GB2597041A

GB2597041A - Improved inertial sensor

Info

Publication number: GB2597041A
Application number: GB1916195.9A
Authority: GB
Inventors: Vercier Nicolas; Martin Nicolas; Coatantiec Jacques; Chaumet Bernard
Original assignee: Thales SA
Current assignee: Thales SA
Priority date: 2018-12-20
Filing date: 2019-11-05
Publication date: 2022-01-19
Anticipated expiration: 2039-11-05
Also published as: DE102019008491A1; FR3098295A1; DE102019008491A8; FR3098295B1; GB2597041B

Abstract

A method for determining a quadrature command and a frequency command for a vibrational wave generated by a resonator of an inertial angular sensor comprises: A determining the electrical angle; B estimating first values of the quadrature and equalization stiffnesses from first and second control operations, said first values being estimated in the wave reference frame X'Y'; C determining second values of the quadrature and equalization stiffnesses in the sensor reference frame XY, from the first values of said stiffnesses estimated in step B; D determining the quadrature command and the frequency command corresponding to said second values determined in step C; and E applying the frequency command and the quadrature command determined in step D. The resonator comprises two vibrating mobile masses coupled by springs. Excitation and detection transducers, quadrature bias transducers and frequency adjustment transducers are also provided.

Description

Title of the invention: Improved inertial sensor FIELD OF THE INVENTION The field of the invention is that of vibrating inertial sensors in which two masses are set in vibration. The invention relates more particularly to MEMS inertial sensors having a planar structure and that are typically micro-machined into a support substrate.

PRIOR ART

Tuning-fork inertial sensors are known to a person skilled in the art. Inertial sensors that are micro-machined into a thin planar substrate, making it possible to measure an angular position (gyroscope) or an angular velocity (gyrometers), are described in document EP2960625. The main features thereof are recalled below.

The manufacture of these micro-machined sensors, also called MEMS (micro-electromechanical systems) sensors, uses collective micro-machining techniques, etching, doping depositions, etc., that are similar to those used to manufacture electronic integrated circuits, allowing low production costs.

These sensors are formed of two vibrating mobile masses M1 and M2 illustrated in Figure 1 that are positioned one around the other (are concentric) and excited so as to vibrate in tuning-fork mode in the plane of the substrate (plane XY in the figure) via one or more excitation transducers. The two masses are suspended at fixed attachment points A of the substrate by (orthotropic) suspension springs RS. The two masses are coupled to one another by elements having rigidities RC. It is sought through construction to achieve a rigidity along X equal to a rigidity along Y and zero coupling rigidity between X and Y. The useful vibration mode corresponds to a linear vibration of the two masses in phase opposition.

This architecture forms a resonant system having two masses that are coupled to one another by Coriolis acceleration. When the gyrometer rotates about the axis Z perpendicular to the plane XY, called sensitive axis, the composition of the forced vibration with the angular rotation vector leads, due to the Coriolis effect, to forces that set the mobile masses in natural vibration perpendicular to the excitation vibration and to the sensitive axis; the amplitude of the natural vibration is proportional to the rotational speed. The electronics associated with the sensor calculate the amplitude of the vibration in the direction orthogonal to the direction of excitation, regardless of the latter (known through assumption).

The sensor may operate in gyrometer mode: the direction of natural vibration is kept fixed with respect to the housing of the sensor by modifying the excitation, and the output information is then an image of the necessary energy that it is necessary to apply to the excitation transducers in order to keep the direction of natural vibration fixed in spite of the movements of the housing. Measuring this counterforce gives access to the angular velocity 0 of the sensor. The sensor may also operate in gyroscope mode: the direction of the natural vibration is left free and is detected so as to give the angular orientation of the sensor.

Gyrometer mode exhibits the following advantages: (i) not having any angular noise, more* precisely any angular error linked to the position of the vibration and (ii) not having any angular velocity error variations (drift) linked to the angle (by definition, since a constant angle is kept with respect to the reference frame of the gyrometer).

Gyroscope mode exhibits the following advantages: (i) having a very low scale factor error in 15 comparison with gyrometer mode and (ii) having very high operating dynamics.

The whole structure of the resonator is axisymmetric about two axes X and Y defining a sensor reference frame, as illustrated in Figure 2. Axisymmetric is understood to mean that the structure is symmetrical about)( and symmetrical about Y. As described below, these axes form the main directions of the actuators/detectors, which operate along these two axes.

To excite the useful vibration mode in any given direction of the plane, the excitation signal is broken down into two components having adjusted respective amplitudes and that are applied respectively to the excitation transducer Ex acting in the direction X and to the excitation transducer Ey acting in the direction Y associated with at least one mobile mass (internal mass M1 in Figure 2). These transducers are able to sustain a forced vibration via an amplitude command (combat the damping of the MEMS) and in any direction of the plane XY, via a precession command (rotate the wave).

The movements of the resulting wave are detected by combining the information gathered by at least one pair of detection transducers Dx, Dy detecting the position of the mass in its travel in the sensor reference frame XY (two of each in Figure 2) and associated with at least one mobile mass.

The transducers are preferably formed by comb electrodes that are interwoven with varying air gaps. There is a fixed comb the teeth of which are joined to a fixed electrode of the machined substrate and a mobile comb the teeth of which are interwoven with the teeth of the fixed comb and are joined to the mobile mass associated with the transducer under consideration.

The excitation consists in applying an AC voltage between the mobile comb and the fixed comb, at the desired vibration frequency (mechanical resonant frequency of the suspended 10 mobile mass). The movement that is brought about is perpendicular to the teeth of the comb.

The detection consists in applying a bias voltage between the fixed comb and the mobile comb and in observing load variations that result from the variations in capacitance between the fixed comb and the mobile comb caused by the variations in the spacing between the teeth of the fixed comb and of the mobile comb. The movement that is measured is the movement perpendicular to the teeth of the comb.

It is well known to a person skilled in the art that imperfections in the production of the sensor lead to errors in the information delivered at the output thereof. The majority of these imperfections need to be compensated by calibrating the gyrometer.

It is known to perform this compensation by locally removing material, for example by laser ablation, so as to modify the mass or rigidity distribution. This method is expensive or even impossible to implement on a gyrometer micro-machined into a thin silicon substrate, the detection and excitation movements of which are situated in the plane of the substrate.

* A distinction is drawn between two types of imperfection in terms of rigidities. The vibrating masses/springs assembly is characterized by a 2x2 rigidity matrix. This matrix is symmetrical, characterized in the reference frame XY by a rigidity Kx along X, a rigidity Ky along Y and a coupling rigidity Kxy between X and Y (where Kyx=Kxy). Due to the production imperfections, Kx is other than Ky is Kxy is nonzero, whereas, for optimum operation of the sensor, it is sought to achieve Kx=Ky. and Kxy=0, that is to say a final rigidity matrix proportional to identity.

The axis of vibration of the wave is called X'. This axis defines a reference frame X'Y', where V is perpendicular to X' in the plane of the MEMS. The axis r forms, with the axis X, an angle called electrical angle 0, and the reference frame WY is called wave reference frame. It is assumed for the time being that the wave vibrates along X (X'=X).

The first type of imperfection is the frequency difference between the main axis of vibration and the axis perpendicular to the vibration in the plane of the MEMS, corresponding to a rigidity matrix of the system in which the rigidity along the axis X is other than the rigidity along the axis Y. It is sought to equalize the resonant frequencies along the two abovementioned axes by way of an adjustable electrostatic rigidity. This electrostatic rigidity, called equalization rigidity, is delivered by frequency adjustment transducers Tx, Ty (at least one-pair on at least one mass, see Figure 2) acting along the directions X and Y. The aim of applying this is to equalize the rigidities along the two axes of the vibration by reducing the value of the highest rigidity, thus making the frequencies equal. The frequency correction is also termed frequency trimming.

A second type of imperfection stems from the mechanical coupling between the axis of the vibration and the perpendicular axis, at the origin of what is known as the quadrature bias. These are anisotropic defects regarding the dynamic rigidity of the assembly of the two vibrating masses, manifested in a vibration that is no longer linear but elliptical and corresponding to the existence of a nonzero coupling rigidity Kxy. One solution is that of cancelling out this term by applying a (sinusoidal) force F to the system via the excitation transducers. The problem is that the application of this force is not exerted at exactly the correct time (phase errors) and in the correct axis (gain error), leading to drift being applied. In order to avoid applying a force F, the term Kxy is physically cancelled out not by applying a force but by directly changing the rigidity of the resonator via at least one pair of transducers Q+ and Q-, as illustrated in Figure 2 (2 pairs Q-P/Q-in Figure 2). These transducers operating on X and Y are positioned on the diagonals so as to comply with symmetry and 'geometric' anisotropy, and for reasons of bulk. Correcting the quadrature bias is also called quadrature trimming (or trim).

The quadrature trim transducers thus modify the features of the MEMS sensor so as to 30 eliminate coupling between the two axes of the wave reference frame, and the frequency trim transducers modify the features of the MEMS sensor so as to eliminate the frequency differences between the two axes of the wave reference frame.

The transducers Tx, Ty, Q+ and Q-are preferably also interwoven combs as illustrated in Figures 2 and 3 that are controlled by DC voltages.

Excitation, detection, frequency adjustment and quadrature bias correction transducers are preferably implemented on the two masses, as illustrated in Figure 3, the index 1 corresponding to the mass M1 and the index 2 corresponding to the mass M2. Figures 2 and 3 represent non-limiting exemplary arrangements, and many other types of arrangement are possible, with the constraint of forming an axisym metric system.

Figure 4 illustrates the operation of an inertial sensor ao according to the prior art, and more particularly the frequency trim and quadrature trim control operations. The resonator Res comprises the various transducers described above and symbolized by E (excitation), D (detection), TQ (trim quadrature) and IF (trim frequency). The vibrational wave OV vibrates along X (X'-=X). The vibration modes along X'Y' coincide with the excitation and detection is modes.

Three control operations control the excitation combs E in parallel: a precession control operation (not shown) keeps the vibrational wave at a predetermined angle (measurement of the reactive force that counteracts the Coriolis force in gyrometer mode); an amplitude control operation (not shown) keeps the vibration of the wave constant, and a quadrature control operation controls the force fy so as to maintain the linear vibration (via the command Ctqe). One problem linked to the quadrature force fy is the accuracy in terms of phase and in terms of gain or direction of the application thereof. A fourth PLL loop (not shown) seeks to identify the phase of the oscillation (position of the mass during travel thereof). This PLL loop does not influence the vibrational wave; it acts as an observer. By virtue of the information delivered by the phase-locked loop, it is possible to position the forces to be sent to Ex and Ey via the three abovementioned control operations with the correct phase, and to demodulate the detection signals.

The detection transducers measure the position of the vibration (x,y) 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 the quadrature trim and the frequency trim. A processing unit UT performs the various calculations and, for the corrections, generates commands for the various transducers: a command CTqe for applying a quadrature force via the E transducer, a frequency trim command CTf for TF, a quadrature trim command CTq for TQ. The commands CTq and CTf for the trims are DC voltages that modify the intrinsic features of the resonator, whereas the command CTqe for the force is a sinusoidal voltage (see above). The quadrature command CTq on TO is adjusted so as to achieve, in steady state, a zero quadrature force (command CTqe) applied to the excitation E, thereby solving the problems linked to applying this force.

The signal from y is cosine-demodulated and sine-demodulated. The cosine demodulation is used for the first control operation relating to the quadrature trim. The resulting signal is processed by a corrector Coql and delivers an estimate of the quadrature rigidity Kq intended to cancel out the coupling rigidity Kxy. Following a second corrector Coq2 (integrator) and converting the rigidity into an electric voltage by way of the device Gq, the quadrature command CTq is applied to TO. The sine demodulation is used for the second control operation relating to the frequency trim. The resulting signal is processed by a corrector Cof, which generates the equalization rigidity AK, and then a device Gf converts the rigidity into an electric voltage so as to generate the frequency trim command CTf.

* The control operations for the frequency correction and quadrature correction were initially developed for non-axisymmetric sensors (X and V do not perform the same role) that are 20 configured so as to operate using a wave vibrating along X. In this case, the first and second control operations operate independently and work correctly.

For an axisymmetric sensor that allows the use of a wave vibrating at an angle 9 other than 00, the trims become dependent on one another and no longer work correctly. For example, for some angles such as 0 = n/4, the quadrature trim no longer has any effect on the coupling rigidity Kxy, and leads to instability in the first and second control operations. The instability described above leads to the actuators saturating, and it is necessary to restart the sensor. Thus, when the MEM5 sensor is operated at an angle 0 other than zero, it may be preferable to stop the trim control operations, thereby leading to measurement errors in the sensor that are linked to the application of additional forces.

One aim of the present invention is to rectify the abovementioned drawbacks by proposing an operating mode for the sensor that allows the frequency and quadrature bias correction control operations to be implemented effectively for a wave vibrating at any electrical angle.

DESCRIPTION OF THE INVENTION

The present invention relates to a method for determining a quadrature command and a frequency command for a vibrational wave generated by a resonator of an inertial angular sensor, the resonator having a planar and axisymmetric structure about two axes X and Y that are perpendicular to one another defining a sensor reference frame XY and comprising two vibrating mobile masses (M1., M2) that are positioned one around the other, coupled to one another by coupling springs and configured so as to vibrate in phase opposition in a direction X' defining a wave reference frame X'Y', the resonator furthermore comprising a plurality of electrostatic transducers controlled by electric voltages and operating along the two axes X and Y, including at least the following transducers on at least one of the two masses: A pair of excitation transducers, called E transducers, configured so as to keep the wave at a constant amplitude via an amplitude command (Ca) and, where necessary, to rotate said vibrational wave via a precession command (Cp), a pair of detection transducers, called D transducers, configured so as to detect the movements of the vibrational wave, a pair of quadrature bias compensation transducers, called TO transducers, configured so as to apply a quadrature rigidity via a quadrature command (CTq), the quadrature rigidity being configured so as to cancel out a coupling rigidity between X' and Y', and a pair of frequency adjustment transducers, called TF transducers, configured so as to apply an equalization rigidity via a frequency command (C11), the equalization rigidity being configured so as to cancel out a difference in rigidity between X' and Y' so as to equalize the resonant frequencies of the vibrational wave on X' and r.

The method is applicable when the inertial sensor is operating with a vibrational wave vibrating along X', characterized by an electrical angle, the method comprising the steps of: -A determining the electrical angle, -B estimating first values of said quadrature and equalization rigidities from a first and from a second control operation, respectively, said first values being estimated in the wave reference frame X'Y',

S

- C determining second values of said quadrature and equalization rigidities in the sensor reference frame XY, from the first values of said rigidities estimated in step B, - D determining the quadrature command and the frequency command corresponding, respectively, to said second values determined in step C, -E applying the frequency command (CTf) and the quadrature command (CTq) determined in step D. According to one variant, the inertial sensor operates in gyrometer mode, the electrical angle determined in step A being equal to an angle imposed via the precession command.

According to another variant, the inertial sensor operates in gyroscope mode, the electrical angle resulting from a rotation of the inertial sensor being measured by said inertial sensor, the electrical angle determined in step A being equal to said measured angle of rotation.

According to yet another variant, the method according to the invention comprises: - a first phase in which the electrical angle describes a plurality of electrical angles obtained by applying said precession command, steps A to E being implemented for each electrical angle, step D furthermore comprising a sub-step of storing the associated frequency command value and a sub-step of determining a variation law for the frequency command as a function of the electrical angle, - a second phase in which the inertial sensor operates in gyroscope mode, the electrical angle that is left free resulting from a rotation of the inertial sensor and being measured by said inertial sensor, the second phase comprising: a step (BO) of placing the second control operation in an open loop, the * frequency command that is applied then being determined from said variation law for said measured angle of rotation, a step of detecting a resonant frequency difference, the open loop placement step being implemented for as long as said resonant frequency difference is less than or equal to a predetermined threshold, a step of placing said second control operation back in a closed loop when the frequency difference is greater than said threshold, the method then looping back to the first phase in order to update said variation law.

According to one embodiment, step B comprises a sub-step B1. of determining a position of the vibrational wave in the wave reference frame X'Y' from the measurement of a position of the vibrational wave in the sensor reference frame XY and from the electrical angle, and a sub-step B2 of estimating first values of said quadrature and equalization rigidities from said position in the wave reference frame.

According to one embodiment, step C consists in determining a vector defined by said second values by applying a rotation by an angle equal to twice the electrical angle to the vector defined by said first values.

According to another aspect, the invention relates to an inertial angular sensor comprising: a resonator having a planar and axisymmetric structure about two axes X and,Y that are perpendicular to one another defining a sensor reference frame XY and comprising two vibrating mobile masses that are positioned one around the other, coupled to one another by coupling springs and configured so as to vibrate in phase opposition along a vibrational wave vibrating in a direction X' characterized by an electrical angle and defining a wave reference frame X'Y', the resonator furthermore comprising a plurality of electrostatic transducers controlled by electric voltages and operating along the two axes X and Y, including at least the following transducers on at least one of the two masses: A pair of excitation transducers, called E transducers, configured so as to keep the wave at a constant amplitude via an amplitude command and, where necessary, to rotate said vibrational wave via a precession command, a pair of detection transducers, called D transducers, configured so as to detect the movements of the vibrational wave, a pair of quadrature bias compensation transducers, called TO transducers, configured so as to apply a quadrature rigidity via a quadrature command, the quadrature rigidity being configured so as to cancel out a coupling rigidity between X' and V', and a pair of frequency adjustment transducers, called IT transducers, configured so as to apply an equalization rigidity via a frequency command, the equalization rigidity being configured so as to cancel out a difference in rigidity between X' and Y' so as to equalize the resonant frequencies of the vibrational wave on X' and Y'. The quadrature and equalization rigidities are determined, respectively, from a first and from a second centre) operation.

The sensor furthermore comprises a processing unit configured so as to determine said electrical angle and comprising: - a first module configured so as to estimate first values of said quadrature and equalization rigidities -from the first and from the second control operations, respectively, said first values being estimated in the wave reference frame X'Y', - a second module configured so as to determine second values of said quadrature and equalization rigidities in the sensor reference frame XY, from the first values of said rigidities, - an assembly of two electrical gain modules that are configured so as to determine, respectively, the quadrature command corresponding to the second value of the quadrature rigidity and the frequency command corresponding to said second equalization rigidity value, -the TF and TQ transducers being configured so as to apply, respectively, said frequency* command and said quadrature command to the resonator.

According to one embodiment, the first module is configured so as to determine a position of the vibrational wave in the wave reference frame X'Y' from the electrical angle and from the measurement of a position of the vibrational wave in the sensor reference frame XY performed by the D transducers, and to estimate first values of said quadrature and equalization rigidities from said position in the wave reference frame.

According to one embodiment, the second module is configured so as to determine a vector defined by said second values by applying a rotation by an angle equal to twice the electrical, angle to the vector defined by said first values.

The following description presents several exemplary embodiments of the device of the invention: these examples do not limit the scope of the invention. These exemplary embodiments present both the essential features of the invention and additional features linked to the embodiments under consideration.

The invention will be better understood and other features, aims and advantages thereof will become apparent during the following detailed description and with reference to the appended drawings, which are given by way of non-limiting example and in which: [Fig.1] Figure 1, already mentioned, shows the structure of a resonator of an inertial sensor to which the invention is applicable.

[Fig.2] Figure 2 illustrates one example of an axisymmetric resonator having a plurality of transducers on the internal mass.

[Fig.3] Figure 3 illustrates one example of an axisymmetric resonator having a plurality of transducers on the two, internal and external, masses.

[Fig.4] Figure 4 illustrates the frequency correction and quadrature bias correction control

operations according to the prior art.

[Fig.5] Figure 5 illustrates the method according to the invention.

[Fig.6] Figure 6 illustrates one variant of the method according to the invention.

[Fig. 71 Figure 7 illustrates one preferred embodiment for implementing steps B and C of the method according to the invention.

[Fig.8] Figure 8 illustrates an inertial sensor according to the invention.

[Fig.9] Figure 9 illustrates one embodiment of the inertial sensor according to the invention from Figure 8 in gyrometer operation.

[Fig.10] Figure 10 illustrates one embodiment of the inertial sensor according to the invention from Figure 8 in gyroscope operation.

[Fig.11] Figure 11 illustrates one embodiment of the inertial sensor according to the invention from Figure 8 during the second phase of the mixed mode.

For the sake of clarity, identical elements will bear the same reference signs in the various figures.

DETAILED DESCRIPTION OF THE INVENTION

In-depth analysis of the operation of the sensor shows that the difficulty of implementing frequency and quadrature bias corrections stems from the fact that the IQ and IF transducers are positioned on and operate along the sensor axes)( and Y and not along the wave axes X'Y'. When the frequency and quadrature trim control operations are applied as they are to a wave vibrating at an electrical angle other than zero, the equalization and quadrature rigidities that are delivered correspond to the values that should be applied with transducers that are positioned on and operate along the axes X'Y' of the wave reference frame. However, these transducers are fixed and positioned along the axes X and V of the sensor. The rigidity values delivered by the first and the second control operation are therefore not optimum for the vibration along X'. The aim of the method according to the invention is that of delivering effective commands CTq and CTf for TO and TF, that is to say commands adapted to the value of the electrical angle, regardless of the value thereof.

Furthermore, the frequency differences between the two modes as well as the quadrature bias vary with the electrical angle of the vibration, and the correction to be made also varies as a function of the angle, due to the non-linearities of the sensor.

Lastly, when the angle changes over time, as the defects depend on the angle, it is no longer possible to perform filtering over lengthy times as the dynamics of the error are fast.

To solve this problem, the invention relates to a method 100 for determining a quadrature command CTq and a frequency command CTf for a vibrational wave generated by a resonator Res of an inertial angular sensor, the method being applicable when the inertial sensor is operating with a vibrational wave vibrating along an axis X', characterized by an electrical angle 0, the various steps of which method are illustrated in Figure 5.

The inertial sensor to which the invention applies comprises a resonator as described in the prior art having a planar and axisymmetric structure about two axes X and Y that are perpendicular to one another defining a sensor reference frame XY and comprising two vibrating mobile masses M1 and M2 that are positioned one around the other, coupled to one another by coupling springs and configured so as to vibrate in tuning-fork mode and in phase opposition in a direction X' defining a wave reference frame X'Y'.

The resonator comprises a plurality of electrostatic transducers controlled by electric voltages 30 and operating along the two axes X and Y, including at least, on one of the two masses: a pair of excitation transducers, called E transducers, configured so as to keep the wave at a constant amplitude via an amplitude command, keep the wave planar and, where necessary, to rotate said vibrational wave via a precession command, -a pair of detection transducers, called D transducers, configured so as to detect the movements of the vibrational wave, - a pair of quadrature bias compensation transducers, called TQ transducers, configured so as to apply a quadrature rigidity via a quadrature command CTq, the quadrature rigidity being configured so as to cancel out a coupling rigidity between X' and Y', -a pair of frequency adjustment transducers, called TF transducers, configured so as to apply an equalization rigidity via a frequency command CTf, the equalization rigidity being configured so as to cancel out a difference in rigidity between X' and Y' so as to equalize the resonant frequencies of the vibrational wave on X' and Y'.

In a first step A, the electrical angle 0 is determined.

In a second step B, first values Kq' and AK' of the quadrature and equalization rigidities are estimated, respectively, from a first control operation TrimQ and from a second control operation TrimF. These values are determined by control operations of the same type as those that work according to the prior art (apart from a few differences that will be described later on) that "ignore" the fact that the vibrational wave vibrates along an axis X' other than X. These values Kq' and AK', called first values, are considered to be estimated in the wave reference frame X'Y', since they correspond to the values delivered by the control operations while the wave is vibrating along X'. They correspond to the values that it would be necessary to apply to TQ and TF with TO and TF operating along X' and W. In a following step C, second values Kq, AK of the quadrature and equalization rigidities in the sensor reference frame XY are determined from the first values of said rigidities KC AK' estimated in step B. These values Kq and AK, called second values, are adapted to the fact that the TQ and IF transducers operate along the axes XY. Kq' and AK' are thus converted into Kq and AK so as to take into account the fact that the transducers applying the equalization and quadrature rigidities 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 AK' estimated in the wave reference frame X'Y', a conversion is performed on these two terms so as to return to the sensor reference frame XY in which the trims operate.

In a step D, the quadrature command CTq and the frequency command CTf corresponding, respectively, to the second values Kq and AK determined in step C are determined in a conventional manner, and lastly, in a step E, the frequency command CTf and the quadrature command CTq determined in step D are applied.

The method according to the invention is thus able to be applied to a sensor using trim control operations of the same type as those from the prior art, that is to say without having to develop new control operations, with a difference in terms of the signal processing, such as a conversion of the rigidities delivered by these control operations, performed in step C of the method. Due to the exactness of the rigidities Kq and AK calculated by the conversion, the force requiring the planar wave to be applied to E returns to zero in steady state, the errors linked to the application of this force are eliminated, and the entire correction (frequency and quadrature) is performed via the TO and TF transducers.

Due to this adaptation, the frequency and quadrature errors are eliminated and the inertial sensor delivers a (velocity or angle) measurement that is no longer sensitive to the errors in the rigidity matrix, regardless of the value of the angle of vibration! of the wave. It is recalled that the method according to the invention is used continuously and in parallel with the delivery of the measurement of the angular velocity or of the angle of rotation about the -sensitive axis Z. By virtue of implementing the method according to the invention, the frequency differences of initially around 3 Hz are brought back to a few mHz, and quadrature errors of around 100°/s are brought back to less than 0.1°/s. These values, coupled with electronics from the 100 ppm class in terms of phase errors, make it possible to achieve drifts of less than one degree per hour.

According to one variant, the method is implemented while the inertial sensor is operating in gyrometer mode. The electrical angle 6 determined in step A is in this case equal to an angle Gimp imposed on the vibration via the precession command. It is possible to use various values of Oimp to average the errors, for example by performing measurements for 0 equal to 30° and then 60° and then 90°. This implementation is made accurate and effective on an MEMS sensor by virtue of the method according to the invention.

According to another variant, the method is implemented while the inertial sensor is operating in gyroscope mode. The electrical angle 0 then results from a rotation of the inertial sensor and is measured thereby. The electrical angle determined in step A is equal to the measured angle of rotation Om.

According to yet another variant, the method according to the invention is implemented in a mixed mode illustrated in Figure 6.

The method comprises a first phase in which the electrical angle describes a plurality of electrical angles 0i, where i is an index, these being obtained by applying the precession command Cp. Steps A to E are implemented successively for each electrical angle Oi. Step D comprises, in addition to determining CTf and CTq, a sub-step MEM of storing the frequency command value CTfi associated with each angle Di and a sub-step MOD of determining a variation law CTf(0i) for the frequency command as a function of the electrical angle. The form of this law is typically of the type gakcos2k0+bksin2k0), k typically varying from 0 to 4, and determination thereof consists in calculating the values of the coefficients ak and bk from smoothing performed on the measurement points Di.

This first phase may be implemented regardless of the operating mode, gyrometer or gyroscope, of the sensor. It is preferably implemented in gyrometer mode. When the sensor is operating in gyroscope mode (typically when the vehicle in which the sensor is embedded is at a standstill), the angle Oils obtained by sending a precession setpoint in order to adopt 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 as a function of the value of the electrical angle.

In a second phase, the inertial sensor operates in gyroscope mode, the electrical angle is left free and results from a rotation of the inertial sensor, which measures the value Om.

The second phase first of all comprises a step BO of placing the second control operation Trim F in an open loop. At this time, the control operation TrimF stops delivering the command CTf in real time, which is replaced by a command CTf(Om) that is determined from said variation ilaw for the measured angle of rotation 13m. The command is applied over time, tracking the variations of Om. At the same time, the resonant frequency difference Af between the two axes of the wave is measured. The principle of frequency trimming is that of sending interference, of measuring Af and then of correcting this via CTf. When operating in open-loop mode, it is possible to continue to send the interference and measure Af, but the correction CTf is no longer applied.

The open loop placement step BO is implemented for as long as the resonant frequency difference is less than or equal to a predetermined threshold S. The difference Af changes as a function of the temperature and during ageing. When the frequency difference Af becomes greater than the threshold, the second control operation TrimF is placed back in a closed loop so as to allow the variation law to be updated, restarting at the first phase. Throughout the entire second phase, the first control operation continues to operate as in the first phase. This mixed mode exhibits numerous advantages.

The frequency trimming injects noise onto the angular velocity measurement when the control operation is in closed-loop mode (hence the benefit of operating in open-loop mode).

The non-intrusive quadrature trimming remains in closed-loop mode.

The frequency differences between the two modes vary with the angle. This is not simply a geometric problem, in which case it would be enough simply to correct the zero-angle frequency difference, and the correction would be applicable for any angle following rotation. There are also frequency differences linked to the non-linearities which have the effect that the correction changes as a function of the angle.

When operating in gyroscope mode, the wave is allowed to rotate. The angle of the vibration may therefore potentially change quickly, and therefore the frequency difference (to be corrected) may change quickly, and therefore the frequency control operation TrimF has to have a bandwidth as high as the maximum angular velocity. This poses a problem as, for this control operation, the signal-to-noise ratio is very low, and it is necessary to perform filtering over a lengthy time in order to achieve an effective control operation. This means that the frequency difference cannot be filtered over a lengthy time, leading to significant frequency differences in the event of noise: hence the benefit of being able to perform the frequency trimming at various angles in gyrometer mode. As the angle is constant in gyrometer mode, the filtering may last longer. Once the frequency differences have been identified, it is possible to correct them in open-loop mode and change back to gyroscope mode. The adapted command is then applied directly, tracking a fast variation of Ak, which is therefore compatible with high dynamics. Gyroscope mode thus benefits from the results of the frequency trimming in gyrometer mode. It should be noted that, for low angular velocities, frequency trimming in gyroscope mode may still be implemented.

Steps B and C are preferably implemented in embodiments that are established based on results of a matrix calculation that is outlined below, the method according to the invention according to this embodiment being illustrated in Figure 7.

Step B of determining the pair (Kg', AK') by signal processing of the control operations TrimF and TrimQ is carried out having performed a reference frame change beforehand, in the form of a sub-step B1 of determining the position (x', y') of the vibrational wave in the wave reference frame X'Y' from the measurement of the position (x, y) of the vibrational wave in *the sensor reference frame XY performed by the transducers D and from the electrical angle 0. It is therefore the case that: x' = cosax + sinay y' = -sine.x + cosily The pair (x1,y') is thus used as processing input.

In a sub-step B2, the first values (Kg', AK') of the quadrature and equalization rigidities are estimated from the position in the wave reference frame (x', y').

Step C consists in determining a vector defined by the second values, having the coordinates (10, AK), by applying a rotation by an angle equal to twice the electrical angle, that is to say 20, to the vector having the first values (Kg', AK') as coordinates.

The conversion of the pair (Kg', AK') into (Kg, AK) is therefore expressed by the matrix relationship (the coordinates (Kq, AK) are expressed in the reference frame XY): [Math. 1] "J cos20 s1n201 1.-sin28 cos201 LAKI That is to say: Kg = cos20.Kq' + sin20.AK' and AKq = -s1n28.Kq' + cos20.AK' These conversion relationships are programmed into the control operations. In theory, once they have been brought back to the sensor reference frame, the values Kq and AK are constant and applicable to all values of B. However, due to non-linearities, these values depend on 9 and are variable over time due to the temperature and the sensor ageing, and it is therefore necessary to recalculate them in real time.

We will now demonstrate how the relationship Mathl is obtained.

We start from the true rigidity matrix K' expressed in the wave reference frame X'Y'. The term will be used for values expressed in the wave reference frame, and the term without a will be used for values expressed in the sensor reference frame XY.

[Math. 2] K, [KO + AKvi Kqv' Kqv' KO -21Kv'i This rigidity matrix is corrected using trimming combs, using the following correction matrix Kc': [Math. 3] Kc' Kg' Kq' The final rigidity matrix Kf' is equal to: [Math. 4] [KO + -AK' Kqv' -Kq' 1 Kf' =K' -Kc' = Kqv' -Kq' KO -LIKV + For a perfect correction, it is the case that: [Math. 5] * Kf, =r0 K 0 00] Once AK' and Kq' have been determined in the reference frame X'Y' (step B), it is necessary to determine AK and Kq In the reference frame XY (step C).

We start from the correction matrix Kc', which is a linear application that converts a vector Ve' expressed in X'Y' into a vector Vs' that is also expressed in the reference frame X'Y': Vs' = Kc'Ve' It is desired to determine the same conversion, which will be denoted Kc, in order to move from a vector ye in the reference frame XY to a vector Vs that is also expressed in the reference frame XY.

R(0) denotes the rotation that makes it possible to move from the reference frame XY to the reference frame X'Y', V denotes a vector expressed in the reference frame XY, and V' is the same vector expressed in the reference frame X'Y'. It is the case that: [Math. 61 cos(0) sin(9)1 V' = R(B)V = [-sin(0) cos(0)IV and Vs' = Kc'.Ve', that is to say: [Math. 7] R(0)Vs = Kc'R(0)Ve Vs = R(-6)K c' R(0)Ve Kc = R(-61)KeR(6) And therefore: [Math. 8] [cos(9) -sin.(61)1111K' K q' cos(9) sin(0)1 Kc' = tsin(0) cos(0) -41(11.-sin(0) cos(0)1 That is to say: [Math. 9] Kc = cos20 -Kq'sin219 AK'sin20 + Kq'cos20 1 LK' sin20 + Kq'cos28 -AK ' cos20 + Kq'sin291 It is also possible to write Kc as a function of AK and Kg: [Math. 10] plc Kg K' C] = [Kg -AK] It is then possible to identify the terms: [Math. 11] Kq = AK' sin261+ Kqicos20 AK = AK'cos20 -Kq'sin261 Giving: [Math. 12] iKqi cos(28) sir-42601E1W] LAM-[-sin(219) cos(20)JEAK11 According to another aspect, the invention relates to an inertial angular sensor 10 illustrated in Figure 8 comprising a resonator Res as described above comprising a plurality of electrostatic transducers controlled by electric voltages and operating along two axes X and Y including at least, on one of the two masses: a pair of excitation transducers, generically called E transducers, a pair of detection transducers, generically called D transducers, a pair of quadrature bias compensation transducers, generically called TQtransducers, and a pair of frequency adjustment transducers, generically called TF transducers.

The quadrature rigidity is determined by a first control operation TrimQ and the equalization. rigidity is determined from a second control operation TrimF. The sensor furthermore comprises a processing unit UT. The unit UT is configured so as to determine the electrical angle 0 of the vibration.

The processing unit UT comprises a first module 20 configured so as to estimate first values Kq' and AK' of the quadrature and equalization rigidities, respectively, from the first control operation TrimQ and from the second control operation TrimF, the first values being estimated in the wave reference frame WY'.

The processing unit also comprises a second module 21 configured so as to determine second values Kq and AK of the quadrature and equalization rigidities in the sensor reference frame XY, from the first values of the rigidities Kq' and AX'.

The unit UT also comprises an assembly of two electrical gain modules Gq and Gf that are configured so as to determine, respectively, the quadrature command CTq corresponding to the second value of the quadrature rigidity Kq and the frequency command CTf corresponding to said second equalization rigidity value AK, the TF and TQ transducers being configured so as to apply, respectively, the frequency command CTf and the quadrature command CTq.

According to one preferred embodiment the first module 20 is configured so as to determine the position (x' y') of the vibrational wave in the wave reference frame X'Y' from the electrical angle 0 and from the measurement of the position (x, y) of the vibrational wave in the sensor reference frame XY performed by the D transducers, and to estimate first values Kq' and AK' of the quadrature and equalization rigidities from said position in the wave reference frame (x', y'). According to one preferred embodiment the second module 21 is configured so as to determine a vector (Kq, AK) the coordinates of which are the second values by applying a rotation by an angle equal to twice the electrical angle 20 to the vector (Kq', AK') the coordinates of which are the first values.

Figure 9 illustrates one embodiment of the inertial sensor 10 according to the invention from Figure 8 in gyrometer operation. The angle 0 is imposed by the precession command Cp applied to the E transducer. The block 20 comprises a module 2 for performing the reference frame change, from the sensor reference frame XY to the wave reference frame X'Y'. The module 2 performs a rotation R1(0). From (x', y'), Kq' and AK' are determined by processing using elements of the processing according to the prior art: the block 3 is equivalent to Coql, 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(20) as explained above.

Figure 10 illustrates one embodiment of the inertial sensor 10 according to the invention from Figure 8 in gyroscope operation. The angle Om is left free and measured. Om is measured in a conventional manner via a module 7 that delivers the rotational speed 0 and an integrator 8.

Figure 11 illustrates one embodiment of the inertial sensor 10 according to the invention from Figure 8 during the second phase of the mixed mode. 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 variation law CTf(0) applied to the angle Om is stored.

Claims

Claims 1. Method (100) for determining a quadrature command (CTq) and a frequency command (CTf) for a vibrational wave generated by a resonator (Res) of an inertial angular sensor (10), the resonator (Res) having a planar and axisymmetric structure about two axes X and Y that are perpendicular to one another defining a sensor reference frame XY and comprising two vibrating mobile masses (M1, M2) that are positioned one around the other, coupled to one another by coupling springs and configured so as to vibrate in phase opposition in a direction X' defining a wave reference frame X'Y', -the resonator furthermore comprising a plurality of electrostatic transducers controlled by electric voltages and operating along the two axes X and V. including at least, on at least one of the two masses: - a pair of excitation transducers, called E transducers, configured so as to keep the wave at a constant amplitude via an amplitude command (Ca) and, where necessary, to rotate said vibrational wave via a precession command (Cp), - a pair of detection transducers, called D transducers, configured so as to detect the movements of the vibrational wave, - a pair of quadrature bias compensation transducers, called TQtransducers, configured so as to apply a quadrature rigidity via a quadrature command (CTq), the quadrature rigidity being configured so as to cancel out a coupling rigidity between X' and V', - a pair of frequency adjustment transducers, called TF transducers, configured so as to apply an equalization rigidity via a frequency command (Cif), the equalization rigidity being configured so as to cancel out a difference in rigidity between X' and Y' so as to equalize the resonant frequencies of the vibrational wave on X' and Y', the method being applicable when the inertial sensor is operating with a vibrational wave vibrating along X', characterized by an electrical angle (0), the method comprising the steps of: - A determining the electrical angle (0), - B estimating first values (Kq', AK') of said quadrature and equalization rigidities from a first (TrimQ) and from a second (TrimF) control operation, respectively, said first values being estimated in the wave reference frame Xi", - C determining second values (Kq, AK) of said quadrature and equalization rigidities in the sensor reference frame XY, from the first values of said rigidities (Kq', AK') estimated in step B, - determining the quadrature command (CTq) and the frequency command (CTf) corresponding, respectively, to said second values (Kq, AK) determined in step C, - E applying the frequency command (CTf) and the quadrature command (CTq) determined in step D.
2. Method according to Claim 1, wherein the inertial sensor operates in gyrometer mode, the electrical angle (0) determined in step A being equal to an angle (Oimp) imposed via the precession command (Cp).
3. Method according to Claim 1, wherein the inertial sensor operates in gyroscope mode, the electrical angle (0) resulting from a rotation of the inertial sensor being measured by said inertial sensor, the electrical angle determined in step A being equal to said measured angle of rotation (Om).
4. Method (100) according to Claim 1, comprising: - a first phase in which the electrical angle describes a plurality of electrical angles (0i) obtained by applying said precession command (Cp), steps A to E being implemented for each electrical angle (0i), step D furthermore comprising a sub-step (MEM) of storing the associated frequency command value (CTfi) and a sub-step (MOD) of determining a variation law (CTf(0)) for the frequency command as a function of the electrical angle, -a second phase in which the inertial sensor operates in gyroscope mode, the electrical angle (0) that is left free resulting from a rotation of the inertial sensor and being measured (em) by said inertial sensor, the second phase comprising: a step (BO) of placing the second control operation (TrimF) in an open loop, the frequency command that is applied then being determined from said variation law for said measured angle of rotation (Om), a step of detecting a resonant frequency difference (Af), the open loop placement step (BO) being implemented for as long as said resonant frequency difference is less than or equal to a predetermined threshold (S), a step of placing said second control operation (TrimF) back in a closed loop when the frequency difference (Af) is greater than said threshold, the method then looping back to the first phase in order to update said variation law.
5. Method according to one of the preceding claims, wherein step B comprises: - a sub-step B1 of determining a position (x', y') of the vibrational wave in the reference frame X'Y' from the measurement of a position (x, y) of the vibrational wave in the sensor reference frame XY and from the electrical angle On - a sub-step B2 of estimating first values (Kq', AK') of said quadrature and equalization rigidities from said position in the wave reference frame (x', y').
6. Method according to one of the preceding claims, wherein step C consists in determining a vector (Kq, AK) defined by said second values by applying a rotation by an angle equal to twice the electrical angle (26) to the vector (Kq', AK') defined by said first values.
7. Inertial angular sensor (10) comprising: a resonator (Res) having a planar and axisymmetric structure about two axes X and Y that are perpendicular to one another defining a sensor reference frame XY and comprising two vibrating mobile masses (M1, M2) that are positioned one around the other, coupled to one another by coupling springs and configured so as to vibrate in phase opposition along a vibrational wave (OV) vibrating in a direction X' characterized* by an electrical angle (0) and defining a wave reference frame X'Y', the resonator furthermore comprising a plurality of electrostatic transducers controlled by electric voltages and operating along the two axes X and Y, including at least, on at least one of the two masses: a pair of excitation transducers, called E transducers, configured so as to keep the wave at a constant amplitude via an amplitude command (Ca) and, where necessary, to rotate said vibrational wave via a precession command (Cp), a pair of detection transducers, called D transducers, configured so as to detect the movements of the vibrational wave, a pair of quadrature bias compensation transducers, called TO transducers, configured so as to apply a quadrature rigidity via a quadrature command (CTq), the quadrature rigidity being configured so as to cancel out a coupling rigidity between X' and V', a pair of frequency adjustment transducers, called TF transducers, configured so as to apply an equalization rigidity via a frequency command (CTf), the equalization rigidity being configured so as to cancel out a difference in rigidity between X' and r so as to equalize the resonant frequencies of the vibrational wave on X' and Y', - said quadrature and equalization rigidities being determined, respectively, from a first (TrimQ) and from a second (TrimF) control operation, the sensor furthermore comprising a processing unit (UT) configured so as to determine said electrical angle (0) and comprising: - a first module (20) configured so as to estimate first values (Kq', AK') of said quadrature and equalization rigidities from the first (TrimQ) and from the second (TrimF) control operations, respectively, said first values being estimated in the wave reference frame X'Y', - a second module (21) configured so as to determine second values (Kq, AK) of said quadrature and equalization rigidities in the sensor reference frame XY, from the first values of said rigidities (Kq', AK'), - an assembly of two electrical gain modules (Gq, GO that are configured so as to determine, respectively, the quadrature command (CTq) corresponding to the second value of the quadrature rigidity (Kq) and the frequency command (CTf) corresponding to said second equalization rigidity value (AK), said TF and TO transducers being configured so as to apply, respectively, said frequency command (CTf) and said quadrature command (CTq) to the resonator.
8. Inertial sensor according to Claim 7, wherein the first module (20) is configured so as to determine a position (x', 1) of the vibrational wave in the wave reference frame X'Y' from the electrical angle (0) and from the measurement of a position (x, y) of the vibrational wave * in the sensor reference frame XY performed by the D transducers, and to estimate first values (Kq', AK') of said quadrature and equalization rigidities from said position in the wave reference frame (x', y').
9. Inertial sensor according to either of Claims 7 and 8, wherein the second module (21) is configured so as to determine a vector (Kq, AK) defined by said second values by applying a rotation by an angle equal to twice the electrical angle (20) to the vector (Kq', AK') defined by said first values.