Improved Inertial Sensor

Abstract

A method (100) for determining a quadrant command (CTq) and a frequency command (CTf) for a vibration wave generated by a resonator (Res) of an inertial angular sensor (10), the method comprising the steps of: - A determining the electrical angle (θ); - B estimating first values (Kq’, ΔK’) of the quadrant stiffness and the equalization stiffness respectively according to a first (TrimQ) control operation and according to a second (TrimF) control operation, the first values being estimated in the wave reference frame X’Y’; - C determining second values (Kq, ΔK) of the quadrant stiffness and the equalization stiffness in the sensor reference frame XY according to the first values (Kq’, ΔK’) of the stiffness estimated in step B; - D determining the quadrant command (CTq) and the frequency command (CTf) respectively corresponding to the second values (Kq, ΔK) determined in step C; - E applying the frequency command (CTf) and the quadrant command (CTq) determined in step D.

Description

Field of the Invention

[0001] The field of the invention is that of vibratory inertial sensors in which two masses are set into vibration. The invention more particularly relates to MEMS inertial sensors having a planar structure and typically microfabricated into a support substrate. Background of the Invention

[0002] Fork inertial sensors are known to those of ordinary skill in the art. In document EP 2960625, an inertial sensor is described which is microfabricated into a thin planar substrate such that it is possible to measure angular position (gyroscope) or angular velocity (gyro). Its main characteristics are recalled below.

[0003] The fabrication of these microfabricated sensors, also known as MEMS (Micro-Electro-Mechanical Systems) sensors, uses microfabrication techniques, etching, doping deposition, etc. common to those used for manufacturing electronic integrated circuits, allowing for low manufacturing costs.

[0004] These sensors are made up of Figure 1 the two vibrating moving masses M1 and M2 shown in, which are positioned one around the other (concentric) and are excited via one or more excitation transducers so as to vibrate in the plane of the substrate (plane XY in the figure) in a tuning fork mode. The two masses are suspended at fixed attachment points A of the substrate by (symmetrical) suspension springs RS. The two masses are coupled to each other by an element having a stiffness RC. It is sought to achieve by construction a stiffness along X equal to the stiffness along Y and a zero coupling stiffness between X and Y. The useful vibration mode corresponds to a linear vibration with the two masses in antiphase.

[0005] This architecture forms a resonant system with two masses coupled to each other by Coriolis acceleration. When the gyroscope rotates about an axis Z (so-called sensitive axis) perpendicular to the plane XY, due to the Coriolis effect, the forced vibration of the constituent having an angular rotation vector results in a force that sets the moving mass into a natural vibration perpendicular to the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotation speed. The electronic components associated with the sensor calculate the amplitude of the vibration in a direction orthogonal to the direction of excitation, independent of the latter (assumed known).

[0006] The sensor can operate in gyro mode: by modifying the direction of excitation of the natural vibration with respect to the housing of the sensor remaining fixed, and then the output information is an image of the necessary energy that has to be applied to the excitation transducer in order to keep the direction of the natural vibration fixed despite the movement of the housing. Measuring this reaction force makes it possible to obtain the angular velocity Ω of the sensor. The sensor can also operate in gyroscope mode: the direction of the natural vibration is free and is detected in order to give the angular orientation of the sensor.

[0007] The gyroscopic mode exhibits the following advantages: (i) it has no angular noise, and more precisely any angular error linked to the position of the vibration; and (ii) it has no variation in angular velocity error (drift) linked to the angle (by definition, since the reference frame with respect to the gyroscope maintains a constant angle).

[0008] The gyroscope mode exhibits the following advantages: (i) it has a very low scaling factor error compared to the gyroscopic mode and (ii) it has very high operating dynamics.

[0009] The entire structure of the resonator is axisymmetric with respect to two axes X and Y that define the sensor reference frame, as illustrated in Figure 2 Axisymmetry is understood to mean that the structure is symmetric with respect to X and symmetric with respect to Y. As described below, these axes form the main directions of the actuators / detectors operating along these two axes.

[0010] To excite useful vibration modes in any given direction in the plane, the excitation signal is decomposed into two components that have adjusted respective amplitudes and are applied separately to an excitation transducer Ex that acts along direction X and an excitation transducer Ey that acts along direction Y, associated with at least one moving mass body ( Figure 2 the internal mass M1 in). These transducers are capable of maintaining forced vibrations via an amplitude command (against the damping of the MEMS) and in any direction in the plane XY, via a precession command (rotating wave).

[0011] The movement of the generated wave is detected by combining information collected by at least one pair of detection transducers Dx, Dy that are used to detect the position of the mass body in its travel in each of the two in the sensor reference frame XY ( Figure 2 ).

[0012] The transducers are preferably formed by comb electrodes interlaced with a varying air gap. There are fixed combs and moving combs, the teeth of the combs are interlaced with the fixed electrodes of the machine substrate, and the teeth of the moving combs are interlaced with the teeth of the fixed combs and are joined to the moving mass body associated with the transducer under consideration.

[0013] The excitation mainly consists of applying an AC voltage between the moving comb and the fixed comb at the desired vibration frequency (the mechanical resonance frequency of the suspended moving mass body). The resulting movement is perpendicular to the teeth of the comb.

[0014] The detection mainly consists in applying a bias voltage between a fixed comb and a moving comb and observing the load variation generated by the capacitance variation between the fixed comb and the moving comb, the capacitance variation being caused by the variation of the spacing between the teeth of the fixed comb and the teeth of the moving comb. The measured movement is a movement perpendicular to the teeth of the comb.

[0015] It is known to those of ordinary skill in the art that production defects of sensors result in errors in the information transmitted at their output. Most of these defects need to be compensated for by calibrating the gyroscope.

[0016] It is known to perform this compensation by locally removing material, for example by laser ablation, in order to modify the mass or stiffness distribution. This method is expensive and even impossible to implement on gyroscopes microfabricated into thin silicon substrates, where the sensing and actuating movements are in the plane of the substrate.

[0017] The difference between two types of defects in terms of stiffness is plotted. The vibrating mass / spring assembly is characterized by a 2*2 stiffness matrix. This matrix is symmetric and is characterized by a reference frame XY with stiffness Kx along X, stiffness Ky along Y, and coupling stiffness Kxy between X and Y (where Kyx = Kxy). Due to production defects, Kx is different from Ky and Kxy is non-zero, but for the optimized operation of the sensor, it is sought to achieve Kx = Ky and Kxy = 0, that is, the final stiffness matrix is proportional to the identity matrix.

[0018] The vibration axis of the wave is called X'. This axis defines a reference frame X'Y', where in the plane of the MEMS, Y' is perpendicular to X'. The axis X' forms an angle called the electrical angle (θ) with the axis X, and the reference frame X'Y' is called the wave reference frame. It is assumed that the time is when the wave vibrates along X (X' = X).

[0019] The first type of defect is the frequency difference between the main axis of vibration and the axis perpendicular to the vibration and corresponding to the stiffness matrix of the system in the plane of the MEMS, where the stiffness along the axis X is different from the stiffness along the axis Y in the stiffness matrix of the system. It is sought to equalize the resonance frequencies along the two above-mentioned axes by means of adjustable electrostatic stiffness. This electrostatic stiffness, called the equalizing stiffness, is transmitted by frequency adjustment transducers Tx, Ty acting along the directions X and Y (at least one pair on at least one mass, see Figure 2 ). The aim of applying it is to equalize the stiffness along the two axes of vibration by reducing the value of the highest stiffness, thus making the frequencies equal. Frequency correction is also called frequency trimming.

[0020] The second type of defect originates from the mechanical coupling between the axis vibrating at the origin, called the quadrant bias, and the vertical axis. These are anisotropic drawbacks regarding the dynamic rigidity of the components of the two vibrating masses, which are manifested in vibrations that are no longer linear but elliptical and correspond to the presence of a non-zero coupling rigidity Kxy. One solution is to apply a (sinusoidal) force F to the system via an excitation transducer to cancel this term. The problem is that the application of this force does not act at the exact right time (phase error) and on the right axis (gain error), resulting in the application of a drift. To avoid applying the force F, instead of applying a force, the term Kxy is physically canceled by directly changing the rigidity of the resonator via at least a pair of transducers Q+ and Q-, as illustrated in Figure 2 ( Figure 2 where there are 2 pairs of Q+ / Q-). These transducers operating on X and Y are located on the diagonal to conform to symmetry and "geometric" anisotropy, and for reasons of large volume. Correcting the quadrant bias is also known as quadrant clipping (or trimming).

[0021] Quadrant trimming transducers thus modify the characteristics of the MEMS sensor to remove the coupling between the two axes of the wave reference frame, and frequency trimming transducers modify the characteristics of the MEMS sensor to remove the frequency difference between the two axes of the wave reference frame.

[0022] The transducers Tx, Ty, Q+ and Q- are preferably also interdigitated combs, as illustrated in Figure 2 and Figure 3 .

[0023] The excitation, detection, frequency regulation and quadrant bias correction transducers are preferably implemented on two masses, as illustrated in Figure 3 where index 1 corresponds to mass M1 and index 2 corresponds to mass M2. Figure 2 and Figure 3 represent non-limiting exemplary arrangements, and many other types of arrangements are possible, with the constraint of forming an axisymmetric system.

[0024] Figure 4 Illustrates the operation of an inertial sensor CI0 according to the prior art, and more specifically illustrates the frequency trimming and quadrant trimming control operations. The resonator Res includes the various transducers described above and is symbolized by E (excitation), D (detection), TQ (trim quadrant) and TF (trim frequency). The vibration wave OV vibrates along X (X’ = X). The vibration mode along X’Y’ is consistent with the excitation and detection modes.

[0025] Three control operations control the excitation comb E in parallel: The precession control operation (not shown) holds the vibration wave at a predetermined angle (measuring the force reacting to the Coriolis force in the gyroscope mode); the amplitude control operation (not shown) keeps the vibration of the wave constant, and the quadrant control operation controls the force fy in order to maintain linear vibration (via the command Ctqe). One problem linked to the quadrant force fy is the precision in terms of phase and in terms of the gain or direction of its application. A fourth PLL loop (not shown) seeks to identify the phase of the oscillation (the position of the mass during its travel). This PLL loop does not affect the vibration wave; it serves as an observer. Using the information transmitted by the phase-locked loop, the force can be positioned so as to be sent to Ex and Ey via the three above-mentioned control operations with the correct phase, and the detection signal can be demodulated.

[0026] The detection transducer measures the position (x, y) vibrating in the sensor reference frame XY. In addition to the three control operations performed on the excitation, a first and a second control operation are performed respectively for detailed trimming and frequency trimming. The processing unit UT performs various calculations and, for correction, generates commands for the various transducers: the command CTqe for applying the quadrant force via the E transducer, the frequency trimming command CTf for the TF, and the quadrant trimming command CTq for the TQ. The commands CTq and CTf for trimming are DC voltages that modify the intrinsic characteristics of the resonator, while the command CTqe for the force is a sinusoidal voltage (see above). The quadrant command CTq for the TQ is adjusted so as to achieve zero quadrant force (command CTqe) applied to the excitation E in the steady state, thus solving the problem linked to the application of this force.

[0027] The signal from y is cosine demodulated and sine demodulated. The cosine demodulation is used for the first control operation related to quadrant trimming. The resulting signal is processed by the corrector Coq1 and transmits an estimate of the quadrant stiffness Kq intended to be used for removing the coupling stiffness Kxy. After the second corrector Coq2 (integrator) and by means of the device Gq, the stiffness is converted into a voltage and the quadrant command CTq is applied to the TQ. The sine demodulation is used for the second control operation related to frequency trimming. The resulting signal is processed by the corrector Cof, which generates the equalization stiffness ΔK, and then the device Gf converts this stiffness into a voltage in order to generate the frequency trimming command CTf.

[0028] The control operations for frequency correction and quadrant correction were initially developed for non-axisymmetric sensors (X and Y do not perform the same function), which are configured to operate using waves vibrating along X. In this case, the first and second control operations operate independently and work correctly.

[0029] For an axially symmetric sensor that allows the use of waves vibrating at an angle (θ) rather than 0°, trimming becomes dependent on each other and no longer works correctly. For example, for some angles such as θ = π / 4, quadrant trimming has no effect on the coupling stiffness Kxy and essentially results in the first and second control operations. The instability described above causes actuator saturation and requires restarting the sensor. Thus, when the MEMS sensor operates at an angle θ rather than zero, it may be preferable to stop the trimming control operation, which results in a measurement error in the sensor connected to apply the additional force.

[0030] An object of the present invention is to correct the above-mentioned drawbacks by proposing an operating mode of a sensor that allows for effective implementation of frequency and quadrant bias correction control operations for waves vibrating at any electrical angle. Summary of the Invention

[0031] The present invention relates to a method for determining quadrant commands and frequency commands for vibration waves generated by a resonator of an inertial angle sensor, the resonator having a planar and axially symmetric structure with two axes X and Y defining a sensor reference frame XY perpendicular to each other, and including two vibrating moving masses (M1, M2), one located around the other, coupled to each other by coupling springs and configured to vibrate in opposite phases in a direction X' defining a wave reference frame X'Y', the resonator further including a plurality of electrostatic transducers controlled by voltage and operating along the two axes X and Y, at least including the following transducers located on at least one of the two masses;

[0032] The resonator further includes a plurality of electrostatic transducers controlled by voltage and operating along the two axes X and Y, at least including the following transducers on at least one of the two masses:

[0033] - A pair of excitation transducers called E transducers, configured to hold the wave at a constant amplitude via an amplitude command (Ca) and, if necessary, rotate the vibration wave via a precession command (Cp), a pair of detection transducers called D transducers, configured to detect the movement of the vibration wave, a pair of quadrant bias compensation transducers called TQ transducers, configured to apply a quadrant stiffness via a quadrant command (CTq), the quadrant stiffness being configured to eliminate the coupling stiffness between X' and Y', and a pair of frequency adjustment transducers called TF transducers, configured to apply an equalizing stiffness via a frequency command (CTf), the equalizing stiffness being configured to eliminate the stiffness difference between X' and Y' so as to equalize the resonance frequency of the vibration wave on X' and Y'.

[0034] The method is used when the inertial sensor operates with a vibration wave vibrating along X' characterized by an electrical angle (θ), and the method includes the steps:

[0035] -A determining the electrical angle;

[0036] -B respectively estimating a first value of the quadrant stiffness and the balance stiffness according to a first control operation and according to a second control operation, the first value being estimated in the wave reference system X'Y';

[0037] -C determining a second value of the quadrant stiffness and the balance stiffness in the sensor reference system XY according to the first value of the stiffness estimated in step B;

[0038] -D determining the quadrant command and the frequency command respectively corresponding to the second value determined in step C;

[0039] -E applying the frequency command (CTf) and the quadrant command (CTq) determined in step D

[0040] According to a variant, the inertial sensor operates in gyroscope mode, and the electrical angle determined in step A is equal to the angle imposed via the precession command.

[0041] According to another variant, the inertial sensor operates in gyroscopic mode, the electrical angle generated by the rotation of the inertial sensor is measured by the inertial sensor, and the electrical angle determined in step A is equal to the measured rotation angle.

[0042] According to still another variant, the method according to the present invention includes:

[0043] -A first stage, in which the electrical angle describes a plurality of electrical angles obtained by applying the precession command, steps A to E are implemented for each electrical angle, and step D further includes a sub-step of storing the associated frequency command value and a sub-step of determining the variation law of the frequency command according to the electrical angle;

[0044] -A second stage, in which the inertial sensor operates in gyroscopic mode, the electrical angle is free due to the rotation of the inertial sensor and is measured by the inertial sensor, and the second stage includes:

[0045] * a step (BO) of placing the second control operation in an open loop, and the applied frequency command is then determined according to the variation law for the measured rotation angle;

[0046] * a step of detecting the resonator frequency difference, and as long as the resonator frequency difference is less than or equal to a predetermined threshold, the open-loop placement step is implemented;

[0047] *When the frequency difference is greater than the threshold value, the step of placing the second control operation back into the closed loop, and the method then loops back to the first stage to update the variation rule.

[0048] According to one embodiment, step B includes a sub-step B1 of determining the position of the vibration wave in the reference frame X'Y' according to the measurement of the position of the vibration wave in the sensor reference frame XY and according to the electrical angle, and a sub-step B2 of estimating a first value of the quadrant stiffness and the balance stiffness according to the position in the wave reference frame.

[0049] According to one embodiment, step C mainly consists of determining the vector defined by the second value by applying a rotation of an angle equal to twice the electrical angle of the vector defined by the first value.

[0050] According to another aspect, the present invention relates to an inertial angle sensor, comprising:

[0051] - A resonator (Res) having a plane and an axisymmetric structure with two axes X and Y that are perpendicular to each other and define a sensor reference frame XY, and including two vibrating moving masses (M1, M2), one of which is positioned around the other, coupled to each other by a coupling spring, and configured to vibrate in opposite phases along a direction X' characterized by an electrical angle and defining a wave reference frame X'Y', the resonator further including a plurality of electrostatic transducers controlled by voltage and operating along two axes X and Y, at least including the following transducers on at least one of the two masses:

[0052] A pair of excitation transducers called E transducers, configured to keep the wave at a constant amplitude via an amplitude command and, if necessary, rotate the vibration wave via a precession command, a pair of detection transducers called D transducers, configured to detect the movement of the vibration wave, a pair of quadrant bias compensation transducers called TQ transducers, configured to apply a quadrant stiffness via a quadrant command, the quadrant stiffness being configured to eliminate the coupling stiffness between X' and Y', and a pair of frequency adjustment transducers called TF transducers, configured to apply a balance stiffness via a frequency command, the balance stiffness being configured to eliminate the stiffness difference between X' and Y' so as to equalize the resonance frequency of the vibration wave on X' and Y'. The quadrant stiffness and the balance stiffness are determined according to a first control operation and a second control operation, respectively.

[0053] The sensor further includes a processing unit, which is configured to determine the electrical angle and includes:

[0054] - A first module configured to estimate first values of the quadrant stiffness and the balance stiffness respectively according to the first control operation and the second control operation, the first values being estimated in the wave reference frame X'Y'.

[0055] - A second module configured to determine second values of the quadrant stiffness and the balance stiffness in the sensor reference frame XY according to the first values of the stiffness.

[0056] - Components of two electrical gain modules configured to determine respectively the quadrant command corresponding to the second value of the quadrant stiffness and the frequency command corresponding to the second balance stiffness value.

[0057] - The TF transducer and the TQ transducer are configured to apply respectively the frequency command and the quadrant command to the resonator.

[0058] According to one embodiment, the first module is configured to determine the position of the vibration wave in the wave reference frame X'Y' according to the electrical angle and according to the measurement of the position of the vibration wave in the sensor reference frame XY performed by the D transducer, and to estimate the first values of the quadrant stiffness and the balance stiffness according to the position in the wave reference frame.

[0059] According to one embodiment, the second module is configured to determine the vector defined by the second value by applying a rotation of an angle equal to twice the electrical angle of the vector defined by the first value.

[0060] The following description provides several exemplary embodiments of the device of the present invention, these examples not limiting the scope of the present invention. These exemplary embodiments provide the basic features of the present invention as well as additional features linked to the embodiments under consideration. Description of the Drawings

[0061] In the following detailed description and with reference to the drawings, the present invention will be better understood and other features, objects and advantages of the present invention will become apparent, the drawings giving non-limiting examples and in the drawings:

[0062] Figure 1 (already mentioned) shows the structure of the resonator of the inertial sensor to which the present invention is applied.

[0063] Figure 2 Illustrates an example of an axisymmetric resonator having a plurality of transducers on an inner mass.

[0064] Figure 3 Illustrates an example of an axisymmetric resonator having a plurality of transducers on two inner and outer masses.

[0065] Figure 4 Illustrates the frequency correction and quadrant bias correction control operations according to the prior art.

[0066] Figure 5 Illustrates the method according to the present invention.

[0067] Figure 6 Illustrates a variant of the method according to the present invention.

[0068] Figure 7 Illustrates a preferred embodiment for implementing steps B and C of the method according to the present invention.

[0069] Figure 8 Illustrates the inertial sensor according to the present invention.

[0070] Figure 9 Illustrates in the gyroscope from Figure 8 an embodiment of the inertial sensor according to the present invention.

[0071] Figure 10 Illustrates in the turn indicator from Figure 8 an embodiment of the inertial sensor according to the present invention.

[0072] Figure 11 Illustrates during the second phase of the hybrid mode from Figure 8 an embodiment of the inertial sensor according to the present invention.

[0073] For clarity, the same elements will be denoted by the same reference numerals in the various figures. DETAILED DESCRIPTION

[0074] A deep analysis of the operation of the sensor shows that the difficulty in implementing frequency and quadrant bias correction comes from the fact that the TQ and TF transducers are located on the sensor axes X and Y and operate along the sensor axes X and Y rather than along the wave axes X'Y'. When the frequency and quadrant trimming control operations are applied as such to a wave vibrating at a non-zero electrical angle, the transmitted balance and quadrant stiffness correspond to the values to be applied to a transducer located on and operating along the axes X'Y' of the wave reference frame. However, these transducers are fixed and located along the axes X and Y of the sensor. The stiffness values transmitted by the first and second control operations are thus not optimal for vibrations along X'. The method according to the present invention aims to transmit effective commands CTq and CTf for TQ and TF, that is, commands suitable for the value of the electrical angle, regardless of its value.

[0075] Moreover, the frequency difference between the two modes and the quadrant bias vary with the electrical angle of vibration, and due to the non-linearity of the sensor, the correction to be made also varies according to this angle.

[0076] Finally, when the angle changes with time, since the defect depends on the angle, it is no longer possible to perform filtering over a long period because the dynamics of the error are rapid.

[0077] To solve this problem, the present invention relates to a method 100 for determining a quadrant command CTq and a frequency command CTf for a vibration wave generated by a resonator Res of an inertial angle sensor, the method being applied when the inertial sensor operates with a vibration wave vibrating along an axis X' (characterized by an electrical angle θ). Figure 5 The various steps of the method are illustrated therein.

[0078] The inertial sensor to which the present invention is applied includes a resonator as described in the prior art, which has a planar and axially symmetric structure with two axes X and Y perpendicular to each other, defining a sensor reference frame XY, and includes two vibrating moving masses M1 and M2, one located around the other, coupled to each other by a coupling spring and configured to vibrate in a tuning fork mode and in opposite phase in the direction X' defining a wave reference frame X'Y'.

[0079] The resonator includes a plurality of electrostatic transducers controlled by voltage and operating along two axes X and Y, including at least the following transducers on one of the two masses:

[0080] – A pair of excitation transducers, called E transducers, configured to hold the wave at a constant amplitude via an amplitude command, maintain the wave plane, and, if necessary, rotate the vibration wave via a precession command.

[0081] - A pair of detection transducers, called D transducers, configured to detect the movement of the vibration wave.

[0082] - A pair of quadrant bias compensation transducers, called TQ transducers, configured to apply quadrant stiffness via a quadrant command CTq, the quadrant stiffness being configured to cancel the coupling stiffness between X' and Y'.

[0083] - A pair of frequency adjustment transducers, called TF transducers, configured to apply equalization stiffness via a frequency command CTf, the equalization stiffness being configured to cancel the stiffness difference between X' and Y' so as to equalize the resonant frequency of the vibration wave on X' and Y'.

[0084] In a first step A, the electrical angle θ is determined.

[0085] In a second step B, a first value Kq’ of the quadrant and a first value ΔK’ of the equalization stiffness are respectively estimated according to a first control operation TrimQ and according to a second control operation TrimF. These values are determined by control operations of the same type as those operating according to the prior art (except for some differences which will be described subsequently), which “ignore” the fact that the vibration wave vibrates along axis X’ instead of X. These values Kq’ and ΔK’, called the first values, are considered to be estimated in the wave reference frame X’Y’, since when the wave vibrates along X’, they correspond to the values transmitted by the control operations. They correspond to the values that will have to be applied to TQ and TF, which operate along X’ and Y’.

[0086] In a following step C, a second value Kq, ΔK of the quadrant and the equalization stiffness in the sensor reference frame XY is determined according to the first values Kq’, ΔK’ of the stiffness estimated in step B. These values Kq, ΔK, called the second values, are suitable for the fact that the TQ and TF transducers operate along axis XY. Kq’ and ΔK’ are thus converted into Kq and ΔK in order to take into account the fact that the buffers applying the equalization and the quadrant stiffness operate in the sensor reference frame XY and not in the wave reference frame X’Y’. In other words, based on the values Kq’ and ΔK’ estimated in the wave reference frame X’Y’, a conversion is performed on these two terms in order to return to the sensor reference frame XY in which the trimming is performed.

[0087] In step D, a quadrant command CTq and a frequency command CTf are respectively determined in a conventional manner corresponding to the second values Kq and ΔK determined in step C, and finally, in step E, the frequency command CTf and the quadrant command CTq determined in step D are applied.

[0088] The method according to the invention can thus be applied to sensors using trimming control operations of the same type as those of the prior art. That is to say, there is no need to develop new control operations, the difference in terms of signal processing being, for example, the conversion of the stiffness transmitted by these control operations performed in method step C. Due to the accuracy of the stiffnesses Kq and ΔK calculated by the conversion, the force applied to E by the plane wave returns to zero in the steady state, the error linked to the application of this force is eliminated, and all corrections (frequency and quadrant) are performed via the TQ and TF transducers.

[0089] Thanks to this adaptation, the frequency and quadrant errors are eliminated and the inertial sensor transmits (speed or angle) measurements that are no longer sensitive to errors of the stiffness matrix, regardless of the value of the vibration angle θ of the wave. Recall that the method according to the invention is used continuously and in parallel with the transmission of measurements of the angular velocity or the rotation angle about the sensing axis Z.

[0090] By implementing the method according to the invention, a frequency difference initially of approximately 3 Hz is brought back to a few mHz, and a quadrant error of approximately 100° / s is brought back to less than 0.1° / s. These values coupled with an electronic device in the category of 100 ppm in terms of phase error make it possible to achieve a drift of less than one degree per hour.

[0091] According to a variant, the method is implemented when the inertial sensor operates in gyroscope mode. In this case, the electrical angle θ determined in step A is equal to the angle θimp imposed on the vibration via the precession command. Various values of θ can be used to average the error, for example by performing measurements for θ equal to 30°, then equal to 60°, and then equal to 90°. With the method according to the invention, this implementation becomes precise and efficient on MEMS sensors.

[0092] According to another variant, the method is implemented when the inertial sensor operates in gyrocompass mode. Then, the electrical angle θ is generated by the rotation of the inertial sensor and is thus measured. The electrical angle determined in step A is equal to the measured rotation angle θm.

[0093] According to yet another variant, the method according to the invention is implemented in the Figure 6 hybrid mode described.

[0094] The method includes a first phase in which the electrical angle describes a plurality of electrical angles θi, where i is an index, which are obtained by applying a precession command Cp. Steps A to E are successively implemented for each electrical angle θ. In addition to determining CTf and CTq, step D includes a sub-step MEM of storing the frequency command value CTfi associated with each angle θi and a sub-step MOD of determining the variation law CTf(θ) for the frequency command according to the electrical angle. The form of this law typically has the type ∑(akcos2kθ + bksin2kθ) where k typically varies from 0 to 4, and determining it consists of calculating the values of the coefficients ak and bk according to the smoothing performed on the measurement points θi.

[0095] This first phase can be implemented independently of the operating mode of the sensor, i.e., gyroscope or gyrocompass. Preferably, it is performed in gyroscope mode. When the sensor operates in gyrocompass mode (typically when the vehicle in which the sensor is embedded is stationary), the angle θi is obtained by sending a precession setpoint in order to take this angle from the known current angle. The first phase thus makes it possible to have a model of the command CTf to be applied according to the value of the electrical angle.

[0096] In the second phase, the inertial sensor operates in gyrocompass mode, the electrical angle is free and is generated by the rotation of the inertial sensor, the measured value of which is θm.

[0097] The second stage first includes the step BO of placing the second control operation TrimF in the open loop. At this moment, the control operation TrimF stops transmitting the real-time command CTf, which is replaced by the command CTf(θ) determined according to the variation law of the measured rotation angle θm. The command is applied over time, tracking the variation of θm. At the same time, the resonant frequency difference Δf between the two wave axes is measured. The principle of frequency trimming mainly lies in transmitting the interference of measuring Δf and then correcting it via CTf. When the operation is in the open-loop mode, it is possible to continue transmitting the interference and measuring Δf, but the correction CTf is no longer applied.

[0098] As long as the resonant frequency difference is less than or equal to the predetermined threshold S, the open-loop placement step BO is achieved. The difference Δf changes according to the temperature and during aging. When the frequency difference Δf becomes greater than the threshold, the second control operation TrimF is placed back in the closed loop to allow the update of the variation law and restart in the first stage. Throughout the second stage, the first control operation continues to operate as in the first stage. This hybrid mode exhibits various advantages.

[0099] When the control operation is in the closed-loop mode, frequency trimming injects noise into the angular velocity measurement (thus the advantage of operating in the open-loop mode). Non-invasive quadrant trimming remains in the closed-loop mode.

[0100] The frequency difference between the two modes changes with the angle. This is not a simple geometric problem. In this case, it would be simple enough to correct the zero-angle frequency difference, and the correction would apply to any angle following the rotation. There is also a frequency difference linked to non-linearity, which has the effect of the correction changing according to the angle.

[0101] When operating in the gyroscope mode, the wave is allowed to rotate. The angle of vibration can thus potentially change rapidly, and thus the frequency difference (to be corrected) can change rapidly, and thus the frequency manipulation operation TrimF has to have a bandwidth as high as the maximum angular velocity. For this control operation, this poses a problem as the signal-to-noise ratio is very low, and it is necessary to perform filtering over a long time to achieve an effective control operation. This means that the frequency difference cannot be filtered over a long time, resulting in a significant frequency difference in the presence of noise: thus the advantage of being able to perform frequency trimming at various angles in the gyroscope mode. Since the angle is constant in the gyroscope mode, the filtering can last longer. Once the frequency differences are identified, they can be corrected in the open-loop mode and then changed back to the gyroscope mode. The adapted commands are then directly applied, tracking the rapid variation of Δk, and thus being compatible with high dynamics. The gyroscope mode thus benefits from the results of frequency trimming in the gyroscope mode. It should be noted that for low angular velocities, it is still possible to achieve frequency trimming in the gyroscope mode.

[0102] In an embodiment established based on the results calculated from the matrix listed below, steps B and C are preferably implemented. Figure 7 The method according to this embodiment of the present invention is described in

[0103] After a frame of reference change has been performed previously, step B of determining the pair (Kq’, ΔK’) by signal processing of the control operations TrimF and TrimWQ is performed. This is in the form of sub-step B1 of measuring the position (x, y) of the vibration wave in the sensor frame of reference XY by the transducer D and determining the position (x’, y’) of the vibration wave in the wave frame of reference X’Y’ according to the electrical angle θ. Thus, the situation is:

[0104] x′ = cosθ.x + sinθ.y

[0105] y′ = -sinθ.x + cosθ.y

[0106] Thus, the pair (x’, y’) is used as the processing input.

[0107] In sub-step B2, the first values (Kq’, ΔK’) of the quadrant and the equalization rigidity are estimated according to the position (x’, y’) in the wave frame of reference.

[0108] Step C mainly consists of determining the vector defined by the second value, having coordinates (Kq, ΔK), by applying a rotation of an angle equal to twice the electrical angle (i.e., 2θ) to the vector having the first values (Kq’, ΔK’) as coordinates.

[0109] Thus, the conversion of (Kq’, ΔK’) to (Kq, ΔK) is represented by a matrix relationship (the coordinates (Kq, ΔK) are represented in the frame of reference XY):

[0110] [Mathematical formula 1]

[0111]

[0112] That is: Kq = cos2θ.Kq′ + sin2θ.ΔK′ and ΔKq = -sin2θ.Kq′ + cos2θ.ΔK′

[0113] These conversion relationships are programmed into the control operations. Theoretically, once they are brought back to the sensor frame of reference, the values of Kq and ΔK are constant and applicable to all values of θ. However, due to non-linearity, these values depend on temperature and vary over time due to temperature and sensor aging, and therefore it is necessary to recalculate them in real time.

[0114] Now, how to obtain the relationship of Mathematical formula 1 will be described.

[0115] We begin with the true stiffness matrix K’ expressed in the wave reference frame X’Y’. The term “ ’ ” will be used for values expressed in the wave reference frame, and terms without “ ’ ” will be used for values expressed in the sensor reference frame XY.

[0116] [Equation 2]

[0117]

[0118] This stiffness matrix is corrected using a trimming comb, with the following correction matrix Kc’:

[0119] [Equation 3]

[0120]

[0121] The final stiffness matrix Kf’ is equal to:

[0122] [Equation 4]

[0123]

[0124] For good correction, the situation is that:

[0125] [Equation 5]

[0126]

[0127] Once ΔK’ and Kq’ are determined in the reference frame X’Y’ (step B), it is necessary to determine ΔK and Kq in the reference frame XY (step C).

[0128] We start with the correction matrix Kc’, which is a linear application that transforms the vector Ve’ expressed in X’Y’ into the vector Vs’ also expressed in the reference frame X’Y’: Vs’ = Kc’Ve’.

[0129] It is desired to determine the same transformation, which will be denoted as Kc, in order to move from the vector Ve in the reference frame XY to the vector Vs also expressed in the reference frame XY.

[0130] R(θ) denotes the rotation that enables moving from the reference frame XY to the reference frame X’Y’, V denotes the vector expressed in the reference frame XY, and V’ is the same vector expressed in the reference frame X’Y’. The situation is:

[0131] [Equation 6]

[0132]

[0133] And Vs’ = Kc’·Ve’, that is:

[0134] [Equation 7]

[0135] R(θ)Vs = Kc′R(θ)Ve

[0136] Vs = R(-θ)Kc′R(θ)Ve

[0137] Kc = R(-θ)Kc′R(θ)

[0138] And thus:

[0139] [Equation 8]

[0140]

[0141] That is:

[0142] [Equation 9]

[0143]

[0144] It is also possible to write Kc as a function of ΔK and Kq:

[0145] [Equation 10]

[0146]

[0147] Next, the terms can be identified:

[0148] [Equation 11]

[0149] Kq = ΔK′sin2θ + Kq′cos2θ

[0150] ΔK = ΔK′cos2θ - Kq′sin2θ

[0151] Giving:

[0152] [Equation 12]

[0153]

[0154] According to another aspect, the present invention relates to an inertial angle sensor 10 as described in Figure 8 , comprising the resonator Res described above, the resonator Res comprising a plurality of electrostatic transducers controlled by voltage and operating along axes X and Y, at least including transducers on one of two masses: a pair of excitation transducers, commonly referred to as E transducers, a pair of detection transducers, commonly referred to as D transducers, a pair of quadrant bias compensation transducers, commonly referred to as TQ transducers, and a pair of frequency adjustment transducers, commonly referred to as TF transducers.

[0155] The quadrant stiffness is determined by a first control operation TrimQ and the balance stiffness is determined by a second control operation TrimF. The sensor also includes a processing unit UT. The unit UT is configured to determine the electrical angle θ of the vibration.

[0156] The processing unit UT includes a first module 20, configured to estimate a first value Kq’ and ΔK’ of the quadrant and balance stiffness respectively according to the first control operation TrimQ and according to the second control operation TrimF, and this first value is estimated in the wave reference frame X’Y’.

[0157] The processing unit also includes a second module 21, configured to determine a second value ΔK and Kq of the quadrant and stiffness in the sensor coordinates XY according to the first values Kq’ and ΔK’ of the stiffness.

[0158] The unit UT also includes a component of two electrical gain modules Gq and Gf, and these two modules Gq and Gf are configured to determine a quadrant command CTq corresponding to the second value of the quadrant stiffness Kq and a frequency command CTf corresponding to the second balance stiffness value ΔK respectively. The TF and TQ transducers are configured to apply the frequency command CTf and the quadrant command CTq respectively.

[0159] According to a preferred embodiment, the first module 20 is configured to determine the position (x’, y’) of the vibration wave in the wave reference frame X’Y’ according to the electrical angle θ and according to the measurement of the position (x, y) of the vibration wave in the sensor reference frame XY performed by the D transducer, and estimate the first values Kq’ and ΔK’ of the quadrant and balance stiffness according to the position (x’, y’) in the wave reference frame. According to a preferred embodiment, the second module 21 is configured to determine a vector (Kq, ΔK) whose coordinates are the second value by applying a rotation of an angle 2θ equal to twice the electrical angle to a vector (Kq’, ΔK’) whose coordinates are the first value.

[0160] Figure 9 Illustrated is an embodiment of the inertial sensor 10 according to the present invention during gyroscope operation Figure 8 from. The angle θ is proposed by the precession command Cp applied to the E transducer. The block 20 includes a module 2 for performing a reference frame change from the sensor reference frame XY to the wave reference frame X’Y’. The module 2 performs a rotation R1(θ). According to (x’, y’), Kq’ and ΔK’ are determined by processing using elements of the prior art processing: the block 3 is equivalent to Coq1, the block 5 is equivalent to Coq2, the block 4 is equivalent to Cof and the block 6 is equivalent to Coq3. The module 21 performs a rotation R2(2θ) as explained above.

[0161] Figure 10 Illustrated is during gyroscope operation from Figure 8An embodiment of the inertial sensor 10 according to the present invention. The angle θm is free and measured. The θm is measured in a conventional manner via the module 7 that transmits the rotational speed Ω and the integrator 8.

[0162] Figure 11 Illustrates during the second stage of the hybrid mode from Figure 8 An embodiment of the inertial sensor 10 according to the present invention. The control operation TrimF is placed in an open loop, and the command applied to the TF transducer comes from the module 9 in which the change law CTf(θ) applied to the angle θm is stored.

Claims

1. A method (100) for determining a quadrant command (CTq) and a frequency command (CTf) for a vibration wave generated by a resonator (Res) of an inertial angular sensor (10), - The resonator (Res) has a planar and axially symmetric structure with two axes X and Y that are perpendicular to each other and define a sensor reference frame XY, and includes two vibrating moving masses (M1, M2), one located around the other, coupled to each other by coupling springs, and configured to vibrate in opposite phases in a direction X' that defines a wave reference frame X'Y'. - The resonator further includes a plurality of electrostatic transducers controlled by voltage and operating along two axes X and Y, at least including the following transducers on at least one of the two masses; - A pair of excitation transducers called E transducers, configured to keep the wave at a constant amplitude via an amplitude command (Ca), and to rotate the vibration wave via a precession command (Cp). - A pair of detection transducers called D transducers, configured to detect the movement of the vibration wave. - A pair of quadrant bias compensation transducers called TQ transducers, configured to apply quadrant stiffness via a quadrant command (CTq), the quadrant stiffness being configured to eliminate the coupling stiffness between X' and Y'. - A pair of frequency adjustment transducers called TF transducers, configured to apply equalization stiffness via a frequency command (CTf), the equalization stiffness being configured to eliminate the stiffness difference between X' and Y' so as to equalize the resonant frequency of the vibration wave on X' and Y'. The method is used when the inertial angular sensor operates with a vibration wave vibrating along X' characterized by an electrical angle (θ), and the method includes the steps: - A Determining the electrical angle (θ); - B Estimating first values (Kq', ΔK') of the quadrant stiffness and the equalization stiffness respectively according to a first control operation (TrimQ) and according to a second control operation (TrimF), the first values being estimated in the wave reference frame X'Y'. - C Determining second values (Kq, ΔK) of the quadrant stiffness and the equalization stiffness in the sensor reference frame XY according to the first values (Kq', ΔK') of the stiffness estimated in step B. - D Determining the quadrant command (CTq) and the frequency command (CTf) corresponding respectively to the second values (Kq, ΔK) determined in step C. - E Applying the frequency command (CTf) and the quadrant command (CTq) determined in step D.

2. The method according to claim 1, wherein The inertial angular sensor operates in gyroscope mode, and the electrical angle (θ) determined in step A is equal to the angle (θimp) imposed via the precession command (Cp).

3. The method according to claim 1, wherein, The inertial angular sensor operates in gyrocompass mode, and the electrical angle (θ) generated by the rotation of the inertial angular sensor is measured by the inertial angular sensor, and the electrical angle determined in step A is equal to the measured rotation angle (θm).

4. The method (100) according to claim 1, including: - The first stage, in which the electrical angles (θi) obtained by applying the precession command (Cp) are described, steps A to E are implemented for each electrical angle (θi), step D further includes a sub-step (MEM) of storing the associated frequency command value (CTfi) and a sub-step (MOD) of determining the variation law (CTf(θ)) of the frequency command according to the electrical angle, - The second stage, in which the inertial angle sensor operates in gyroscope mode, the electrical angle (θ) is free due to the rotation of the inertial angle sensor and is measured by the inertial angle sensor (θm), and the second stage includes: * The step (BO) of placing the second control operation (TrimF) in open loop, and the applied frequency command is then determined according to the variation law for the measured rotation angle (θm), * The step of detecting the resonator frequency difference (Δf), and as long as the resonator frequency difference is less than or equal to a predetermined threshold (S), the step (BO) of placing the second control operation (TrimF) in open loop is implemented, * When the frequency difference (Δf) is greater than the threshold, the step of placing the second control operation (TrimF) back in closed loop, and the method then loops back to the first stage to update the variation law.

5. The method according to any one of the preceding claims, wherein, Step B includes: - Sub-step B1 of determining the position (x’, y’) of the vibration wave in the reference frame X’Y’ according to the measurement of the position (x, y) of the vibration wave in the sensor reference frame XY and according to the electrical angle (θ), - Sub-step B2 of estimating the first values (Kq’, ΔK’) of the quadrant stiffness and the balance stiffness according to the position (x’, y’) in the wave reference frame.

6. The method according to any one of claims 1-4, wherein Step C mainly consists of determining the vector (Kq, ΔK) defined by the second value by applying a rotation of an angle equal to twice the electrical angle (2θ) of the vector (Kq’, ΔK’) defined by the first value.

7. An inertial angle sensor (10), comprising: - A resonator (Res) having a planar and axially symmetric structure with two axes X and Y perpendicular to each other and defining a sensor reference frame XY, and including two vibrating moving masses (M1, M2), one located around the other, coupled to each other by a coupling spring, and configured to vibrate in opposite phases along a vibration wave (DV) characterized by an electrical angle (θ) and defining a wave reference frame X’Y’ in the direction X’, - The resonator further includes a plurality of electrostatic transducers controlled by voltage and operating along two axes X and Y, at least including the following transducers on at least one of the two masses; - A pair of excitation transducers called E transducers, configured to keep the wave at a constant amplitude via an amplitude command (Ca), and to rotate the vibration wave via a precession command (Cp), - A pair of detection transducers called D transducers, configured to detect the movement of the vibration wave, - An object quadrant bias compensation transducer, called the TQ transducer, is configured to apply quadrant stiffness via a quadrant command (CTq), and the quadrant stiffness is configured to eliminate the coupling stiffness between X' and Y'. - A pair of frequency adjustment transducers, called the TF transducers, are configured to apply equalizing stiffness via a frequency command (CTf), and the equalizing stiffness is configured to eliminate the stiffness difference between X' and Y' to equalize the resonance frequency of the vibration wave on X' and Y'. - Determine the quadrant stiffness and the equalizing stiffness respectively according to a first control operation (TrimQ) and a second control operation (TrimF). - The sensor further includes a processing unit (UT), which is configured to determine the electrical angle (θ) and includes: - A first module (20), configured to estimate first values (Kq', ΔK') of the quadrant stiffness and the equalizing stiffness respectively according to the first control operation (TrimQ) and the second control operation (TrimF), and the first values are estimated in the wave reference frame X'Y'. - A second module (21), configured to determine second values (Kq, ΔK) of the quadrant stiffness and the equalizing stiffness in the sensor reference frame XY according to the first values (Kq', ΔK') of the stiffness. - A component of two electrical gain modules (Gq, Gf), configured to determine the quadrant command (CTq) corresponding to the second value (Kq) of the quadrant stiffness and the frequency command (CTf) corresponding to the second value (ΔK) of the equalizing stiffness respectively. - The TF transducers and the TQ transducers are configured to apply the frequency command (CTf) and the quadrant command (CTq) to the resonator respectively.

8. The inertial angle sensor (10) according to claim 7, wherein, The first module (20) is configured to determine the position (x', y') of the vibration wave in the wave reference frame X'Y' according to the electrical angle (θ) and according to the measurement of the position (x, y) of the vibration wave in the sensor reference frame XY performed by the D transducer, and estimate the first values (Kq', ΔK') of the quadrant stiffness and the equalizing stiffness according to the position (x', y') in the wave reference frame.

9. The inertial angle sensor (10) according to any one of claims 7 and 8, wherein, The second module (21) is configured to determine the vector (Kq, ΔK) defined by the second value by applying a rotation of an angle equal to twice the electrical angle (2θ) of the vector (Kq', ΔK') defined by the first value.

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