Method for calibrating stiffness and / or orthogonality differences of a vibratory inertial sensor

Abstract

This invention relates to a method for calibrating a stiffness mismatch ΔK or orthogonality Kxy in a vibration angle sensor, the sensor comprising: - a resonator extending about two axes x and y defining a sensor coordinate system xy, comprising a vibration verification mass having two portions configured to vibrate in opposite phase relative to each other in a direction x' defining a wave coordinate system x'y', the direction x' forming an electrical angle (θ) with the axes x; and - a detection, excitation, orthogonal compensation, and stiffness adjustment transducer; the resonator having a stiffness matrix K in the sensor coordinate system. C And has a stiffness matrix K in the wave coordinate system. O The method includes the following steps: A. Determining the electrical angle; B. Recovering the stiffness matrix K in the wave coordinate system. O The orthogonal or stiffness term, which is the sum of functions of the form cos(iθ) and sin(iθ); or for multiple electrical angles (θ). k Either steps A and B are iterated repeatedly over a certain duration during which the vibration wave continuously rotates through an electrical angle (θ(t)) that varies as a function of time; C determines the amplitude of the function in the form of cos(iθ) and sin(iθ); then D determines the stiffness mismatch ΔK and orthogonality Kxy based on the amplitude.

Description

Technical Field

[0001] This invention belongs to the field of vibration inertial sensors, wherein vibrating at least two masses, or even vibrating a single mass comprising at least two parts, allows one mass or a portion of a mass to deform relative to the other mass or the other portion. The invention relates to such an inertial vibration sensor with at least one mass, comprising one or more stiffness-correcting transducers (also known as stiffness-trimming transducers) and one or more quadrature-correcting transducers (also known as quadrature-trimming transducers). The invention is not limited to, but particularly relates to, MEMS inertial sensors capable of having planar structures, such as sensors micromachined in a wafer. More specifically, the invention relates to a method for calibrating stiffness mismatch and / or orthogonality in a vibration inertial sensor. Background Technology

[0002] Vibration (or tuning fork) inertial sensors are known to those skilled in the art. A vibration inertial sensor includes a resonator, which may or may not be axisymmetric, associated with modules for vibrating the resonator and for detecting the orientation of the vibration (vibration wave) relative to a sensor frame. These modules generally include at least two sets of actuators fixed to the sensor housing and / or the resonator, and at least two sets of detectors also fixed to the housing and / or the resonator.

[0003] For the sake of simplicity, the terms "inertial sensor," "angle sensor," and the simplest "sensor" are used interchangeably throughout this manual, all of which refer to vibration inertial sensors.

[0004] Such sensors are mounted on a carrier to measure the angle and / or angular velocity of the carrier. The carrier can be all or part of an aircraft, ship, train, or any other land, sea, or air transport.

[0005] Inertial sensors, micromachined on thin planar wafers and capable of measuring angular position (gyroscope) or angular velocity (gyroscope tester), are particularly well known, and such sensors are described in particular in document EP2960625. Their main characteristics will be reviewed below.

[0006] These micromachined sensors, also known as MEMS sensors (MEMS is an abbreviation for Microelectromechanical Systems), are fabricated using wafer-scale micromachining, etching, doping, and deposition techniques, similar to those used in the fabrication of electronic integrated circuits, thus allowing for low manufacturing costs.

[0007] The MEMS sensor described in patent application EP2960625 consists of two vibration-verified masses M1 and M2.Figure 1 (As shown) are configured such that one surrounds another (concentrically) and is excited by one or more excitation transducers, thereby illuminating the plane of the wafer ( Figure 1 The two masses vibrate in a tuning fork mode in the xy plane. They are suspended from anchor point A on the wafer by a suspension spring RS. The two masses are coupled together by a rigid element RC. The aim is to obtain, by means of construction, stiffness along x and an equal stiffness along y, as well as zero-coupling stiffness between x and y. Available vibration modes correspond to the linear vibration of these two masses in anti-equivalence.

[0008] More generally, more than two verification masses can be used. For example, four verification masses can be used, or conversely, a single mass consisting of at least two parts, one of which can deform relative to the other, can be used, for example, in a micro-hemispherical resonant gyroscope (μHRG).

[0009] The structure described in patent application EP2960625 forms a resonant system (referred to as a "resonator") based on two masses coupled together by Coriolis acceleration. As the sensor rotates about a z-axis perpendicular to the xy-plane (the z-axis is denoted as the "sensing axis"), the combination of forced vibration and the angular rotation vector generates a force via the Coriolis effect. This force places the verification mass in a natural vibration perpendicular to both the excitation vibration and the sensing axis; the amplitude of this natural vibration is proportional to the rotational speed. Electronic components associated with the sensor calculate the amplitude of this vibration in a direction orthogonal to the excitation direction, regardless of the excitation direction (by assuming it is known).

[0010] The sensor can operate in gyroscope tester mode: by modifying the excitation to keep its direction fixed and then keeping the axis perpendicular to this vibration fixed relative to the sensor housing, the output information is an image of the energy required to apply to the excitation transducer so that the direction of the natural vibration remains fixed regardless of the movement of the housing. The measurement of this reaction force allows the determination of the sensor's angular velocity Ω.

[0011] The sensor can also operate in gyroscope mode: allowing the direction of the excitation vibration to remain free and detecting that direction to provide the sensor's angular orientation. It is also possible to derive the sensor's angular velocity by differentiating this angle measurement.

[0012] The terms “angle orientation” and “angle” are interchangeable.

[0013] The entire structure of the resonator described in patent application EP2960625 is axially symmetric about the two axes x and y that define the sensor coordinate system, for example, Figure 1As illustrated in the example. Axisymmetry means that the structure is symmetric about the x-axis and symmetric about the y-axis. However, it should be understood that this definition can cover any possible small asymmetries. As described below, these axes constitute the main directions of the actuator / detector operating along these two axes.

[0014] To excite a useful vibration mode in any given direction of the plane, the excitation signal is decomposed into two components with adjusted corresponding amplitudes. These two components are applied, respectively, to an excitation transducer Ex acting in the x-direction and an excitation transducer Ey acting in the y-direction, the transducers being coupled with at least one verification mass ( Figure 2 The inner mass M1 is associated with this. Therefore, an excitation force is applied to these transducers to generate and maintain a vibration wave: the transducers are able to maintain forced vibration via amplitude command Ca (to counteract the damping of the sensor) and via precession command Cp (to cause the wave to rotate) in any direction in the xy plane.

[0015] The movement of the generated wave is detected by combining information collected by at least one pair of detection transducers Dx and Dy, wherein the at least one pair of detection transducers acquire the position of the mass during its travel in the sensor coordinate system xy. Figure 2 (Two pairs of transducers in the middle) and associated with at least one verification quality.

[0016] Preferably, the transducer is manufactured on two mass plates, such as Figure 3 As shown, index 1 corresponds to mass M1, and index 2 corresponds to mass M2. Figure 2 and Figure 3 Examples of non-restrictive arrangements: many other types of arrangements are also possible, and these arrangements are not necessarily axisymmetric.

[0017] The transducer is preferably an interdigitated comb electrode, whose gap variation will be sensed. There is a fixed comb whose teeth are fixed to a fixed mass of the machined wafer, and a movable comb whose teeth (interdigitated with the fixed comb's teeth) are fixed to a verification mass associated with the transducer in question.

[0018] The excitation involves applying an excitation force via AC voltage between the moving and stationary combs at a predetermined vibration frequency (the mechanical resonant frequency of the suspended verification mass, typically on the order of several kHz). The resulting movement is perpendicular to the comb teeth.

[0019] The detection involves applying a bias voltage between the stationary and moving combs and observing the change in charge between them caused by a change in capacitance due to a change in the spacing between the teeth of the stationary and moving combs. The measured movement is perpendicular to the comb teeth. Alternatively, in another configuration, longitudinal movement with respect to the comb teeth can be measured.

[0020] The vibrating component consisting of mass / spring is characterized by a symmetric 2×2 stiffness matrix (denoted by K). To achieve optimal sensor operation, a final stiffness matrix proportional to the identity matrix is ​​sought. However, this is generally not the case due to manufacturing defects (see below).

[0021] The x' axis represents the vibration axis of the wave. This axis defines the coordinate system x'y', where y' is perpendicular to x' in the plane of the sensor. The x' axis makes an angle θ with respect to the x axis, which is called the "electric angle", and the coordinate system x'y' is called the "wave coordinate system".

[0022] It is currently assumed that the wave vibrates along x (x' = x).

[0023] The dynamic equations describing a vibration inertial sensor can be simplified to a model of a single mass M, whose movements X and Y are modeled as follows:

[0024] [Mathematical Expression 1]

[0025]

[0026] Where M is the mass matrix (which will be considered a scalar for simplicity below), A is the damping matrix, K is the stiffness matrix, and C is the Coriolis matrix.

[0027] The Coriolis matrix C is:

[0028] [Mathematical Expression 2]

[0029]

[0030] Where M is the mass and Ω is the angular velocity of the sensor.

[0031] FX and FY are excitation forces applied along the x and y axes of the sensor. These forces are generated by commands Cr, Ca, Cq, and Cp calculated in the wave coordinate system by the servo system in a manner known to those skilled in the art, based on the demodulation of the movement of the detected signal relative to the vibration. Based on measurements of the wave movement X and Y (obtained in coordinate system xy), a rotation is applied to transmit to the wave coordinate system x'y', then the commands are determined (by demodulating the detected signal), and a reverse rotation is applied to transmit back to the sensor coordinate system xy (in which the excitation forces are applied). These commands are determined to cause the movement of the mass (i.e., the vibration wave of the sensor) to take the desired form. Ideally, the desired waveform is an oscillatory linear movement relative to the sensor coordinate system xy in a given direction. However, the wave generally has an elliptical shape, but is substantially flat in the direction perpendicular to the given direction (in other words, the minor axis of the ellipse is very small relative to the major axis, which corresponds to the given direction).

[0032] The command Cr corresponds to the stiffness force used to control the natural frequency of the resonator; since phase is equal to the integral of frequency, Cr controls the phase of the wave. Cr is an external force applied to the resonator (based on an estimate of the resonator's movement) that modifies the frequency of vibration by slowing or speeding up the vibration while the resonator is vibrating, but does not modify the resonator's inherent stiffness.

[0033] Command Ca corresponds to a force with a certain amplitude that compensates for the effect of the sensor's damping force and keeps the amplitude of the vibration constant: this force thus allows the amplitude of the wave to be controlled.

[0034] The command Cp corresponds to the precession force, which allows the angular velocity of the wave to be controlled. When the sensor is operating in gyroscope tester mode, applying the precession command Cp thereby servo-controls the orientation (or electrical angle) of the vibration to a constant setpoint value.

[0035] The command Cq corresponds to the orthogonal force used to control the orthogonality of the wave, that is, to ensure the linearity of the wave, or to control the minor axis of the ellipse when the wave is an elliptical wave.

[0036] As is particularly well known to those skilled in the art in the publication “Mechanical / Neon-Mechanical Resonant Sensors and Non-linear Effects” (Najib Kacem et al., Acoustics and Technology, Chapter 57), defects in the manufacture of sensors, especially asymmetries in their mass or nonlinearities of mechanical or electrostatic origin, lead to errors in the information output by them. Most of these defects must be compensated for by equalizing the vibrating inertial sensor.

[0037] This compensation is known to be performed by locally removing material (e.g., by laser ablation) to modify the distribution of mass or stiffness. This process is costly and not even feasible to implement on sensors micromachined in thin silicon wafers (where detection and excitation movement occur in the plane of the substrate).

[0038] The first type of defect leading to nonlinearity in the stiffness matrix K is a stiffness mismatch between the principal axis of vibration and the axis perpendicular to the vibration in the sensor plane. This corresponds to a system stiffness matrix where the stiffness along axis x differs from that along axis y. The aim is to utilize adjustable electrostatic stiffness to equalize the stiffness along these two axes. This electrostatic stiffness, also known as equalization stiffness, is achieved by stiffness-adjusting transducers Tx and Ty (at least one pair of Tx / Ty located on at least one mass, such as...) acting in directions x and y. Figure 2 The purpose of applying the equalizing stiffness is to make the stiffness along the two axes of the vibration equal, by reducing the value of the highest stiffness so that the frequencies are equal. This stiffness correction is called "stiffness trimming".

[0039] The second type of defect stems from the mechanical coupling between the vibrating axis and the vertical axis, leading to what is known as orthogonal deviation. The anisotropic defect present in the dynamic stiffness of the two vibrating masses (or two parts of a single mass) in the aforementioned set will cause the vibration to no longer be linear but elliptical, corresponding to the presence of non-zero coupling stiffness. A known prior art solution is to counteract this by applying a (sinusoidal) force F to the system via an excitation transducer. The problem is that this force may not be applied at exactly the correct time (phase error) along the correct axis (gain error), resulting in drift. To avoid applying the force F, it is possible to do so directly via, for example... Figure 2 At least one pair of transducers Q+ and Q- shown Figure 2The two Q+ / Q- pairs in the transducer alter the stiffness of the resonator to physically cancel out the coupling term. These transducers, operating along the x and y axes, are arranged diagonally for spatial reasons and to account for symmetry. This orthogonal correction is called "orthogonal trimming". The transducers Tx, Ty, Q+, and Q- are also preferably interdigitated combs, such as... Figure 2 and Figure 3 As shown, these combs are controlled using DC voltage and are referred to as "trimming combs".

[0040] Therefore, the orthogonal "trimming" transducer modifies the characteristics of the MEMS sensor, thereby eliminating coupling between the two axes of the sensor coordinate system, and the stiffness "trimming" transducer modifies the characteristics of the MEMS sensor, thereby eliminating stiffness mismatch between the two axes of the sensor coordinate system. They modify the inherent characteristics of the resonator. In other words, if the trimming voltage is adjusted, the stiffness of the resonator changes even when the resonator is not vibrating, which contrasts with the command Cr described above, which slows down or speeds up the vibration when the resonator is vibrating.

[0041] The trimmed transducer is controlled by a trimmed servo system, as is known to those skilled in the art, particularly from the published document "Quadrature-Error Compensation and Corresponding Effects on the Performance of Fully Decoupled MEMS Gyroscopes" (Erdinc Tatar et al., Journal of Microelectromechanical Systems, Vol. 21, Chapter 3, June 20). This servo system generates an orthogonal trimming command CTq, a stiffness trimming command along the x-axis CTx, and a stiffness trimming command along the y-axis CTY. The trimming commands are DC voltages.

[0042] Therefore, by adjusting the comb, the stiffness matrix K is directly modified using matrix Kt, and the dynamic equation of the vibration inertial sensor is:

[0043] [Mathematical Expression 3]

[0044]

[0045] The comb used to trim the stiffness along x modifies the resonator's stiffness by generating a matrix Kt:

[0046] [Mathematical Expression 4]

[0047]

[0048] The comb used to adjust the stiffness along y modifies the resonator's stiffness by generating a matrix Kt:

[0049] [Mathematical Expression 5]

[0050]

[0051] Orthogonal trimming combs modify the stiffness of the resonator by generating matrix Kt:

[0052] [Mathematical Expression 6]

[0053]

[0054] Stiffnesses Kx, Ky, and Kxy correspond to commands CTx, CTy, and CTq (DC voltages) within a certain gain coefficient. Commands CTx, CTy, and CTq are voltages that modify stiffnesses Kx, Ky, and Kxy through the comb. Applying the trimming commands is actually modifying matrix K in mathematical expression 1, which is a differential equation, by transforming K into K-Kt.

[0055] Figure 4 The general operation of an inertial sensor according to the prior art is illustrated. The resonator Res comprises various transducers described above and represented by symbols E (excitation), D (detection), TQ (orthogonal trimming), and TF (stiffness trimming). The vibration wave OV vibrates along x' at an electrical angle θ. The processing unit UT performs various servo calculations and generates all the commands / forces Cr, Ca, Cq, and Cp mentioned above regarding the correction of the various transducers. The excitation and trimming commands are determined by different servo systems as explained below.

[0056] In this processing unit, the movements X and Y detected in the sensor plane are first transformed into the wave coordinate system x'y' by means of a rotational transformation through an electrical angle θ. Then, the servo system determines the excitation command in the wave coordinate system in the form of voltages U'x and U'y in the wave coordinate system, for example, as follows:

[0057] [Mathematical Expression 7]

[0058] U′ x =iC a +C r ;as well as

[0059] [Mathematical Expression 8]

[0060] U′ y =iC p +C q

[0061] In addition to the excitation servo system, the first and second servo systems are used to generate stiffness trimming commands CTx and CTY, and orthogonal trimming command CTq, respectively. Therefore, these commands are determined by a dedicated servo system.

[0062] Then, all these commands are transposed to the sensor coordinate system xy by inverse rotation, and in this sensor coordinate system, all these commands are applied to various transducers (within a certain gain factor).

[0063] Vercier N et al., in “A new Silicon axisymmetric Gyroscope for Aerospace Applications” (2020 DGON Inertial Sensors and Systems (ISS), IEEE (2020)), disclosed a method for correcting angular velocity errors by wave rotation and for correcting stiffness and orthogonality errors by trimming. One problem is that even after applying stiffness and orthogonality trimming commands to counteract the detected errors, residual stiffness mismatch Kx-Ky (also known as ΔK) and residual orthogonality mismatch Kxy remain. Furthermore, the stiffness and orthogonality trimming commands themselves may generate stiffness and orthogonality mismatches, even if these mismatches are smaller than those sought to be rectified. Specifically, the trimmed transducers, preferably interdigitated combs, themselves induce electrostatic nonlinearities, which will introduce errors in the stiffness matrix, even if these errors are smaller than the stiffness errors of mechanical origin intended to correct these transducers.

[0064] Therefore, when attempting to correct the stiffness mismatch ΔK by applying a trimming command of -ΔK, a residual stiffness mismatch ε1K may still exist, potentially caused by the trimming itself. This mismatch must be known if it is to be considered. After correcting ε1K, a new residual mismatch ε2K may still exist, which can be negligible or at least acceptable, where...

[0065] [Mathematical Expression 9]

[0066] ΔK>>ε1K>>ε2K

[0067] The same problem exists when attempting to correct orthogonality (Kxy) by applying a trimming command—that is, residual orthogonality ε1Kxy may still exist, possibly generated by the trimming itself. After correcting ε1Kxy, new residual orthogonality ε2Kxy may still exist, which can be negligible or at least acceptable, where...

[0068] [Mathematical Expression 10]

[0069] Kxy >> ε1Kxy >> ε2Kxy

[0070] However, in vibration inertial sensors, stiffness mismatch and orthogonality, when coupled with phase error, can cause sensor drift. Here we will recall that excitation phase error is the error between the force estimated by the excitation servo and the force actually applied to the resonator (the excitation matrix represents the effect of a flawed excitation chain). Similarly, detection phase error is the error between the actual movement of the resonator and the estimated movement (the detection matrix represents the effect of a flawed detection chain).

[0071] The overall problem of this invention is to minimize the stiffness mismatch and orthogonality of the vibration inertial sensor, thereby reducing sensor drift as much as possible.

[0072] Known solutions generally employ invasive trimming techniques to locate stiffness mismatches (or orthogonality), which in particular involve the application of interference. For example, patent application US20060020409A1 describes a method for identifying stiffness mismatches that requires the application of interference to measure the mismatch. More precisely, the described principle involves applying a sinusoidal interference to an orthogonal loop, which, coupled with the stiffness mismatch, generates wave precession. Using the loop, the aim is to counteract the interference's influence on the wave precession by reducing the amplitude of the interference in that precession, thus allowing the determination of the stiffness mismatch. However, such a method introduces interference into the useful signal (often within the bandwidth of interest). Consequently, it generates residual lines at the applied frequency, thus creating parasitic signals. Furthermore, the method utilizes a loop employing servo-controlled voltages, making it sensitive to phase errors and increasing noise.

[0073] The present invention aims to overcome the aforementioned shortcomings of the prior art.

[0074] More specifically, the present invention aims to provide a method for identifying stiffness mismatch and orthogonality in a vibration inertial sensor for correction within the sensor, preferably performed in real time and without interfering with the sensor with interference that may ultimately remain in the measurements provided by the sensor. Summary of the Invention

[0075] The first subject of this invention, which allows for overcoming these deficiencies, is a method for calibrating the stiffness mismatch ΔK and / or orthogonality Kxy of a vibrational inertial angle sensor, the inertial sensor comprising a resonator extending about two mutually perpendicular axes x and y defining a sensor coordinate system xy and including:

[0076] - At least one vibration verification mass, the at least one verification mass comprising at least two portions configured to vibrate in opposite phase relative to each other in the direction x' of the defined wave coordinate system x'y' at vibration angular frequency ω, the vibration wave along x' forming an electrical angle θ with the axis x;

[0077] - A plurality of electrostatic transducers controlled by voltage and operating along the two axes x or y, comprising at least:

[0078] --A pair of detection transducers configured to detect the movement of vibration waves along these two axes, x and y;

[0079] --A pair of excitation transducers, which are subjected to excitation forces along two axes x and y respectively by a plurality of excitation commands determined by a servo system based on the detected movement. These forces are configured to keep the wave at a constant amplitude by amplitude commands and, where appropriate, to rotate the vibration wave by precession commands.

[0080] --A pair of orthogonally compensated transducers controlled by orthogonal commands; and

[0081] --A pair of stiffness-adjustable transducers, which are controlled by stiffness commands that set the stiffness along the x-axis and stiffness commands that set the stiffness along the y-axis respectively, thus forming stiffness commands;

[0082] The resonator has a stiffness matrix K in the sensor coordinate system. C And it has a stiffness matrix K in the wave coordinate system. O ;

[0083] This calibration method is applied when the inertial sensor is in operation with a vibration wave vibrating along axis x'.

[0084] The calibration method includes the following steps:

[0085] -A determines the electrical angles θk and θ(t);

[0086] -B Recovers the stiffness matrix K in the wave coordinate system x'y'. O At least one term, which can be an orthogonal term K O (2,1) or stiffness term K O (1,1), the term takes the form of a sum of functions of the form cos(iθ) and sin(iθ), where i is an integer varying between 1 and n, and n is greater than or equal to 1; or for multiple electrical angles θ k Steps A and B are iterated repeatedly, where k is an integer varying between 1 and m, where m is greater than or equal to 2, or steps A and B are iterated repeatedly for a certain duration T, during which the vibrating wave continuously rotates through an electrical angle θ(t) that varies as a function of time t; then

[0087] -C determines the magnitudes of functions of the form cos(iθ) and sin(iθ); and

[0088] -D determines the stiffness mismatch ΔK and orthogonality Kxy based on the determined amplitude.

[0089] The calibration method according to the invention may further include one or more of the following features, which may be taken individually or in any possible combination of techniques.

[0090] According to one embodiment, electrical angles describe a plurality of electrical angles θ. k Where k is an integer varying between 1 and m, where m is greater than or equal to 2, and step C for determining the amplitude includes applying a least-squares filter to the recovered term, with electrical angle θ. k The quantity m is at least equal to the quantity of amplitudes to be determined.

[0091] According to an alternative embodiment, the vibration wave continuously rotates through an electrical angle θ(t) that varies as a function of time t over a certain duration T, and step C, which determines the amplitude, includes demodulating recovery terms in the form of cos(iθ) and sin(iθ) for each i that varies between 1 and n, thereby determining the amplitude of the functions in the form of cos(iθ) and sin(iθ); and step D, which determines the stiffness mismatch ΔK and orthogonality Kxy respectively, is performed based on the determined amplitude.

[0092] According to one embodiment, the inertial sensor operates in gyroscope tester mode, and the electrical angle determined in step A is equal to the applied angle set by the precession command.

[0093] According to an alternative embodiment, the inertial sensor operates in gyroscope mode, and the electrical angle obtained by the rotation of the inertial sensor is measured by the inertial sensor, which may be superimposed on the precession command. The electrical angle determined in step A is equal to the measured rotation angle.

[0094] According to one embodiment, the calibration method further includes the following additional steps:

[0095] -E applies the stiffness command and the orthogonality command respectively based on the stiffness mismatch ΔK and orthogonality Kxy determined in step D.

[0096] According to a particular embodiment, steps A to E are included in a closed-loop servo system, or steps A to E are implemented iteratively in an open loop, preferably twice.

[0097] A second aspect of the invention is an inertial angle sensor comprising a resonator extending about two mutually perpendicular axes x and y that define a sensor coordinate system xy, and including:

[0098] - At least one vibration verification mass, the at least one verification mass comprising at least two portions configured to vibrate in opposite phase relative to each other in the direction x' of the defined wave coordinate system x'y' at vibration angular frequency ω, the vibration wave along x' forming an electrical angle θ with the axis x;

[0099] - A plurality of electrostatic transducers controlled by voltage and operating along the two axes x or y, comprising at least:

[0100] --A pair of detection transducers configured to detect the movement of vibration waves along these two axes, x and y;

[0101] --A pair of excitation transducers, which are subjected to excitation forces along two axes x and y respectively by a plurality of excitation commands determined by a servo system based on the detected movement. These forces are configured to keep the wave at a constant amplitude by amplitude commands and, where appropriate, to rotate the vibration wave by precession commands.

[0102] --A pair of orthogonally compensated transducers controlled by orthogonal commands; and

[0103] --A pair of stiffness-adjustable transducers, which are controlled by stiffness commands that set stiffness along axis x and stiffness commands that set stiffness along axis y respectively, thus forming stiffness commands;

[0104] The resonator has a stiffness matrix K in the sensor coordinate system. C And it has a stiffness matrix K in the wave coordinate system. O ;

[0105] The inertial angle sensor further includes:

[0106] - Used to determine the electrical angle θ k The module for θ(t);

[0107] - Used to recover the stiffness matrix K in the wave coordinate system x'y' O A module of at least one term, wherein the at least one term may be an orthogonal term K. O (2,1) or stiffness term K O (1,1); and

[0108] - A processing unit configured to perform at least steps A to D of the calibration method according to the invention, and optionally step E;

[0109] The stiffness-adjusting transducer and the orthogonal bias-compensating transducer are respectively configured to apply the stiffness command and the orthogonal command to the resonator.

[0110] According to a particular embodiment, the inertial sensor is axisymmetric.

[0111] According to one particular embodiment, which can be combined with previous specific embodiments, the inertial sensor includes at least two vibration verification masses forming at least two portions configured to vibrate in opposite phases to each other. One verification mass may be arranged around the other verification mass.

[0112] A third aspect of the present invention is a method for measuring the angular velocity or angular orientation of a carrier on which an inertial sensor according to the present invention is disposed, the measurement method comprising:

[0113] - The inertial sensor is calibrated by implementing the calibration method according to the invention; and

[0114] - To measure angular velocity or angular orientation, an inertial sensor is used in gyroscope tester mode or gyroscope mode.

[0115] The calibration method, inertial sensor, and measurement method according to the present invention may include any of the foregoing features, which may be taken individually or in any possible technical combination with other features.

[0116] The following description presents several examples of embodiments of the calibration apparatus according to the present invention, which do not limit the scope of the invention. These examples of embodiments not only include the essential features of the invention, but also additional features relevant to the embodiments discussed. Attached Figure Description

[0117] Other features, details, and advantages of the invention will become apparent from the description given with reference to the accompanying drawings, which are provided by way of example and illustrate, respectively:

[0118] Figure 1 (As cited) shows an axisymmetric resonator for a MEMS sensor according to the prior art, which is based on two vibration verification masses arranged in a manner that one surrounds the other.

[0119] Figure 2 (As cited) shows the structure of a MEMS sensor according to the prior art, which has a resonator symmetrical about two axes, x and y, that define the sensor coordinate system.

[0120] Figure 3 (As cited) shows a MEMS sensor according to the prior art, which has transducers located on two masses.

[0121] Figure 4 (As cited) illustrates the operation of an inertial sensor according to the prior art.

[0122] Figure 5 A first embodiment of the calibration method according to the present invention is shown.

[0123] Figure 6 A second embodiment of the calibration method according to the present invention is shown.

[0124] Figure 7 A third embodiment of the calibration method according to the present invention is shown.

[0125] Figure 8 A fourth embodiment of the calibration method according to the present invention is shown.

[0126] In all these figures, equivalent reference numerals may denote equivalent or similar elements.

[0127] Furthermore, the various parts shown in the accompanying drawings are not necessarily drawn to a uniform scale, thus making the drawings more readable. Detailed Implementation

[0128] The calibration method according to the invention is applicable to an inertial angle sensor including a resonator Res, which is associated with a module for vibrating the resonator and with a module for detecting the orientation of the vibration (vibration wave) relative to the sensor's coordinate system, for example, associated with an excitation transducer E and a detection transducer D controlled by an excitation command (E), and associated with trimming transducers TF and TQ controlled by trimming commands (TF, TQ).

[0129] This invention is particularly applicable to the above-mentioned contact information. Figures 1 to 3 The sensor described herein or is applicable to variations of the sensor also described above (at least one mass or at least two masses, axisymmetric or non-axisymmetric sensor, planar or non-planar structure; the MEMS sensor is merely one example of the embodiments).

[0130] In addition, refer to Figure 4 The general operation of the UE, wherein the processing unit UT is configured to apply the steps of the method according to the invention. Adding one or more modules to the UE from the perspective of performing the steps of the calibration method according to the invention may be a problem.

[0131] The vibration wave OV vibrates according to the vibration angular frequency ω. The calibration method according to the present invention is applicable to inertial sensors operating in gyroscope mode or gyroscope tester mode, and the excitation command is correspondingly servo-controlled during operation.

[0132] In vibration inertial angle sensors, especially axisymmetric ones, there are two coordinate systems: the sensor coordinate system xy, whose axes x and y are the axes containing the sensor's excitation and detection transducers; and the wave coordinate system x'y', where axis x' is the vibration axis of the wave OV, and axis y' is an axis perpendicular to x' in the sensor's plane. Axis x' makes an angle θ with respect to axis x, which is called the "electric angle," and coordinate system x'y' is called the "wave coordinate system."

[0133] In vibration inertial angle sensors, drift originates from the product of stiffness or orthogonality error and phase error. Recall that stiffness error corresponds to the stiffness mismatch between the vibrating axis and the axis perpendicular to the vibration, and orthogonality error arises from the mechanical coupling between the vibrating axis and the axis perpendicular to the vibration.

[0134] The vibration inertial angle sensor, including the one that adjusts the transducer, has an actuator that allows for stiffness and orthogonality corrections. However, even with stiffness and orthogonality correction commands, residual stiffness mismatch ΔK and / or residual orthogonality Kxy still exist.

[0135] One object of the present invention is to eliminate stiffness mismatch and orthogonality, or at least reduce them to values ​​acceptable to the operator, thereby making the sensor less sensitive to phase errors or even more sensitive.

[0136] The calibration method according to the invention can be applied to inertial angle sensors operating in gyroscope tester mode, or to inertial sensors operating in gyroscope mode. In the case of a gyroscope, each angle θ is a measured or empirical angle (resulting from changes in the angle of the carrier), while in the case of a gyroscope tester, the angle θ is set via a wave rotation command. In both gyroscope tester mode and gyroscope mode, the method according to the invention requires the use of multiple different angles θ.

[0137] The vibration gyroscope tester has a stiffness matrix, which has the following form K in the sensor coordinate system. C (This is given either before or without using the trim command.)

[0138] [Mathematical Expression 11]

[0139]

[0140] Where Kx and Ky are the stiffness along the x and y axes in the sensor coordinate system, and Kxy is the orthogonality in the sensor coordinate system.

[0141] The stiffness matrix K in the wave coordinate system (at an angle θ relative to the sensor coordinate system) O It is given by the following formula:

[0142] [Mathematical Expression 12]

[0143]

[0144] [Mathematical Expression 13]

[0145]

[0146] [Mathematical Expression 14]

[0147]

[0148] Using the trimming commands TFx, TFy (stiffness), and TQ (orthogonality), the stiffness matrix K can be directly modified using the trimming matrix Kt in the sensor coordinate system. C ,in:

[0149] [Mathematical Expression 15]

[0150]

[0151] Therefore, matrix K becomes K in the sensor coordinate system. mod .

[0152] [Mathematical Expression 16]

[0153]

[0154] Where Ktx and Kty are the corrections for the stiffness-adjusting transducer, and Kq is the correction for the positive transducer. These corrections are expressed in the sensor coordinate system. According to the present invention, the aim is to eliminate stiffness mismatch and reduce orthogonality to zero; therefore, the aim is to find a method that will make K... mod Let Kt be a matrix proportional to the identity matrix, i.e., such that:

[0155] [Mathematical Expression 17]

[0156]

[0157] When the sensor is in operation, that is, when it is being servo controlled, it is possible to measure the orthogonal term in the wave coordinate system, which is determined by term K. O (2,1) indicates that the term is:

[0158] [Mathematical Expression 18]

[0159] K O (2, 1) = K O (1,2)=(ΔK)sin(2θ)+(Kxy)cos(2θ)

[0160] It is possible to measure the stiffness term corresponding to the frequency along the wave axis x', which is given by term K. O (1,1) indicates that the term is:

[0161] [Mathematical Item 19]

[0162] K O (1,1)=K+(ΔK)cos(2θ)-(Kxy)sin(2θ)

[0163] From the last two equations, it can be concluded that if ΔK and Kxy are fixed terms, then it can be easily solved by measuring the orthogonal term K for at least two electrical angles. O (2,1)(and / or stiffness term K) O The value of (1,1) is used to determine ΔK (and Kxy).

[0164] The problem is that vibration gyroscope testers generally use electrostatic transducers that generate nonlinearity, which means that K, Kxy, and ΔK are not fixed, but also depend on the electrical angle θ, making it difficult to identify mismatches ΔK and Kxy.

[0165] Therefore, the stiffness matrix can be expressed in the sensor coordinate system in the following form:

[0166] [Mathematical Expression 20]

[0167]

[0168] Here, i is an integer varying between 1 and n, where n is greater than or equal to 1, and Aic, Ais, Bic, Bis, Cic, Cis, Dic, and Dis are values ​​that vary slowly with temperature and can therefore be considered constants with respect to the corrections made; some of these values ​​can be zero. Therefore, the terms Kx, Ky, and Kxy are more complex and depend on the electrical angle θ.

[0169] In other words, each term of the stiffness matrix consists of the sum of cosine and sine harmonics depending on the electrical angle θ. In other words, these sine terms are modulated by multiples of the angle θ.

[0170] To switch to wave coordinates, a fundamental change is made. Therefore, the stiffness matrix in wave coordinates is:

[0171] [Mathematical Expression 21]

[0172]

[0173] Stiffness matrix K O It has the same form as before, except that ΔK and Kxy, as well as K, have more complex forms and depend on the angle θ.

[0174] As indicated above, while the sensor is in operation, before calibration, it is possible to measure the value of term K in the wave coordinate system. O (2,1) expresses orthogonality and may be able to measure the term K O (1,1) represents the stiffness along the wave axis x'.

[0175] As indicated above, the excitation and trim commands are determined in the wave coordinate system, but are applied in the sensor coordinate system, while the measurements mentioned above are performed in the wave coordinate system.

[0176] However, the object of the present invention is to eliminate stiffness mismatch, that is, to make K O (1,1)–K O (2,2) is reduced to zero, and orthogonality is eliminated, that is, term K is reduced to zero. O (1,2) and K O (2,1) drops to zero. The problem is that it's possible to only measure K. O (1,1) and K O (2,1), but K is not measured. O (2,2). Therefore, there are two equations for three unknowns, and it is impossible to use multiple electrical angles because the terms of these equations vary as a function of the angles. These terms must be reprojected into the sensor coordinate system to determine the trimming corrections Ktx, Kty, and Kq to be applied to compensate for ΔK and Kxy.

[0177] The inventors have discovered that in the stiffness matrix K C The K coordinates are projected from the sensor coordinate system to the wave coordinate system to obtain K. O In this case, a stiffness mismatch (Kx-Ky) will appear in the term corresponding to the orthogonal measurement results in the wave coordinate system, and it is found that it can be isolated. Similarly, orthogonal Kxy appears in the term corresponding to the stiffness measurement results along the vibration axis x', and can be isolated, thus allowing the inference of orthogonal Kxy. Several simple examples will be used to illustrate this below.

[0178] First example: Consider the first stiffness matrix K in the sensor coordinate system. C1 This matrix has the following form:

[0179] [Mathematical Expression 22]

[0180]

[0181] Where a corresponds to Kx and b corresponds to Ky.

[0182] In the wave coordinate system, we obtain the following equation:

[0183] [Mathematical Expression 23]

[0184]

[0185] It should be noted that the stiffness mismatch ab appears in the term K representing the orthogonal term in the wave coordinate system. O1 In (2,1), the term is:

[0186] [Mathematical Expression 24]

[0187]

[0188] The unknown is expected to be (ab), since θ is known.

[0189] Second example: Now consider the second stiffness matrix K in the sensor coordinate system. C2 This matrix has the following form:

[0190] [Mathematical Expression 25]

[0191]

[0192] Here, acos(2θ) corresponds to Kx, and bcos(2θ) corresponds to Ky.

[0193] In the wave coordinate system, we obtain the following equation:

[0194] [Mathematical Expression 26]

[0195]

[0196] It can be seen that the stiffness mismatch (ab)cos(2θ) (the expected unknown is (ab), since θ is known) appears in term K. O2 In (2,1), the term is:

[0197] [Mathematical Expression 27]

[0198]

[0199] Third example: For the third stiffness matrix K in a sensor coordinate system having the following form C3 Similar results can be observed:

[0200] [Mathematical Expression 28]

[0201]

[0202] Here, asin(2θ) corresponds to Kx, and bsin(2θ) corresponds to Ky.

[0203] In this case, stiffness mismatch (ab)sin(2θ) appears in term K. O3 In (2,1), the term is:

[0204] [Mathematical Expression 29]

[0205]

[0206] It is possible to determine (ab) since θ is known, then (ab)sin(2θ) can be determined.

[0207] Fourth example: Now consider the fourth stiffness matrix K in the sensor coordinate system. C4This matrix has the following form:

[0208] [Mathematical Expression 30]

[0209]

[0210] Where c corresponds to Kxy.

[0211] In the wave coordinate system, we obtain the following equation:

[0212] [Mathematical Expression 31]

[0213]

[0214] It can be seen that orthogonal c appears in term K. O4 In (1,1), i.e. (-c.sin(2θ)), it represents the stiffness term in the wave coordinate system; and c can be determined because θ is known.

[0215] Fifth example: Now consider the fifth stiffness matrix K in the sensor coordinate system. C5 This matrix has the following form:

[0216] [Mathematical Expression 32]

[0217]

[0218] Where c.cos(2θ) corresponds to Kxy.

[0219] In the wave coordinate system, we obtain the following equation:

[0220] [Mathematical Expression 33]

[0221]

[0222] It can be seen that the orthogonal error c.cos(2θ) appears in term K. O5 In (1,1), the term is:

[0223] [Mathematical Expression 34]

[0224]

[0225] It is possible to determine c because θ is known, and thus c.cos(2θ) is determined.

[0226] Sixth example: Now consider the sixth stiffness matrix K in the sensor coordinate system. C6 This matrix has the following form:

[0227] [Mathematical Expression 35]

[0228]

[0229] Where c.sin(2θ) corresponds to Kxy.

[0230] In the wave coordinate system, we obtain the following equation:

[0231] [Mathematical Expression 36]

[0232]

[0233] It can be seen that the orthogonal error c.sin(2θ) appears in term K. O6 In (1,1), the term is:

[0234] [Mathematical Expression 37]

[0235]

[0236] It is possible to determine c because θ is known, and thus c.sin(2θ) can be determined.

[0237] In all the examples, it can be seen that it is therefore possible to utilize term K. O (1,1) Determine stiffness mismatch and / or utilize term K O (2,1) Determine orthogonality. More generally, it is possible to determine stiffness mismatch and / or orthogonality using one of the terms of the stiffness matrix in the wave coordinate system.

[0238] Generally, as indicated above, the stiffness matrix has a more complex form in the sensor coordinate system, namely, it takes the form of the sum of cos(iθ) and sin(iθ) harmonics, where i is an integer varying between 0 and n, and n is greater than or equal to 1, as expressed in mathematical formula 20. Typically, n can be contained between 2 and 4. Subsequently, it is possible to decompose the stiffness matrix into various simpler matrix sums, such as those in the four previous examples (K... C1 K C2 K C3 K C4 K C5 K C6 ...), these matrices are generally weighted by values ​​that can be considered constants. Therefore, it is possible to express stiffness error and orthogonality as a sum of terms, as explained below.

[0239] In each of the described cases, the inventors have determined that by performing an analysis of the cosine and sinusoidal harmonics (depending on the electrical angle θ) of the terms representing stiffness and / or orthogonality in the stiffness matrix in the wave coordinate system, it is possible to infer the nonlinear-related stiffness mismatch and orthogonality in the sensor coordinate system by isolating the amplitudes of these terms.

[0240] According to the present invention, multiple electrical angles (applied and / or measured depending on whether the sensor is operating in gyroscope tester mode or gyroscope mode) are determined to obtain angle modulation. This operation can employ continuous angle values ​​θ(t) (wave continuous rotation) or discontinuous angle values ​​θ(t) (multiple angles θ) k )Finish.

[0241] When the electrical angle of a wave has discontinuous values, filtering the orthogonal and / or stiffness terms in the stiffness matrix representing the wave coordinate system, for example, by using a least-squares filter, isolates and restores the constants (amplitudes) of these terms.

[0242] As the wave rotates continuously, demodulation with respect to angles is then performed; more precisely, demodulation is performed on the orthogonal and / or stiffness terms in the stiffness matrix representing the wave coordinate system. This demodulation involves applying a filter, such as a low-pass filter, to allow the isolation and recovery of the constants (amplitudes) of the orthogonal and / or stiffness terms. These amplitudes allow for the inference of stiffness mismatch and orthogonality.

[0243] Figure 5 A first embodiment of the calibration method of the present invention is shown, in which the following operations are performed:

[0244] A: Determine (apply or measure) the electrical angle (θ) k );

[0245] B: Recover the stiffness matrix K in the wave coordinate system x'y' O orthogonal term K O (2,1), the term is in the form of the sum of functions of the form cos(iθ) and sin(iθ), where i is an integer varying between 1 and n, and n is greater than or equal to 1;

[0246] For multiple, i.e., k electrical angles θ k Repeat steps A and B, where k is an integer varying between 1 and m, where m is greater than or equal to 2.

[0247] C: Determine the magnitudes of functions in the forms cos(iθ) and sin(iθ);

[0248] D: Determine the stiffness mismatch ΔK based on the determined amplitude; and

[0249] E: Apply stiffness adjustments Ktx and Kty based on the determined stiffness mismatch ΔK.

[0250] By examining the orthogonal term K O (2,1) Step C, which determines the amplitude, is performed by applying a least-squares filter. In this case, at least as many angles θ as the amplitude to be determined are required. k .

[0251] Figure 6 A second embodiment of the calibration method of the present invention is shown, in which the following operations are performed:

[0252] A: Determine (apply or measure) the electrical angle (θ) k );

[0253] B: Recover the stiffness matrix K in the wave coordinate system x'y' O stiffness term K O (1,1), the term is in the form of the sum of functions of the form cos(iθ) and sin(iθ), where i is an integer varying between 1 and n, and n is greater than or equal to 1;

[0254] For multiple, i.e., k electrical angles θ k Repeat steps A and B, where k is an integer varying between 1 and m, where m is greater than or equal to 2.

[0255] C: Determine the magnitudes of functions in the forms cos(iθ) and sin(iθ);

[0256] D: Determine the orthogonal Kxy based on the determined amplitude; and

[0257] E: Apply orthogonal adjustment Kq based on the determined orthogonal Kxy.

[0258] This can be achieved by adjusting the stiffness term K. O (1,1) Step C, which determines the amplitude, is performed by applying a least-squares filter. In this case, at least as many angles θ as the amplitude to be determined are required. k .

[0259] Obviously, according to Figure 5 and Figure 6 The calibration methods of the two embodiments can be combined to correct both stiffness mismatch and orthogonality.

[0260] Figure 7 A third embodiment of the calibration method of the present invention is shown, in which the vibration wave rotates continuously and performs the following operations:

[0261] A: Determine (apply or measure) the electrical angle θ(t);

[0262] B: Recover the stiffness matrix K in the wave coordinate system x'y' O orthogonal term K O (2,1), the term is in the form of the sum of functions of the form cos(iθ) and sin(iθ), where i is an integer varying between 1 and n, and n is greater than or equal to 1;

[0263] Repeating iterative steps A and B over a duration T makes it possible that:

[0264] C: For each i varying between 1 and n, demodulate orthogonal terms in the form of cos(iθ) and sin(iθ), the demodulation including the application of a low-pass filter to determine the magnitude of the functions in the form of cos(iθ) and sin(iθ);

[0265] D: Determine the stiffness mismatch ΔK based on the determined amplitude; and

[0266] E: Apply stiffness adjustments Ktx and Kty based on the determined stiffness mismatch ΔK.

[0267] If the terms are in the form of cos(iθ) and sin(iθ) as indicated above, then the duration T can correspond to one full rotation; or alternatively, if the terms are in the form of cos(2iθ) and sin(2iθ), then the duration T can correspond to half a rotation. The wave can (for example) rotate at a speed of 1° per second, but this is not a limitation.

[0268] The orthogonal term K can be restored as follows: O (2,1). The command Cq corresponds to the orthogonal force Fq used to control the wave within a known gain (also known as the scaling factor), with a correction Ko(2,1).x0, where x0 is the amplitude of the wave. Therefore, it is possible to obtain K using the following formula. O (2,1):

[0269] [Mathematical Expression 38]

[0270] K O (2,1)=Fq / x0

[0271] Figure 8 A fourth embodiment of the calibration method of the present invention is shown, in which the vibration wave rotates continuously and performs the following operations:

[0272] A: Determine (apply or measure) the electrical angle θ(t);

[0273] B: Recover the stiffness matrix K in the wave coordinate system x'y' O stiffness term K O (1,1), the term is in the form of the sum of functions of the form cos(iθ) and sin(iθ), where i is an integer varying between 1 and n, and n is greater than or equal to 1;

[0274] Repeating iterative steps A and B over a duration T makes it possible that:

[0275] C: For each i varying between 1 and n, demodulate orthogonal terms in the form of cos(iθ) and sin(iθ), the demodulation including the application of a low-pass filter to determine the magnitude of the functions in the form of cos(iθ) and sin(iθ);

[0276] D: Determine the orthogonal Kxy based on the determined amplitude; and

[0277] E: Apply orthogonal adjustment Kq based on the determined orthogonal Kxy.

[0278] If the terms are in the form of cos(iθ) and sin(iθ) as indicated above, then the duration T can correspond to one full rotation; or alternatively, if the terms are in the form of cos(2iθ) and sin(2iθ), then the duration T can correspond to half a rotation. The wave can (for example) rotate at a speed of 1° per second, but this is not a limitation.

[0279] The stiffness term K can be recovered by evaluating the angular frequency ω of the wave's vibration. O (1,1).

[0280] [Mathematical Expression 39]

[0281] KK O (1,1)=M×ω 2

[0282] Where M is mass and is known.

[0283] Obviously, according to Figure 7 and Figure 8 The calibration methods of the two embodiments can be combined to correct both stiffness mismatch and orthogonality.

[0284] In any of these four embodiments, and generally in the calibration method according to the invention, it is also possible to use the stiffness term K of the stiffness matrix in the wave coordinate system. O (1,1) is used to determine stiffness mismatch and / or the orthogonality term K of the stiffness matrix in the wave coordinate system is used. O (2,1) is used to determine orthogonality. More generally, it is possible to determine stiffness mismatch and / or orthogonality using any of the terms of the stiffness matrix in the wave coordinate system.

[0285] In any of these four embodiments, and generally in the calibration method according to the invention, the method can be implemented while the inertial sensor is operating in gyroscope mode. The electrical angle θ determined in step A... k Or, in this case, θ(t) is equal to the angle θ applied to the vibration by the precession command Cp. k_imp Or θ(t) imp It is possible to use θ.k_imp Or θ(t) imp Various values ​​of θ(t) average out the error, either through continuous rotation of θ(t). imp For example, within a full rotation or half rotation (or multiple full rotations or multiple half rotations), either through discontinuous rotations, for example, the measurement is for θ equal to 30°, then equal to 60°, and then equal to 90°. k_imp Executed. For each electrical angle θ k_imp Or θ(t) imp Implement steps A through B in sequence.

[0286] Alternatively, this calibration method can be performed while the inertial sensor is operating in gyroscope mode. Thus, the electrical angle θ k Alternatively, θ(t) originates from the rotation of the inertial sensor and is measured by it. The electrical angle determined in step A is equal to the measured rotation angle θ. k_m Or θ(t) m For each electrical angle θ k_m Or θ(t) m Steps A through B are performed sequentially. Angle θ k_m It can originate from modifications associated with the movement of the carrier, or it can originate from modifications associated with precession commands.

[0287] Moreover, alternatively, the calibration method according to the invention can be implemented in a hybrid gyroscope tester / gyroscope mode.

[0288] Therefore, trimming commands can be executed by modifying Ktx, Kty, and Kq based on stiffness mismatch and orthogonality determined by the electrical angle. This makes it possible to correct nonlinearities.

[0289] Therefore, it is possible to continuously determine stiffness mismatches and orthogonality, and correct them through trimming. The closed loop can update the trimming matrix, i.e., the values ​​Ktx, Kty, and Kq, thereby continuously correcting nonlinear errors. The corrections can also be applied in a predefined manner, or even only if the correction exceeds a predetermined threshold, which allows for reduction of noise associated with closed-loop control applications.

[0290] Steps A to E mentioned above can be performed in the servo system until ΔK and Kxy have dropped to zero.

[0291] Steps A through D of the calibration method will now be illustrated for each of the first four examples given above. In the first three illustrative examples, stiffness mismatch is determined, and in the fourth illustrative example, orthogonality is determined.

[0292] First Example

[0293] For the stiffness matrix K in the wave coordinate system x'y' O1 And for multiple electrical angles θ:

[0294] A. Determine the electrical angle θ;

[0295] The term K of the stiffness matrix in the B-recovery wave coordinate system x'y' O1 (2,1)(It is equal to term K) O1 (1,2)), i.e., mathematical expression 24

[0296]

[0297] (Note the stiffness matrix K in the sensor coordinate system) C1 In the equation, a corresponds to Kx, and b corresponds to Ky); then C demodulates the term K of the form sin(2θ). O1 (1,2) and obtain the following formula:

[0298] [Mathematical Expression 40]

[0299] Then, a low-pass filter was used to obtain the constant (amplitude): (ab) / 4;

[0300] Therefore, it is deduced that Kx–Ky is equal to four times (ab) / 4.

[0301] Second example

[0302] For the stiffness matrix K in the wave coordinate system x'y' O2 And for multiple electrical angles θ:

[0303] A. Determine the electrical angle θ;

[0304] The term K of the stiffness matrix in the B-recovery wave coordinate system x'y' O2 (2,1)(It is equal to term K) O2 (1,2)), i.e., mathematical expression 27

[0305]

[0306] (Note the stiffness matrix K in the sensor coordinate system) C2 In the equation, acos(2θ) corresponds to Kx, and bcos(2θ) corresponds to Ky; then C demodulates the term K of the form sin(2θ). O1 (1,2) and obtain the following formula:

[0307] [Mathematical Expression 41]

[0308]

[0309] Then, a low-pass filter was used to obtain the constant (amplitude): (ab) / 8;

[0310] Therefore, it is deduced that Kx–Ky is equal to (ab) / 8 multiplied by eight times cos(2θ).

[0311] Third Example

[0312] For the stiffness matrix K O3 The difference is that it must be multiplied by sin(2θ) instead of cos(2θ).

[0313] Fourth example

[0314] For the stiffness matrix K in the wave coordinate system x'y' O4 And for multiple electrical angles θ:

[0315] A. Determine the electrical angle θ;

[0316] The term K of the stiffness matrix in the B-recovery wave coordinate system x'y' O4 (1,1), that is: -c.sin(2θ);

[0317] (Note the stiffness matrix K in the sensor coordinate system) C4 In this context, c corresponds to Kxy: Then...

[0318] C demodulates the term K in the form of sin(2θ). O4 (1,1) and obtain the following expression:

[0319] [Mathematical Expression 42]

[0320]

[0321] Then, a low-pass filter was used to obtain a constant (amplitude): -c / 2;

[0322] Therefore, we can deduce that Kxy is equal to -c / 2 multiplied by (-2).

[0323] The same logic applies to examples five and six.

[0324] In the fifth example, the term K of the stiffness matrix in the wave coordinate system x'y' is recovered. O5 (1,1), that is, mathematical expression 34

[0325]

[0326] This term is demodulated with sin4θ and filtered to extract the constant (amplitude) c, which can then be multiplied by cos2θ.

[0327] In the sixth example, the term K of the stiffness matrix in the wave coordinate system x'y' is recovered. O6 (1,1), that is, mathematical expression 37

[0328] This term is demodulated with cos4θ and filtered to extract the constant (amplitude) c, which can then be multiplied by sin2θ.

[0329] As indicated above, when the stiffness matrix has a more complex form, i.e., when it takes the form of the sum of cos(iθ) and sin(iθ) harmonics (where i is an integer varying between 1 and n, and n is greater than or equal to 1), it is possible to make the stiffness matrix K... C Decomposed into various simpler matrices (e.g., those described above (K) C1 K C2 K C3 K C4 K C5 K C6 The sum of ... is generally weighted by values ​​that are considered constants for these matrices. Thus, stiffness errors and / or orthogonality errors correspond to the sum of terms determined in various steps D for each of these simple matrices.

[0330] An alternative is to use term K. O (1,1) Determine the stiffness mismatch, and / or use term K O (2,1) determines orthogonality, which is clearly seen in various examples. For example:

[0331] In the second example:

[0332] [Mathematical Expression 25]

[0333]

[0334] Switch to:

[0335] [Mathematical Expression 26]

[0336]

[0337] It can be seen that item K may be used. O2 (1,1) is determined (ab).

[0338] In the fourth example:

[0339] [Mathematical Expression 30]

[0340]

[0341] Switch to:

[0342] [Mathematical Expression 31]

[0343]

[0344] It is also possible to use item K. O4 (2,1) determines c.

[0345] Therefore, this invention uses a modified transducer to correct stiffness mismatch and orthogonality, and most importantly, it utilizes the fact that the harmonics are transformed from the sensor coordinate system to the wave coordinate system, and thus stiffness mismatch and orthogonality appear in some form in one or more terms of the stiffness matrix in the wave coordinate system. Since orthogonality and stiffness can be determined without applying any interference, it is possible to observe and correct both orthogonality and stiffness mismatch in real time without interfering with the sensor through interference that might ultimately remain in the measurements provided by the sensor.

[0346] The various embodiments described can be combined with each other.

[0347] Furthermore, the present invention is not limited to the embodiments described above, but covers any embodiments that fall within the scope of the claims.

Claims

1. A method (100) for calibrating the stiffness mismatch ΔK and / or orthogonality Kxy of a vibration inertial angle sensor (10), said inertial sensor comprising a resonator (Res) extending about two mutually perpendicular axes x and y defining a sensor coordinate system xy and comprising: - At least one vibration verification mass (M1), the at least one verification mass comprising at least two portions configured to vibrate in opposite phase relative to each other at vibration angular frequencies (ω) in the direction x' of the defined wave coordinate system x'y', the vibration wave (OV) along x' forming an electrical angle (θ) with the axis x; - A plurality of electrostatic transducers controlled by voltage and operating along two axes x or y, said plurality of electrostatic transducers comprising at least: -- A pair of detection transducers (Dx, Dy) configured to detect the movement of the vibration wave along the x-axis and the y-axis; -- A pair of excitation transducers (Ex, Ey) apply excitation forces to the pair of excitation transducers along the x-axis and the y-axis respectively by a plurality of excitation commands determined by a servo system based on detected movement. The excitation forces are configured to keep the wave at a constant amplitude by an amplitude command (Ca) and, where appropriate, to rotate the vibration wave by a precession command (Cp) and a command (Cq) for controlling the orthogonality of the wave. -- A pair of orthogonally compensated transducers (Q+, Q-) controlled by the orthogonal command (CTq); and -- A pair of stiffness-adjustable transducers (Tx, Ty) are controlled by a stiffness command (CTx) that sets the stiffness along the x-axis and a stiffness command (CTy) that sets the stiffness along the y-axis, respectively, thereby forming a stiffness command (CTf). The resonator (Res) has a stiffness matrix K in the sensor coordinate system C and a stiffness matrix K in the wave coordinate system O ; The calibration method is applied when the inertial sensor is in operation with an vibration wave (OV) vibrating in the direction x'. The calibration method includes the following steps: - A determines the electrical angle (Θ k , Θ(t)); - B Recover the stiffness matrix K in the wave coordinate system x'y' O At least one term, said at least one term being an orthogonal term K O (2,1) or stiffness term K O (1,1), the term is in the form of the sum of functions of the form cos(iθ) and sin(iθ), where i is an integer between 1 and n, and n is greater than or equal to 1; Either for multiple electrical angles (θ) k The iterations are repeated for steps A and B, where k is an integer varying between 1 and m, where m is greater than or equal to 2, or steps A and B are repeated for a certain duration (T), during which the vibration wave (OV) continuously rotates through an electrical angle (θ(t)) that varies as a function of time (t); thereafter - C determines the magnitudes of the functions in the forms cos(iθ) and sin(iθ); and - D determines the stiffness mismatch ΔK and the orthogonality Kxy based on the determined amplitude.

2. The calibration method according to claim 1, wherein the electrical angle describes a plurality of electrical angles (θ). k ),in, k is an integer varying between 1 and m, where m is greater than or equal to 2. Step C for determining the amplitude includes applying a least-squares filter to the recovered term, and the electrical angle (θ). k The number (m) is at least equal to the number of amplitudes to be determined.

3. The calibration method according to claim 1, wherein the vibration wave (OV) continuously rotates through an electrical angle (θ(t)) that varies as a function of time (t) over a certain duration (T), step C of determining the amplitude includes demodulating recovery terms in the form of cos(iθ) and sin(iθ) for each i varying between 1 and n, thereby determining the amplitude of the function in the form of cos(iθ) and sin(iθ); and - Based on the determined amplitude, perform step D to determine the stiffness mismatch ΔK and the orthogonality Kxy respectively.

4. The calibration method according to any one of claims 1 to 3, wherein, The inertial sensor operates according to the gyroscope tester mode, and the electrical angle (θ) determined in step A... k θ(t) is equal to the applied angle (θ) set by the precession command (Cp). k_imp θ(t) imp ).

5. The calibration method according to any one of claims 1 to 3, wherein, The inertial sensor operates in gyroscope mode, and the electrical angle (θ) obtained from the rotation of the inertial sensor... k The electrical angle (θ(t)) is measured by the inertial sensor and can be superimposed on the precession command (Cp). The electrical angle determined in step A is equal to the measured rotation angle (θ). k_m θ(t) m ).

6. The calibration method according to any one of claims 1 to 3, further comprising the following additional steps: - E applies the stiffness command (CTf) and the orthogonality command (CTq) respectively based on the stiffness mismatch ΔK and the orthogonality Kxy determined in step D.

7. The calibration method according to claim 6 can incorporate steps A to E into a closed-loop servo, or can iteratively implement steps A to E in an open loop.

8. The calibration method according to claim 7, wherein, Steps A through E are performed twice.

9. An inertial angle sensor (10) comprising a resonator (Res) extending about two mutually perpendicular axes x and y defining a sensor coordinate system xy and including: - At least one vibration verification mass (M1), the at least one verification mass comprising at least two portions configured to vibrate in opposite phase relative to each other at vibration angular frequencies (ω) in the direction x' of the defined wave coordinate system x'y', the vibration wave (OV) along x' forming an electrical angle (θ) with the axis x; - A plurality of electrostatic transducers controlled by voltage and operating along two axes x or y, said plurality of electrostatic transducers comprising at least: -- A pair of detection transducers (Dx, Dy) configured to detect the movement of the vibration wave along the x-axis and the y-axis; -- A pair of excitation transducers (Ex, Ey) apply excitation forces to the pair of excitation transducers along the x-axis and the y-axis respectively by a plurality of excitation commands determined by a servo system based on detected movement. The excitation forces are configured to keep the wave at a constant amplitude by an amplitude command (Ca) and, where appropriate, to rotate the vibration wave by a precession command (Cp) and a command (Cq) for controlling the orthogonality of the wave. -- A pair of orthogonally compensated transducers (Q+, Q-) controlled by the orthogonal command (CTq); and -- A pair of stiffness-adjustable transducers (Tx, Ty) are controlled by a stiffness command (CTx) that sets the stiffness along the x-axis and a stiffness command (CTy) that sets the stiffness along the y-axis, respectively, thus forming a stiffness command (CTf). The resonator (Res) has a stiffness matrix K in the sensor coordinate system. C And it has a stiffness matrix K in the wave coordinate system. O ; The inertial angle sensor further includes: - Used to determine the electrical angle (θ) k The module for θ(t)); - Used to recover the stiffness matrix K in the wave coordinate system x'y' O A module of at least one term, wherein the at least one term is an orthogonal term K. O (2,1) or stiffness term K O (1,1); and - A processing unit (UT) configured to perform at least steps A to D of the calibration method according to any one of claims 1 to 7, and optionally step E of the calibration method. The stiffness-adjusting transducers (Tx, Ty) and the orthogonal bias-compensating transducers (Q+, Q-) are respectively configured to apply the stiffness command (CTf) and the orthogonal command (CTq) to the resonator.

10. The inertial angle sensor (10) according to claim 9, wherein the inertial sensor is axisymmetric.

11. The inertial angle sensor (10) according to claim 9 or claim 10, comprising at least two vibration verification masses (M1, M2) forming the at least two portions configured to vibrate in opposite phases relative to each other, wherein one verification mass is capable of being arranged around the other verification mass.

12. A method for measuring the angular velocity or angular orientation of a carrier on which an inertial sensor (10) according to any one of claims 9 to 11 is disposed, the measurement method comprising: - The inertial sensor is calibrated by implementing the calibration method (100) according to any one of claims 1 to 8; as well as - To measure angular velocity or angular orientation. The inertial sensor is used in either gyroscope tester mode or gyroscope mode.

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