor according to any one of the preceding claims, wherein the quadrature control error Yq is obtained by the following formula: -x3sin@+ x^cosO where $ is an estimate of an angle of the deformation in the modal reference frame, ^3 is a quadrature component of the first measurement signal and -^4 is a quadrature component of the second measurement signal.

8. Sensor according to any one of the preceding claims, wherein the angle estimation error Yp is obtained by the following formula: x2cos0- x^ind where is an estimate of an angle of the deformation in the modal reference frame, -^1 is a phase component of the first measurement signal and ^2 is a phase component of the second measurement signal.

9. Sensor according to any one of the preceding claims, wherein the phase estimation error Xq is obtained by the following formula: x3cos0+ x4sine where $ is an estimate of an angle of the deformation in the modal reference frame, -^3 is a quadrature component of the first measurement signal and -^4 is a quadrature component of the second measurement signal.

10. Sensor according to any one of the preceding claims, wherein the electronic processing circuit (7) is arranged to determine a precession command (Cp) by difference between an angle setpoint and an estimate g of an angle of the deformation in the modal reference frame.

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