Measurement method and gyroscopic sensor

Abstract

The present invention relates to a method for gyroscopic measurement by means of a sensor (10) comprising a housing (12) and a vibrating element (15) able to vibrate relative to the housing (12) simultaneously in a direction (x) of a pilot mode and a direction (y) of a detection mode, comprising the closed-loop control (110) of first and second vibration amplitudes of the vibrating element (15) in the directions of the pilot mode and the detection mode at a predetermined pilot amplitude (xmax) and a predetermined detection amplitude (ymax), respectively, and determining (120) an instantaneous angular velocity (Ωmes) of the housing (12). A predetermined bias (ξ(t)) is introduced into a measurement of an angular position (θ) of the direction (x) of the pilot mode used to determine a biased force (Fass,biais) to be applied to the vibrating element (15) for closed-loop control of the first and / or second vibration amplitude, in order to produce a controlled rotation of the direction of the pilot mode (x) in the vibration plane (XY).

Description

[0001]TITLE: Gyroscopic measurement method and sensor The present invention relates to a gyroscopic measurement method. The invention also relates to a gyroscopic sensor for implementing the gyroscopic measurement method, as well as a computer program comprising instructions which cause the sensor to execute the step of determining the instantaneous angular velocity of the gyroscopic sensor of this method. A Coriolis Vibratory Gyroscope (CVG) sensor makes it possible to measure the component along an axis, called the sensitivity axis, of an instantaneous rotation velocity vector of a reference frame linked to a housing of the sensor with respect to an inertial reference frame. The CVG therefore comprises a vibrating element of the sensor capable of vibrating with respect to the housing. The measurement is carried out thanks to the effects of the Coriolis inertial force which is exerted on the vibrating element. The vibrating element of a CVG is capable of vibrating in two directions ofcoplanar and perpendicular vibration, called the pilot mode direction and the detection mode direction, the work of the Coriolis force allowing a transfer of mechanical energy between the two directions. The CVG sensitivity axis is orthogonal to the plane of the perpendicular directions of the pilot mode and the detection mode. For measurements, the vibrating element is excited along the pilot mode direction at its resonant frequency by the excitation system. The amplitude of the vibrations along the pilot mode is kept constant by means of an amplitude control applied to the excitation system. Any variations in the resonant frequency, particularly related to variations in the temperature of the vibrating element, are monitored by means of a phase-locked loop. If the component along the sensitivity axis of the instantaneous rotational speed vector of the housing relative to an inertial reference frame is non-zero, the displacement of the elementvibrating along the direction of the pilot mode generates a Coriolis force. This Coriolis force excites the vibrating element along the direction of the detection mode perpendicular to the direction of the pilot mode, at an amplitude which is proportional to the component along the sensitivity axis of the instantaneous rotational speed vector. A CVG can operate in two modes: gyroscope mode and gyrometer mode. In gyroscope mode, the position of the direction of the pilot mode in the vibration plane is free. The instantaneous rotational speed to be measured is then deduced from the angular position of the vibration plane of the vibrating element in the frame of reference linked to the housing. In gyrometer mode, the direction of the pilot mode in the vibration plane is controlled by sending an electronic command and the instantaneous rotational speed to be measured is deduced from the force to be exerted to control this direction. Whether the CVG is used in gyroscope mode or in gyrometer mode, the measurementsare tainted by intrinsic errors linked to defects in the CVG. Among these defects, we can cite the anisotropies of stiffness or damping of the vibrating element, the defects of the excitation control electronics or the electronics for detecting the position of the vibrating element, the defects of the reference electrical voltage for the excitation, etc. Among these errors, some are called harmonics because they are proportional to cosine or sine functions of an angle that is an even multiple of the angle characterizing the direction of the pilot mode in the reference frame linked to the housing. US 6598455 describes a method of gyroscopic measurements in which the geometric vibration position of the gyroscope is deliberately modified by electrostatic means over time, in order to improve the calibration of the gyroscope. US 7 093370 also describes a MEMS gyrometer in which an angular velocity is deliberately imposed on the sensor by mechanical means, the direction ofthe rotation of the sensor being periodically alternated in order to reduce measurement errors and in particular errors in the scale factors of the gyrometer. FR 2937414 describes a vibrating gyroscope which combines the principles of patents US 6598455, by injecting an electronic signal to rotate the vibration wave, and US 7 093370, by imposing a periodically alternating electrical rotation to minimize harmonic errors. The control signal is adapted to rotate the geometric vibration position of the gyroscope in a first direction during part of the period of the control signal according to a first speed profile, then in an opposite direction according to a second speed profile. The vibrating gyroscope then provides a corrected signal which is based on the difference between the measurement signal and the control signal. However, due to the errors which affect the chain for converting the control signal into electrostatic force, the force actuallyapplied to the vibrating element of the gyroscope to obtain its alternating rotation is different from the force that should theoretically be obtained from the control signal. If the errors in the conversion chain are perfectly stable over time, the error made on the angle measurement can be zero over a period characteristic of the variations in the control signal. However, this is very unlikely, because the sources of error are numerous and of different natures. These include detection errors of the detection combs, excitation errors of the excitation combs, as well as instabilities of the reference voltage used for the operation of these combs, and errors in the electronic cards that coordinate the implementation of the gyroscopic measurement process. Ultimately, in most situations, the average value of the error made is not zero over a period of the alternating rotation of the sensor position in thereference frame linked to the sensor housing. Furthermore, during the round trip of the wave, the angular errors of the sensor are all the greater as the defects mentioned above are significant. Such a device reduces the impact of the defects on the measurement without, however, making it possible to evaluate the measurement error linked to these defects. In addition, the control signal used in FR 2937414 must make it possible to return to the same angular position between the start and the end of the control period. In cases where the gyroscope is moving in the inertial frame of reference and not at rest, such a signal will not make it possible to have at the same time a zero-mean control signal and to return to the same angular position. An aim of the invention is then to propose a gyroscopic measurement method in which an alternating rotation of the directions of the pilot and detection modes of the gyroscopic sensor is controlled and in which the measurement errors, in particular the scale factor error,are reduced. To this end, the subject of the invention is a method of gyroscopic measurement by means of a sensor comprising a housing and a vibrating element capable of vibrating relative to the housing in a vibration plane linked to the housing simultaneously in a direction of a pilot mode and in a direction of a detection mode different from the direction of the pilot mode, the method comprising the following steps of: a) controlling a first amplitude of vibrations of the vibrating element in the direction of the pilot mode to a predetermined pilot amplitude, and a second amplitude of vibrations of the vibrating element in the direction of the detection mode to a predetermined detection amplitude, and b) determining an instantaneous angular velocity of the housing relative to a sensitive axis of the sensor from measurements of the vibrations of the vibrating element and the pilot amplitude, the method being characterized in that a predetermined bias is introduced into ameasurement of an angular position of the pilot mode direction used to determine a biased force to be exerted on the vibrating element for the control of the first and / or second vibration amplitude, the introduction of the predetermined bias causing a controlled rotation of the pilot mode direction in the vibration plane, the instantaneous angular velocity of the housing being further determined from the predetermined bias. The introduction of a predetermined bias during the method results in the exertion of an amplitude control force which no longer has as its direction that of the pilot mode, as in the methods of the prior art, but an offset direction. The offset is a function of the bias which has been introduced. This offset implies that the force exerted for the amplitude control has a component orthogonal to the direction which would be desired in the absence of bias, which is added to the Coriolis force due to the rotational movement of the housingin the inertial frame of reference. A rotation of the perpendicular directions of the pilot mode and the detection mode is caused, without an additional force, the control of which would present defects that are difficult to control, being necessary. The bias can also be a predetermined function that varies over time. If this function is chosen judiciously, it is possible to cancel the harmonic defects of the sensor on which the method is implemented. The gyroscopic measurement method according to the invention therefore makes it possible to carry out gyroscopic measurements of increased precision. According to other advantageous aspects of the invention, the gyroscopic measurement method comprises one or more of the following characteristics, taken individually or in all technically possible combinations: - the predetermined bias is configured to cause a rotation of the direction of the pilot mode by a predetermined angle alternately in a first direction and in a second directionopposite to the first direction; - the predetermined angle is equal to 90°; - the detection amplitude is chosen to be zero; - the control step comprises: 1) a measurement of the vibrations of the vibrating element; 2) an estimation of a characteristic phase of the vibrations of the vibrating element according to the direction of the pilot mode from the results of the measurement; 3) a first estimation of a first force whose direction is the direction of the pilot mode to be exerted on the vibrating element to control the first amplitude from the results of the measurement and the estimated phase; 4) a second estimation of a second force whose direction is the direction of the pilot mode to be exerted on the vibrating element to control the second amplitude from the results of the measurement and the estimated phase; 5) the introduction of the predetermined bias in the directions of the first force and the second force; 6) the control of the biased force which is equal to the resultant of the first forceand the second force after introduction of the predetermined bias in the directions of these two forces; - the second force comprises only a component in phase with the vibrations of the vibrating element according to the direction of the pilot mode. The invention also relates to a gyroscopic sensor comprising a housing and a vibrating element capable of vibrating relative to the housing in a vibration plane linked to the housing simultaneously in a direction of a pilot mode and in a direction of a detection mode different from the direction of the pilot mode and configured to implement the steps of the method according to any one of the preceding embodiments. According to other advantageous aspects of the invention, the gyroscopic sensor comprises one or more of the following characteristics, taken in isolation or in all technically possible combinations: - the sensor comprises: a) a first servo module, configured to estimate a first force atexert according to the direction of the pilot mode to control a first amplitude of vibrations of the vibrating element according to the direction of the pilot mode to a predetermined pilot amplitude; b) a second control module, configured to estimate a second force to be exerted according to the direction of the detection mode to control a second amplitude of vibrations of the vibrating element according to the direction of the detection mode to a predetermined detection amplitude; c) a measurement module, configured to generate measurements of the vibrations of the vibrating element according to two directions of a reference frame linked to the housing contained in the vibration plane; d) a control module, configured to determine a biased force to be exerted on the vibrating element for the control of the first and / or the second amplitude of vibrations, from the first force and the second force and from a biased angular position of the direction of the pilot mode in the reference frame linked to thehousing which corresponds to an angular position of the direction of the pilot mode in the frame linked to the housing after introduction of a predetermined bias, and to exert the biased force; e) biasing means, configured to provide the biased angular position to the control module from the measurements of the vibrations of the vibrating element along the two directions of a frame linked to the housing and the predetermined bias, the introduction of the predetermined bias being configured to cause a controlled rotation of the direction of the pilot mode in the vibration plane when the biased force is exerted; and f) a determination module, configured to determine an instantaneous angular velocity of the housing relative to a sensitive axis of the sensor from the measurements of the vibrations of the vibrating element, the pilot amplitude and the predetermined bias. - the biasing means of the sensor comprise: 1) a frame change module, configured to generate estimates of thevibrations of the vibrating element according to the direction of the pilot mode and the direction of the detection mode from the measurements of the vibrations of the vibrating element according to the two directions of a reference frame linked to the housing provided by the measurement module and the biased angular position provided by a bias means correction module; 2) a phase module, configured to receive as input estimates of the vibrations of the vibrating element according to the direction of the pilot mode from the reference frame change module and to estimate a phase characterizing a position of the vibrating element according to the direction of the pilot mode at a current date; 3) a precession module, configured to receive the estimates of the vibrations of the vibrating element according to the directions of the pilot mode and the detection mode from the reference frame change module and the phase of the phase module, and to provide as output an estimated difference between the angular position of the direction of the pilot mode and the detection mode.pilot in the frame linked to the housing at the current date and a biased angular position previously provided by the corrector module, and 4) the corrector module, configured to provide the biased angular position to the control module from the estimated difference, the corrector module comprising: i) a summing stage, configured to add the predetermined bias to said estimated difference; and ii) a feedback loop to the frame change module, the feedback loop comprising a gain stage and an integrator stage, the corrector module being configured so that the estimated difference converges towards a zero value. The invention also relates to a computer program comprising instructions which cause the sensor according to one of the preceding embodiments to execute the method according to any one of the embodiments described above. The invention will appear more clearly on reading the description which follows, givensolely by way of non-limiting example, and made with reference to the drawings in which: [Fig.1] Figure 1 is a schematic representation of part of the elements of an embodiment of a CVG according to the invention, including the vibrating element and the detection and excitation devices of this vibrating element; [Fig.2] Figure 2 is a schematic representation of the trajectory of the vibrating element of Figure 1 and the directions of its pilot and detection modes in a spatial reference frame linked to the housing; [Fig.3] Figure 3 is a partial representation of an embodiment of the CVG, complementary to the representation of Figure 1; [Fig. 4] Figure 4 is a representation in the form of a flowchart of the method according to the invention; [Fig.5] Figure 5 is a schematic representation of a CVG of the prior art; [Fig.6] Figure 6 is a schematic representation of an embodiment of an excitation device of Figure 1; and [Fig.7] theFigure 7 shows a particular embodiment of the corrector module of Figure 3. The Coriolis effect gyroscopic sensor 10, designated by the abbreviation CVG in the following, according to the invention is described with reference to Figures 1 and 3. The CVG 10 comprises a housing 12 and a vibrating element 15 capable of vibrating relative to the housing 12. The CVG 10 is for example produced in the form of a microelectromechanical system (in English "Micro Electromechanical Sensor", MEMS). The vibrating element 15 and the housing 12 are then cut from a block of silicon or quartz by micromachining and the vibrating element 15 is set into vibration by an electrical process. This arrangement makes it possible to minimize the size and / or the manufacturing cost of the CVG 10. Three axes X, Y, Z of the XYZ space frame of a reference frame (XYZ, t) linked to the housing 12 are shown in FIG. 1, the Z axis being of fixed direction in a space frame of an inertial reference frame. The CVG 10 is configured to measure ainstantaneous angular velocity Ω(t) of the sensor relative to the Z axis, which therefore constitutes the sensitivity axis (or equivalently the sensitive axis) of the CVG 10. To this end, the vibrating element 15 comprises a test mass M, capable of vibrating in the XY plane in two directions x and y, with a specific pulsation ω 0x , respectively ω 0y close to ω 0x. In the following, we consider that the direction x is the direction of the pilot mode and that the direction y is the direction of the detection mode. The direction y of the detection mode is perpendicular to the direction x of the pilot mode. The test mass M is capable of vibrating in the direction x of the pilot mode x and the direction y of the detection mode, with a resonance pulsation ^ close to ω0x. The CVG 10 comprises a measurement module 20 capable of generating measurements of the vibrations of the vibrating element 15 in the directions X and Y of the reference frame linked to the housing 12. In particular, the measurement module 20 is capable of measuring the position X(t) (respectively Y(t)) of the vibrating element 15, and / or indirectly its speed dX / dt(t) (respectively dY / dt(t)), and / or indirectly its acceleration d 2 X / dt 2 (t) (respectively d 2 Y / dt 2(t)) along the X direction (respectively along the Y direction) of the reference mark linked to the housing 12. For this purpose, the measurement module 20 may comprise suitable detection means, such as, for example, electrostatic detection means 20A along the X direction of the reference mark linked to the housing 12 and electrostatic detection means 20B along the Y direction of the reference mark linked to the housing 12. Advantageously, the electrostatic detection means 20A and 20B each form with the proof mass M a set of interdigitated combs, on the geometric principle shown in FIG. 6. The measurement module 20 advantageously comprises a proximity card configured to amplify the signals detected by the measurement module 20. The measurement module 20 is capable of transmitting the measurements of the vibrating element to a reference change module 21.The reference frame change module 21 is capable of generating estimates of the vibrations of the vibrating element 15 along the directions x of the pilot mode and y of the detection mode, from measurements of the vibrations of the vibrating element along the directions X and Y of the reference frame linked to the housing 12 and from a biased estimate θbias of an angular position θ of the direction x of the pilot mode in the reference frame linked to the housing 12 received from a corrector module 50 which will be described later. In particular, the reference frame change module 21 is capable of estimating the position x(t) (respectively y(t)) of the vibrating element 15 and / or indirectly its speed dx / dt(t) (respectively dy / dt(t)) and / or indirectly its acceleration d. 2 x / dt 2 (t) (respectively d 2 y / dt 2(t)) along the x direction of the pilot mode (respectively along the y direction). The reference change module 21 is capable of transmitting the generated estimates to a phase module 30, a first servo module 35 and a second servo module 40. The phase module 30 is configured to estimate a phase φ(t) characterizing the position of the mass M along the x direction of the pilot mode at the current date t. For example, the phase φ(t) is of the form φ(t) = ωt+φ0, where φ0 denotes a phase at the origin of the dates t. The phase module 30 is configured to receive as input estimates of the position of the mass M in the direction x of the pilot mode from the reference change module 21. The phase module 30 is configured to transmit the estimated phase φ(t) to the first servo module 35 and to the second servo module 40.The first servo module 35 is configured to estimate, from the estimates of the vibrations of the vibrating element 15 along the direction x of the pilot mode and the phase φ(t), a first force Fass,x whose direction is the direction x of the pilot mode. The first force Fass,x is the force that must be exerted on the vibrating element 15 to servo a first characteristic amplitude of vibrations of the vibrating element 15 to a predetermined non-zero pilot amplitude xmax, the vibrating element 15 vibrating in sinusoidal mode, at the resonance pulsation ω, along the direction x of the pilot mode. The first servo module 35 is configured to transmit the estimated first force Fass,x to a control module 45 which will be described later.The first servo module 35 comprises for example a processor or a programmable logic circuit (such as a “Field Programmable Gate Array”, FPGA), configured to manage the estimation of the first force Fass,x, as well as a proximity card configured to transmit this estimation to the control module 45. The second servo module 40 is able to estimate, from the estimations of the vibrations of the vibrating element 15 along the direction y of the detection mode transmitted by the reference change module 21 and from the phase φ(t), a second force Fass,y whose direction is the direction y of the pilot mode. The second force F. ass,y is the force that must be exerted to control a second characteristic amplitude of vibrations of the vibrating element 15 along the direction y of the detection mode to a detection amplitude y max, the vibrating element 15 vibrating in sinusoidal mode along the direction y of the detection mode at the resonance pulsation ω. The second servo module 40 is configured to transmit the second force F ass,yestimated at the control module 45. The second servo module 40 comprises for example a processor or a programmable logic circuit, such as an FPGA. The processor or programmable logic circuit of the second servo module 40 may be the same as that of the first servo module 35. This arrangement is advantageous without being obligatory. The proximity card of the second servo module 40 is for example the same as that of the first servo module 20. This arrangement is advantageous without being obligatory.The control module 45 is configured to: a) determine a third biased force Fass,X,bias and a fourth biased force Fass,Y,bias to actually be exerted along the X direction and the Y direction of the XYZ reference frame linked to the housing 12, from: - the estimated first force Fass,x, - the estimated second force Fass,y, and - a biased angular position θbiais of the x direction of the pilot mode, and b) to actually exert the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias on the vibrating element 15. The control module 45 comprises for example a processor or a programmable logic circuit, such as an FPGA, 45A configured to determine the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias. The control module 45 comprises excitation means 45B and 45C of the vibrating element 15 respectively following the direction X and the direction Y of the XYZ reference frame linked to the housing 12.These means are not shown in detail in Figures 1 and 3. These are, for example, the excitation means described in document EP2960625. By way of example, the excitation means 45B comprise an electrostatic device configured to exert on the vibrating element 15 the third biased force Fass,X,bias along the X direction of the XYZ reference frame linked to the housing 12. By way of example, the excitation means 45C comprise an electrostatic device configured to exert on the vibrating element 15 the fourth biased force F. ass,Y,biaisaccording to the Y direction of the XYZ reference frame linked to the housing 12 The electrostatic device of the excitation means 45B and / or 45C and the proof mass M of the vibrating element 15 form, for example, a set of interdigitated combs, as shown in FIG. 6. In this case, the control module 45 advantageously comprises a proximity card, configured to inject an amplitude control signal into each of the electrostatic devices of the excitation means 45B and / or 45C. The processor or the programmable logic circuit of the control module 45 is advantageously configured to manage the control of the pulsation of the vibrations of the vibrating element 15 according to the y direction of the detection mode, for example to the resonance pulsation ω. The control module 45 receives the biased angular position θbias of the x direction of the pilot mode from a corrector module 50.The corrector module 50 is configured to receive from the precession module 25 an estimated difference δ between the angular position θ of the x direction of the pilot mode estimated by the precession module 25 and the biased angular position θbiais and a bias function ξ(t), and to output the biased angular position θbiais. For this purpose, the corrector module 50 comprises a processor or a programmable logic circuit (such as an FPGA). The bias function ξ(t) may be constant or depend on the date t at which the biased angular position θbiais is calculated. The biased angular position θbias of the rotating reference frame is the result of the application of the bias function ξ(t) in the estimation of the angle θ by the correction module 50. It is understood in light of Figure 3 that the biased angular position θbiais at the output of the correction module 50 is used by the reference frame change module 21.The precession module 25 is used to determine the estimated difference δ provided as input to the correction module 50. The estimated difference δ used by the correction module 50 to determine the biased angular position θbiais at a given date t is calculated, among other things, from a biased angular position θbiais measured at a date prior to the date t. The precession module 25 is configured to receive estimates of the vibrations of the vibrating element 15 along the directions x of the pilot mode and y of the detection mode from the reference frame change module 21 and the phase φ(t) from the phase module 30 and to output the estimated difference δ. The precession module 25 constitutes an element of a tracking loop configured to estimate the biased angular position θ. biais from near to near, from an initial unbiased angular position θ initialeknown and a demodulation of the estimation of the position of the vibrating element 15 according to the directions of the pilot and detection mode. In particular, the tracking loop also comprises the corrector module 50, the corrector module 50 itself comprising an integrator assembly 504 and a gain module 503 which will be described later with reference to FIG. 7, the variation of the biased angular position θ biais over an integration period T being calculated on the basis of the following equations: ^ ^^^ = ∫ x(t) . cos( φ(t) )dt (^^−1)^^ ^^^^ = ∫ y(t) . cos( φ(t) )dt (^^−1)^^ dt) = θbias(t) + ^^ tan−1(^^^^, ^^^^) ^^^^The precession module 25 is capable of transmitting the estimated difference δ to the correction module 50. The CVG 10 also includes a determination module 55 capable of determining a measured instantaneous angular velocity Ω mes(t), which is an estimator of the desired angular velocity Ω(t), from the biased angular position θ biais estimated and the bias function ξ(t). The method 100 according to the invention will now be described with reference to FIG. 4, in comparison with a method 200 of the prior art implemented on the CVG shown in FIG. 5. The method 100 according to the invention comprises: a) a step 110 of controlling the first amplitude of the vibrations of the vibrating element 15 along the direction x of the pilot mode to the pilot amplitude x max predetermined, and from the second amplitude of the vibrations of the vibrating element 15 along the direction y of the detection mode to the detection amplitude y max predetermined, during which the predetermined bias function ξ(t) is introduced into the measurement of the angular position θ of the pilot mode direction used to determine a force F assto be exerted on the vibrating element for the control of the first and second amplitude of vibrations, and b) the determination 120 of an instantaneous angular velocity Ω mesof the housing 12 relative to the sensitive axis Z of the sensor 10 from measurements of the vibrations of the vibrating element (15), of the pilot amplitude xmax and of the predetermined bias function ξ(t). The control step 110 is shown in detail in FIG. 4. The control step 110 comprises a first calculation step 1101 of the first force Fass,x, the direction of which is the direction x of the pilot mode, to be exerted on the vibrating element 15 to control the first amplitude to the pilot amplitude xmax. The first calculation step 1101 is implemented by the first control module 35. For this, the first control module 35 receives from the reference change module 21 estimates of the vibrations of the vibrating element 15 along the direction x of the pilot mode.These estimations are carried out on the basis of measurements previously carried out by the measurement module 20 during a measurement step 1102a of the vibrations of the vibrating element 15, and obtained during a reference change step 1102b carried out by the reference change module 21. The first servo-control module 35 also receives the phase φ previously estimated by the phase module 30 in a phase estimation step 1103 from the measurements of the vibrations of the vibrating element 15 along the direction x of the pilot mode carried out in the measurement step 1102. Simultaneously, the servo-control step 110 comprises a second estimation step 1104 of the second force Fass,y whose direction is the direction y of the detection mode to be exerted on the vibrating element 15 to servo-control the second amplitude to the detection amplitude ymax.The second estimation step 1104 is implemented by the second servo module 40 from the estimations of the vibrations of the vibrating element 15 along the direction y of the detection mode resulting from the reference frame change step 1102b and transmitted by the reference frame change module 21, and from the phase φ(t) estimated by the phase module 30 in the phase estimation step 1103. It will be noted that the fact that the reference frame change module receives the biased angular position θbiais and not the angular position θ has a negligible impact on the accuracy of the estimation of the vibrations of the vibrating element 15 along the direction x of the pilot mode and the direction y of the detection mode. In particular, the difference between the biased angular position θbiais and the angular position θ of the ellipse described by the oscillation can be limited by the choice of an appropriate bias function.The servo-control step 110 further comprises a third estimation step 1105 of the difference δ. The third estimation step 1105 is implemented by the precession module 25 from the estimations of the vibrations of the vibrating element 15 along the x direction of the pilot mode and along the y direction of the detection mode resulting from the reference frame change step 1102b, as well as from the phase φ(t) estimated by the phase module 30. It will be noted that it is in no case necessary to use an explicit calculation of the angular position θ to estimate the difference δ. Indeed, this difference is estimated step by step thanks to the tracking loop comprising the precession module 25 and the corrector module 50, from the initial angular position θ. initialeknown. At the end of the third estimation step 1105, a bias step 1106 is implemented by the correction module 50. During the bias step 1106, the biased angular position θ biaisof the direction of the pilot mode is determined step by step by the corrector module 50 from a difference δ estimated at the previous instant and from the bias function ξ(t). A control step 1107 is then implemented by the control module 45. The control step comprises a determination substep 1107a and an exercise substep 1107b. During the determination substep 1107a, the processor 45A of the control module 45 receives the first force Fass,x estimated during the first estimation step 1101 and the second force Fass,y estimated during the second estimation step 1104. The processor 45A also receives the biased angular position θbiais.The processor 45A then determines the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias to actually be exerted in the X direction and the Y direction of the XYZ reference frame linked to the housing 12 from the first estimated force Fass,x, the second estimated force Fass,y, and the biased angular position θbias of the x direction of the pilot mode, considering that the biased angular position is the actual angular position of the x direction of the pilot mode. Then during the exercise sub-step 1107b, the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias are exerted by the excitation means 45B, 45C on the vibrating element 15. Due to the introduction of the bias, the resultant of the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias does not have the direction necessary for the control, but a biased direction, as visible in Figure 2.As a result, an additional rotation of the direction of the detection mode is caused, this rotation being controlled by means of the bias function ξ(t). This additional rotation is added to the rotation caused by the Coriolis force associated with the angular velocity Ω(t) that is to be measured. To better understand the effects obtained during the control step 1107, we will first describe the operating equations of the CVG 10 common to the method 100 according to the invention and to a method of the prior art and, then we will describe more precisely a method of the prior art and finally, we will detail the particularities of the method according to the invention.I) OPERATING EQUATIONS COMMON TO THE METHODS OF THE PRIOR ART AND TO THE METHOD ACCORDING TO THE INVENTION The following section describes the operating equations common to the methods of the prior art and to the method according to the invention, equations which underlie the operation of the first and second servo modules 35 and 40 and of the control module 45 in the case of the sensor 10 according to the invention. To simplify the writing of the equations making it possible to understand the method of the prior art and the method 100 according to the invention, the vibrating element 15 is modeled in the following by a mass M suspended on a rigid frame C by means of two pairs of springs 15A, 15B of respective stiffnesses Kx and Ky, as shown in FIG. 1. Furthermore, it is considered in the following that the stiffness constants and the specific pulsations of the vibrating element 15 are identical according to the pilot mode x and the mode y.In this particular case, it can therefore be written that Kx = Ky = K and that ω0x = ω0y = ω0. This simplification should in no case be considered as limiting for the operation of the sensor 10 according to the invention, the following equations being able to be rewritten without difficulty in the most general case. In general, the trajectory of the mass M in forced sinusoidal mode is an ellipse in the plane (X, Y). This ellipse is reduced to a straight line segment whose direction is the direction x of the pilot mode in the case where the amplitude of the vibrations according to the detection mode is controlled by a zero detection amplitude ymax.Without making any assumption at this stage on the value of the detection amplitude ymax, the position x of the mass M along the direction x of the pilot mode as a function of the date t is of the form x(t) = xmax cos(ωt+φ0) and the position y of the mass M along the direction y of the detection mode as a function of the date t is of the form y(t) = ymax sin(ωt+ φ0). To simplify the writing of the equations, it is considered that the phase at the origin of the dates φ0 is zero, without this having any impact on the operation of the method according to the invention. If the direction x of the pilot mode relative to the axis X of the XYZ reference frame linked to the housing 12 is identified by the angle θ represented in Figure 2, the coordinates X and Y of the mass M in the XYZ reference frame linked to the housing 12 are linked to the coordinates x and y of the mass M in the xyZ reference frame by the equation 1:. in which R(θ) is the transition matrix from the xy frame to the XY frame: The passage matrix R(θ) is a function of time if the direction of the pilot mode is not constant in the XYZ frame linked to the box 12. The first time derivatives dX / dt and dY / dt of the X and Y coordinates of the mass M therefore verify: The second time derivatives of 2 X / dt 2 and d 2 Y / dt 2 the X and Y coordinates of the mass M verify: In a forced sinusoidal regime at pulsation ω, if we neglect the terms which are not proportional to a positive integer power of the pulsation ω in front of the other terms, equation 4 can be written in the simplified form of equation 5: In the frame of reference of box 12, the mass M is subject to the resultant F ass forces exerted by the excitation means 45B, 45C for its control, the component of which following the direction x of the pilot mode (respectively the direction X of the reference linked to the housing 12) is noted F ass,x(respectively F ass,X ) and the component along the y direction of the detection mode (respectively the Y direction of the reference frame linked to the box 12) is noted F ass,y (respectively F ass,Y ) The mass M is also subjected to the restoring forces of the springs, as well as to damping which is modeled by a fluid friction force along each of the x and y directions associated with a quality factor Q. The damping matrix A of the vibrating element 15, taking into account damping anisotropies, is of the form: ^^ [ 1 ^^2 −^^1] (6)The stiffness matrix K1 of the vibrating element 15, taking into account stiffness anisotropies, is of the form: Furthermore, when the frame of reference of the housing 12 is animated by a rotational movement of component Ω(t) in the Z direction relative to the inertial frame of reference, the mass M, due to its non-zero relative speed in the frame of reference of the housing 12, is subjected to a Coriolis inertial force in this frame of reference of the housing 12. Newton's second law applied to the mass M in the non-Galilean frame of reference linked to the housing 12 therefore takes the following form: where Fass,X and Fass,Y respectively designate the component the resultant Fass of the forces exerted by the excitation means 45B, 45C in the X direction of the frame of reference linked to the housing 12 and in the Y direction of the frame of reference linked to the housing 12. To simplify the writing of the equations, the damping anisotropies and the stiffness anisotropies are neglected in the following, without this being limiting for the implementation of the method.Neglecting the damping and stiffness anisotropies, the previous equation, after multiplication by R(-θ), is written as follows:. If we separate, along the x direction of the pilot mode, the terms in phase or phase opposition with the position x of the mass M from the terms in quadrature with this position, by decomposing Fass,x into:^^^^^^^^,^^ = ^^^^^^^,^^,^^ℎ^^^^^^ + ^^^^^^^,^^,^^^^^^^^ (10) we obtain the following system of equations, ABS designating the absolute value: in which Fass,x,phase and Fass,x,quad are the amplitudes of the terms of the Fass,x component respectively in phase and in quadrature with the position x of the mass M. Similarly, if we separate along the direction y of the detection mode the terms of the Fass,y component in phase or phase opposition with the position x of the mass M from the terms in quadrature with this position in:^^^^^^^^,^^ = ^^^^^^^,^^,^^ℎ^^^^^^ + ^^^^^^^^,^^,^^^^^^^^ (12)we obtain the following system of equations: In sinusoidal mode at resonance pulsation ω, if we neglect the terms which are not proportional to a positive integer power of the pulsation ω in front of the other terms, and taking into account the fact that the resonance pulsation ω and the natural pulsation ω0 are close, we can write: When the direction of the pilot mode is constant in the frame linked to the box 12, equation 14a shows that the phase component F ass,x,phase of force F ass,xto be exerted along the x direction of the pilot mode for the control of the mass M is zero. Equation 14b shows that the quadrature component F ass,x, quad of force F ass,x is non-zero and helps to combat the damping of oscillations along the x direction of the pilot mode. Equation 14c shows that, when the amplitude of the vibrations of the mass M along the direction of the detection mode is controlled by a detection amplitude y max non-zero, the component in phase F ass, y, phase of force F ass,y to be exercised along the y direction of the detection mode for the control of the mass M is also non-zero and makes it possible to combat the damping of oscillations along the y direction of the detection mode. At the relative equilibrium of the mass M in the reference frame linked to the box 12, if the quadrature component F ass,y,quad of force F ass,yis taken as zero, then the angular speed of rotation of the direction x of the pilot mode in the reference frame linked to the housing 12 is the opposite of the angular speed Ω of the housing in the inertial reference frame that one seeks to measure. II) METHOD ACCORDING TO THE PRIOR ART In the method according to the prior art described with reference to the sensor 200 partially represented in FIG. 5, the amplitude xmax of the oscillation in the direction x of the measurement mode is equal to a constant non-zero value, the amplitude ymax of the oscillation in the direction y of the detection mode is zero and the rotating reference frame (x,y) is aligned on the main axes of the ellipse described by the oscillation, thanks to four control loops, namely an amplitude loop 210, a quadrature loop 220, a phase loop 230 and a precession loop 240.The amplitude loop 210 is configured to calculate the component Fass,x to be exerted on the mass M in the direction x of the pilot mode for the control of its vibrations. For this, a processor of the amplitude loop 210 receives as input information on the position of the mass M in the direction x of the pilot mode from a reference change module 250a, as well as information on the phase φ(t) = ωt+φ0 of the position of mass M in the direction x of the pilot mode at the current date t. The information on the position of the mass M in the direction x of the pilot mode is calculated by the reference frame change module 250a from measurements of the position of the mass M in the directions X and Y of the reference frame linked to the housing 12 transmitted by a measurement module 250. The quadrature loop 220 is configured to estimate the component Fass,y to be exerted on the mass M in the direction y of the detection mode for the control of its vibrations.For this, a processor of the quadrature loop 220 receives as input information on the position of the mass M in the direction y of the detection mode from the measurement module 250, as well as information on the phase φ(t) = ωt+φ0 of the position of mass M in the direction x of the pilot mode at the current date t. The information on the position of the mass M in the direction y of the detection mode is calculated by the reference frame change module 250a from the measurements of the position of the mass M in the directions X and Y of the reference frame linked to the housing 12 transmitted by the measurement module 250. The phase loop 230 is configured to estimate the phase φ(t) = ωt+φ0 of the position of mass M in the direction x of the pilot mode at the current date t and transmit it to the processors of the amplitude loop 210 and the quadrature loop 220.For this, in a step of estimating the phase φ(t), the processor of the phase loop 230 receives as input information on the position of the mass M in the direction x of the pilot mode, for example from measurements of the position of the mass M in the direction X of the reference frame linked to the housing 12 carried out by the measurement module 250. The phase φ(t) estimated by means of the phase loop is provided as input to the amplitude loop 210 and the quadrature loop 220. The precession loop 240 is configured to estimate the angular position θ of the direction x of the pilot mode corresponding to the main axis of the ellipse described by the oscillation.To this end, in a step of estimating the angular position θ, the processor of the precession loop 240 receives as input information on the position of the mass M in the direction x of the pilot mode and in the direction y of the detection mode, for example from measurements of the position of the mass M in the directions X and Y of the reference frame linked to the housing 12. In a control step, a processor 260A of a control module 260 then receives the angular position θ, the force F. ass,x and the force F ass,y thus estimated and deduces the forces F ass,X and F ass,Yto be controlled to excitation devices 260B, 260C of the mass M according to the X and Y directions of the reference frame linked to the housing 12. The excitation devices 260B, 260C implement this control so that the force Fass = Fass,X + Fass,Y is actually exerted. In particular, equations 14a to 14d show that if the detection amplitude ymax is zero, the resultant Fass of the forces Fass,X and Fass,Y actually exerted must be the force Fass,x,quad whose direction is the x direction of the pilot mode and in quadrature with the vibrations of the vibrating element according to the x direction of the pilot mode. P lus précisément, III) METHOD ACCORDING TO THE INVENTION In the method 100 according to the invention, the bias ξ(t) is introduced into the estimation of the angular position θ(t) of the direction x of the pilot mode, so that the control module 45 receives a biased angular position θbiais(t) of this direction. Figure 7 shows a particular embodiment of the corrector module 50, making it possible to understand the influence of the bias function ξ(t) on the position of the rotating frame in which the first force Fass,x and the second force Fass,y are estimated with respect to the real positions of the directions x of the pilot mode and y of the detection mode. In the case of Figure 7, the corrector module 50 is placed at the output of a comparator stage 251 comprising the frame change module 21 and the precession module 25.The corrector module 50 receives from the precession module 25 the estimated difference δ(t) between the angular position θ(t) of the pilot mode direction and the biased position θbiais(t) of the rotating reference frame used by the control module 45. The corrector module 50 comprises a summing stage 502, configured to add the bias function ξ(t) to the estimated difference δ(t). The corrector module 50 finally comprises a feedback loop to the comparator stage 251. The feedback loop comprises the gain stage 503 and an integrator stage 504 of the corrector module 50. The corrector module 50 is configured so that the signal supplied at the input of the comparator stage 251 converges towards a zero value. In steady state, due to the introduction of the bias function ξ(t), the estimated difference δ(t) is therefore equal to the opposite of the bias function ξ(t). We therefore understand that the biased angle θ. biaisdiffers in the method 100 from the angular position of the direction θ of the pilot mode, unlike the method of the prior art. With the exception of their directions, the estimated first force Fass,x and second force Fass,y are identical to those of the method of the prior art. In particular, in the simplified case where the detection amplitude ymax is zero, only the phase component Fass,x, is non-zero. Due to the introduction of the bias ξ(t), the transition matrix from the xyZ frame linked to the wave to the XYZ frame linked to the housing is a biased matrix R(θbias), so that the third biased force Fass,X,bias and the fourth biased force Fass,Y,bias controlled by the control module 40 are different from the forces Fass,X and Fass,Y of the method of the prior art. For example, in the simplified case where the detection amplitude ymax is zero, It is therefore understood that the direction of the resultant Fass,bias of the forces exerted for the control of the vibrations of the vibrating element 15 is not the necessary direction but a biased direction, namely the direction of the biased pilot mode in the simplified case where the detection amplitude ymax is zero. This is shown in Figure 2. In other words, Fass,bias is not perfectly aligned with the x direction of the pilot mode in this simplified case. The FN component of this resultant Fass,bias normal to the direction of the pilot mode x has the consequence of rotating the direction of the pilot mode in the XY vibration plane, in addition to the rotation imposed by the Coriolis force. It should be noted that the effect of introducing the bias on the control of the second amplitude according to the direction of the detection mode is generally negligible.Preferably, the bias function remains permanently lower in absolute value than 5°, or even lower than 4°, lower than 3°, lower than 2°, or preferably lower than 1°. The additional angular rotation speed Δ^̇^ imposed by the introduction of the bias is known. It has the expression, in the simplified case where the detection amplitude ymax is zero:. The force to be exerted for the control of the second amplitude therefore becomes The determination module 55 can therefore, at the determination step 120, provide an estimator Ω mes of the desired angular velocity Ω based on the biased position θ biais estimated from these measurements, as well as from the bias function ξ(t) and the pilot amplitude x max . In particular, the desired angular velocity Ω can be determined on the basis of the following equation: (^^ (t + dt) − ξ (t + dt)) − (^^ (t) − ξ ( )Ω = ^^^^^^^^^^^ ^^^^^^^^^ t)^^^^^^ ^^^^ In a particular embodiment, the bias function ξ(t) is chosen to cause additional rotations of the x direction of the pilot mode by an angle α, alternately in the trigonometric direction and in the anti-trigonometric direction, the direction of rotation being changed at times t ifor i integer. The angle α can be bounded in absolute value by a predetermined threshold value αmax. is for example equal to π / 2. The instants ti can in this case be the successive instants for which the angle α reaches in absolute value the predetermined threshold value αmax. The bias function can ξ(t) be constant and equal in absolute value to a value ξcons between the instants ti and ti+1, the sign of the bias function being modified at each new date ti so as to modify the direction of the additional rotation imposed on the direction x of the pilot mode by the introduction of the bias function ξ(t). Preferably, if the bias function ξ(t) is constant in absolute value, this constant absolute value being noted ξ cons , each time the sign of the bias function ξ(t) is modified, therefore at each time t i , the value θ biaisat the output of the corrector module 50 is corrected by adding the opposite of twice the bias function at date t, i.e. - 2ξ(ti), over an integration time step of the integrator stage 504 from time ti. This arrangement makes it possible to limit the duration of the transient regime linked to the change in direction of the imposed additional rotation, the measurement of the desired angular velocity being carried out in steady state. In particular, if we denote by K the gain of the gain stage 503 and dt the integration time step of the integrator stage 504, steady state, i.e. ^^(^^^^+1) = −ξcons steady state, i.e. ^^(^^^^+2) = + ξcons. Adding double ξ cons on the integration time step following time t i+1allows the estimated difference δ at the output of the precession module 25 to be brought more quickly to the zero value towards which it must converge at the end of the time interval ^T which follows. The invention finally relates to a computer program comprising instructions which cause the sensor 10 as described previously to execute the method 100.

Claims

CLAIMS 1. Method (100) for gyroscopic measurement by means of a sensor (10) comprising a housing (12) and a vibrating element (15) capable of vibrating relative to the housing (12) in a vibration plane (XY) linked to the housing (12) simultaneously in a direction (x) of a pilot mode and in a direction (y) of a detection mode different from the direction (x) of the pilot mode, the method comprising the following steps of: a) controlling (110) a first vibration amplitude of the vibrating element (15) in the direction (x) of the pilot mode to a predetermined pilot amplitude (xmax), and a second vibration amplitude of the vibrating element (15) in the direction (y) of the detection mode to a predetermined detection amplitude (ymax), and b) determining (120) an instantaneous angular velocity (Ωmes) of the housing (12) relative to a sensitive axis (Z) of the sensor (10) from measurements of the vibrations of the vibrating element (15) and the pilot amplitude (xmax),the method being characterized in that a predetermined bias (ξ(t)) is introduced into a measurement of an angular position (θ) of the direction (x) of the pilot mode used to determine a biased force (Fass,bias) to be exerted on the vibrating element (15) for the control of the first and / or the second vibration amplitude, the introduction of the predetermined bias (ξ(t)) causing a controlled rotation of the direction of the pilot mode (x) in the vibration plane (XY), the instantaneous angular velocity (Ωmes) of the housing (12) being further determined from the predetermined bias (ξ(t)).

2. A gyroscopic measurement method (100) according to claim 1, wherein the predetermined bias (ξ(t)) is configured to cause a rotation of the direction of the pilot mode by a predetermined angle (αmax) alternately in a first direction and in a direction opposite to the first direction.

3. A gyroscopic measurement method (100) according to claim 2, wherein the predetermined angle (α,max ) is equal to 90°.

4. Method (100) of gyroscopic measurement according to any one of the preceding claims, in which the detection amplitude (y max ) is chosen to be zero.

5. Method (100) of gyroscopic measurement according to any one of the preceding claims, in which the servo-control step (110) comprises: - a measurement (1102) of the vibrations of the vibrating element (15); - an estimation (1103) of a phase (φ(t)) characteristic of the vibrations of the vibrating element (15) according to the direction (x) of the pilot mode from the results of the measurement (1102); - a first estimation (1101) of a first force (F ass,x) whose direction is the direction (x) of the pilot mode to be exerted on the vibrating element (15) to control the first amplitude from the results of the measurement (1102) and the estimated phase (φ(t)); - a second estimation (1104) of a second force (Fass,y) whose direction is the direction (x) of the pilot mode to be exerted on the vibrating element (15) to control the second amplitude from the results of the measurement (1102) and the estimated phase (φ(t)); - the introduction (1106) of the bias (ξ(t)) predetermined in the directions of the first force (Fass,x) and the second force (Fass,y); - the command (1107) of the biased force (Fass,bias) which is equal to the resultant of the first force (Fass,x) and the second force (Fass,y) after introduction of the bias (ξ(t)) predetermined in the directions of these two forces. 6.Method (100) for gyroscopic measurement according to claim 5, wherein the second force (Fass,y) comprises only a component (Fass,y,phase) in phase with the vibrations of the vibrating element in the direction (x) of the pilot mode.

7. Gyroscopic sensor (10) comprising a housing (12) and a vibrating element (15) capable of vibrating relative to the housing (12) in a vibration plane (XY) linked to the housing (12) simultaneously in a direction (x) of a pilot mode and in a direction (y) of a detection mode different from the direction (x) of the pilot mode and configured to implement the steps of the method according to any one of the preceding claims. 8.Gyroscopic sensor (10) according to claim 7, comprising: - a first servo module (35), configured to estimate a first force (Fass,x) to be exerted in the direction (x) of the pilot mode to servo a first amplitude of vibrations of the vibrating element (15) in the direction (x) of the pilot mode to a predetermined pilot amplitude (xmax); - a second servo module (40), configured to estimate a second force (F. ass,y ) to be exerted in the direction (y) of the detection mode to control a second amplitude of vibrations of the vibrating element (15) in the direction (y) of the detection mode to a detection amplitude (y max ) predetermined; - a measurement module (20), configured to generate measurements of the vibrations of the vibrating element (15) along two directions (X,Y) of a reference frame linked to the housing (12) contained in the vibration plane (XY); - a control module (45), configured to determine a biased force (F ass,biais ) to be exerted on the vibrating element (15) for the control of the first and / or the second amplitude of vibrations, from the first force (F ass,x ) and the second force (F ass,y ) and from a biased angular position (θ biais) of the direction (x) of the pilot mode in the frame linked to the housing (12) which corresponds to an angular position (θ) of the direction (x) of the pilot mode in the frame linked to the housing (12) after introduction of a predetermined bias (ξ(t)), and to exert the biased force (Fass,bias); - biasing means (21, 25, 30, 50), configured to provide the biased angular position (θbias) to the control module (45) from the measurements of the vibrations of the vibrating element (15) along the two directions (X,Y) of a frame linked to the housing (12) and the predetermined bias (ξ(t)), the introduction of the predetermined bias (ξ(t)) being configured to cause a controlled rotation of the direction of the pilot mode (x) in the vibration plane (XY) when the biased force is exerted (Fass,bias);and - a determination module (55), configured to determine an instantaneous angular velocity (Ωmes) of the housing (12) relative to a sensitive axis (Z) of the sensor (10) from the measurements of the vibrations of the vibrating element (15), the pilot amplitude (xmax) and the predetermined bias (ξ(t)).

9. Gyroscopic sensor according to the preceding claim, wherein the bias means (21, 25, 30, 50) comprise: - a reference frame change module (21), configured to generate estimates of the vibrations of the vibrating element (15) according to the direction (x) of the pilot mode and the direction (y) of the detection mode from the measurements of the vibrations of the vibrating element (15) according to the two directions (X,Y) of a reference frame linked to the housing (12) provided by the measurement module (20) and the biased angular position (θbias) provided by a correction module (50) of the bias means;- a phase module (30), configured to receive as input estimates of the vibrations of the vibrating element (15) along the direction (x) of the pilot mode from the reference frame change module (21) and to estimate a phase (φ(t)) characterizing a position of the vibrating element (15) along the direction (x) of the pilot mode at a current date (t); - a precession module (25), configured to receive the estimates of the vibrations of the vibrating element (15) along the directions (x) of the pilot mode and (y) of the detection mode from the reference frame change module (21) and the phase (φ(t)) of the phase module (30), and to provide as output an estimated difference (δ) between the angular position (θ) of the direction (x) of the pilot mode in the reference frame linked to the housing (12) at the current date and a biased angular position (θ; biais ) previously provided by the corrector module (50), and - the corrector module (50), configured to provide the biased angular position (θ biais ) to the control module (45) from the estimated difference (δ), the corrector module (50) comprising: i) a summing stage (502), configured to add the predetermined bias (ξ(t)) to said estimated difference (δ); and ii) a feedback loop to the reference change module (21), the feedback loop comprising a gain stage (503) and an integrator stage (504), the corrector module (50) being configured so that the estimated difference (δ) converges to a zero value.

10. Computer program comprising instructions which cause the sensor (10) according to any one of claims 7 to 9 to execute the method (100) according to any one of claims 1 to 6.

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