Inertial angular sensor with compensation for speed variations

Abstract

The invention relates to an angular sensor comprising: a resonator (2) capable of supporting a radial mode of vibration with respect to an axis of symmetry of the resonator (2); transducers (5.1, 5.2, 6.1, 6.2) for delivering a first measurement signal and a second measurement signal concerning a deformation of the resonator (2) in a first direction and a second direction, respectively, said directions being orthogonal to one another in a reference frame of the mode of vibration, and for applying a force to the resonator (2) in these two orthogonal directions; and an electronic processing circuit (7) electrically connected to the transducers (5, 6) and designed to determine, on the basis of the measurement signals, an estimate (Formula) of an angular speed applied to the angular sensor and to output control signals for the transducers (6.1, 6.2) in order to generate and keep a vibration of the resonator (2) at a frequency corresponding substantially to a theoretical natural angular frequency ω0 and with a substantially constant amplitude a and a substantially zero quadrature component q, by processing an amplitude servo-control error X p — a 0 where X p is an amplitude servo-controlled to an amplitude setpoint a 0 , a quadrature servo-control error Y q , an angle estimation error Y p and a phase estimation error X q , characterized in that the electronic processing circuit (7) is designed to carry out compensation that makes the errors insensitive to a variable angular speed of the sensor taking into account the theoretical natural angular frequency ω0 and the estimate of the angle of the angular sensor.

Description

[0001] INERT ANGULAR SENSOR I EL A COMPENSATION FOR SPEED VARIATIONS

[0002] The present invention relates to the field of inertial angular sensors such as vibrating resonator gyroscopes and gyroscopes.

[0003] BACKGROUND OF THE INVENTION

[0004] A known angular sensor, described in document FR-A-2749394, comprises: a resonator capable of exhibiting a second-order, planar, stationary, and radial vibration mode about an axis of the resonator; detector transducers for measuring a deformation of the resonator in two orthogonal directions relative to a reference frame of the vibration mode; and actuator transducers for applying a force to the resonator along these two orthogonal directions. The resonator and transducers are mounted in a housing, and electronic means are electrically connected to the transducers. The actuator transducers must be powered to excite the resonator in the specified vibration mode at a natural frequency ω of the resonator, and the detector transducers will emit, respectively, a first measurement signal and a second measurement signal of the deformation.The measurement signals each have an in-phase component and a quadrature component which are modulated at the natural frequency ω. The electronic means are arranged so as to receive the measurement signals and emit the supply signals to the actuator transducers in opposite phase to generate and maintain a vibration of the resonator at its resonant frequency by maintaining the vibration amplitude at a constant value via amplitude control and canceling a quadrature component of the vibration via quadrature control.

[0005] During operation, if the casing is rotated around the resonator axis by an angle 6 at a speed Q, the vibration field tends to shift under the effect of Coriolis forces: each vibration node then moves relative to the transducers by an angle 6 e(commonly called electric angle) proportional to the rotation Q, undergone by the case, integrated over a time interval.

[0006] The commonly accepted mathematical model for perfect vibrating gyroscopes, i.e., without defects, is:

[0007]

[0008] In this model:

[0009] (1 = 0 is the angular velocity applied by the carrier to the angular sensor (the electrical angle 0 e r corresponding to the angle of the vibration deformation in the modal frame, is ideally equal to ad) ); r|i and r|2 are the coordinates of the vibration in the modal frame;

[0010] a is a form factor that depends on the shape of the resonator and is determined empirically during a calibration step;

[0011] œ is the natural frequency of the resonator.

[0012] The estimated vibration state is affected by several errors, including an amplitude control error, an angle estimation error, a phase estimation error, and a quadrature control error. For simplicity, we will refer to the amplitude control error here as X. p — a0(X p (being an amplitude controlled by the setpoint of amplitude a0), the error in estimating angle Y p , the X phase estimation error q r the quadrature control error Y q .

[0013] These errors are defined as follows:

[0014]

[0015] In these formulas: 6 is the estimate of angle 0 e of the deformation in the modal frame of reference (angle 0 e is commonly called electric angle);

[0016]

[0017] is the in-phase component of the first measurement signal and x3 is the quadrature component of the first measurement signal;

[0018] x2 is the in-phase component of the second measurement signal and x4 is the quadrature component of the second measurement signal;

[0019] ao is an amplitude control setpoint. In order to improve the performance of these angular sensors, enriched models have been proposed, notably that of the document DD Lynch, Vibratory Gyro Analysis by the Method of Averaging, Proceedings 2nd Saint Petersburg Int. Conf, on Gyroscopic Technology and Navigation, pp. 26-34, 1995.

[0020] This model takes the following form:

[0021]

[0022] In this model:

[0023] Q is equal to 0';

[0024] r|i and r|2 are the coordinates of the vibration in the modal frame of reference;

[0025] a is the traditional form factor

[0026] 3 is a second form factor dependent on the shape of the resonator;

[0027] œ is the natural frequency of the resonator.

[0028] For the sake of simplicity, it is common to disregard terms ending in aü.

[0029] The inventors, however, observed that this term introduces a significant error between the estimated value of the angle applied to the angular sensor and the actual value of the angle applied to the angular sensor when the rotational speed of the housing is not constant. This error leads to an error in the estimation of the angular position of the vibration and therefore in the measurement of amplitude control errors, quadrature control errors, angle estimation errors, and phase estimation errors.

[0030] SUBJECT OF THE INVENTION

[0031] The invention aims in particular to improve the performance of inertial angular sensors.

[0032] SUMMARY OF THE INVENTION

[0033] For this purpose, the invention provides an angular sensor comprising: a resonator capable of exhibiting a radial vibration mode with respect to an axis of symmetry of the resonator; detector transducers to provide a first measurement signal and a second measurement signal of a deformation of the resonator respectively along a first direction and a second direction orthogonal to each other of a reference frame of the vibration mode; actuator transducers to apply a force on the resonator along these two orthogonal directions;and an electronic processing circuit electrically connected to the transducers and arranged to determine from the measurement signals an estimate Ω̂ of an angular velocity applied to the angular sensor and to emit power signals to the actuator transducers to generate and maintain a vibration of the resonator at a frequency corresponding substantially to a theoretical natural frequency o>0 and with an amplitude a substantially constant and a quadrature component q substantially zero, by treating an amplitude control error X; p — a0 where Xp is an amplitude of the vibration controlled by a setpoint of amplitude a0, a quadrature control error Y q and an error in estimating angle Y pThe electronic processing circuit is arranged to perform compensation that makes these errors insensitive to variable sensor rotation speeds, taking into account the theoretical natural frequency. o and the estimation of the angle of the angular sensor.

[0034] By making the error measurement insensitive to the movements of the angular sensor, the performance of the angular sensor is improved. Using the theoretical natural frequency of the resonator instead of its actual natural frequency provides a sufficient approximation for compensation.

[0035] Preferably, the electronic processing circuit is arranged to generate and maintain the resonator vibration while also processing a phase estimation error x q .

[0036] According to a first embodiment, the electronic processing circuit is arranged so that the processing includes a phase of calculating compensated errors X p , Y q , Y p , Xq used for subsequent processing and such as:

[0037]

[0038] Indeed, from model (2), we can write the vibration in the following form:

[0039]

[0040] / cos(— a0)\ / — sin(— ad)\ \ + a£lj{a[., „ A cosûJt + q, sm it

[0041] \ \sin(— ad)) \ cos(— ad) / /

[0042]

[0043] Let d be the estimate of the vibration angle (commonly called the electric angle) and p the estimate of the phase. Using the error definition mentioned above and dividing the variables by the theoretical natural frequency co0, we obtain:

[0044] fX p \ co a£l

[0045] I v I = — (a V A0 coszlip + qJV àQ sinzl o) - / (-aVAe sin 1^ + qJV àQ cosZli ) \ip / i)0w0

[0046] / Xa\ co all

[0047] I v 1 = — (-a V0sin^ç) + qJV^ Q cos Ap) H - J(aV à Q cosAcp + qJV àQ sin 1 <p) k)0Û Q

[0048] In order to reduce angle and phase estimation errors and amplitude and quadrature control errors, it appears necessary to compensate for the n terms

[0049] However, "il" and "a" are two unknowns in the problem:

[0050] Ci) is an unknown constant and £1 is the angular velocity information that the angular sensor must measure. To compensate for these terms as much as possible, we use £1 and co0, which are known and close to al and Ci respectively.

[0051] We then define the compensated errors X p , Ÿ q , Ÿp X q :

[0052]

[0053] Finally, assuming that £1 = ail and û)0 = Ci), we obtain:

[0054]

[0055] It is noted that the compensation carried out has allowed for the cancellation of

[0056] 1st the terms in —.

[0057] a>

[0058] According to a second embodiment, each measurement signal has a phase component x l r x2 and a quadrature component x3, x4 and the electronic processing circuit is arranged to perform compensation on the x components lr x2x3x4 measurement signals. Preferably

[0059]

[0060] Depending on optional features, used individually or in whole or in part in any technically feasible combination:

[0061] - the electronic processing circuit is arranged to filter compensated errors in order to obtain vibration control signals and / or estimation signals.

[0062] - the amplitude X p is obtained using the following formula:

[0063]

[0064] in which ao is an amplitude control setpoint, x is a phase component of the first measurement signal and x2 is a phase component of the second measurement signal.

[0065] - the quadrature control error Y q is obtained using the following formula

[0066] —x3sin§

[0067]

[0068] where 0 is an estimate of an angle of deformation in the modal reference frame, x3 is a quadrature component of the first measurement signal and x4 is a quadrature component of the second measurement signal.

[0069] - the error in estimating angle Y p is obtained using the following formula:

[0070] x2cos§ — x^sind

[0071] where 9 is an estimate of the angle of the deformation in the modal frame of reference, j is a phase component of the first measurement signal, and x2 is a phase component of the second measurement signal. - the phase estimation error X q is obtained using the following formula

[0072]

[0073] where 9 is an estimate of an angle of deformation in the modal reference frame, x3 is a quadrature component of the first measurement signal and x4 is a quadrature component of the second measurement signal.

[0074] - The electronic processing circuit is arranged to determine a precession command by subtracting an estimated angle θ̂ from a deformation angle in the modal frame of reference. Other features and advantages of the invention will become apparent from the following description of a particular, non-limiting embodiment of the invention.

[0075] BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Reference will be made to the attached drawings, among which:

[0077] [Fig. 1] is a schematic top view of an angular sensor according to the invention;

[0078] [Fig. 2] is a representation of the vibration of the resonator in Figure 1, in a reference frame linked to the vibrational mode;

[0079] [Fig. 3] is a functional diagram of the angular sensor according to a first version of the invention; [Fig. 4] is a functional diagram of the angular sensor according to a second version of the invention.

[0080] DETAILED DESCRIPTION OF THE INVENTION With reference to Figure 1, the angular sensor according to the invention comprises a housing or support 1 and a hemispherical resonator 2 rigidly connected to the support 1 by a central foot 3 extending along a central axis of symmetry of the resonator 2 between the support 1 and a pole of the resonator 2 such that the resonator 2 has a flat annular edge 4 extending parallel to the support 1. The resonator 2 is, for example, made of quartz. Of course, other resonator shapes are usable; this is only one example of an embodiment.

[0081] Resonator 2 exhibits a second-order, stationary, radial vibration mode with respect to its axis of symmetry, at a frequency corresponding to a natural frequency ω of resonator 2. The annular plane edge 4 of resonator 2 is circular when resonator 2 is at rest and deforms into an elliptical shape when resonator 2 vibrates in this vibration mode. A network of elliptical standing waves of this vibration mode is represented by a dashed line in Figure 1, and a wave is represented by a thin line in Figure 2. Note that the "actual" natural frequency ω of resonator 2 is not known but is close to the theoretical natural frequency ω₀, taking into account manufacturing defects and dispersions of resonator 2.

[0082] The angular sensor also includes transducers 5 and 6, namely: a first detector transducer 5.1, a second detector transducer 5.2, a first actuator transducer 6.1 and a second actuator transducer 6.2. The first transducers 5.1, 6.1 are placed on either side of the resonator 2 on a first axis Al intersecting the central axis of symmetry of the resonator 2 and the second transducers 5.2, 6.2 are placed on either side of the resonator 2 on a second axis A2 intersecting the central axis of symmetry of the resonator 2. The axes Al, A2 extend in a plane perpendicular to the central axis of symmetry of the resonator 2 and constitute the axes of a reference frame of the second-order vibration mode mentioned above. Transducers 5.1 to 6.2, known in themselves, can for example be of piezoelectric or electrostatic type and include electrodes fixed to support 1 and / or resonator 2 and connected to an electronic processing circuit 7.

[0083] The physical arrangement and operating principle of the angular sensor are identical here to those described in document FR-A-2749394. Model 2 indicated above is applicable to the angular sensor of the invention.

[0084] When the actuator transducers 6.1 and 6.2 are powered in opposite phase by the processing electronic circuit 7 to excite the resonator 2 at the frequency corresponding to the natural frequency ω, the resonator 2 vibrates and its annular edge 4 takes the elliptical shape shown in Figure 2 with an amplitude component a along the major axis of the ellipse and an amplitude component b, or spatial quadrature, along the minor axis of the ellipse. The detector transducers 5.1 and 5.2 provide the processing electronic circuit 7 with a first and a second measurement signal, respectively, both having an in-phase component xi and X2, respectively, and a quadrature component X3 and X4, respectively, which are modulated at the said frequency corresponding to the natural frequency ω.

[0085] Thus, when a rotation of a determined angle is imparted to support 1 around the central axis of resonator 2, the vibration field tends to rotate relative to support 1, around the central axis of resonator 2, by an angle 0 e (commonly called electric angle) proportional to the angle of rotation of the support 1 (provided that the electronic processing circuit 7 allows this rotation to be free by operating in gyroscope mode).

[0086] The measurement signals provided by the transducer detectors 5.1, 5.2 to the electronic processing circuit 7 allow for an estimation θ̂ of the electric angle θ e and to deduce from this an estimate Ω̂ of the angular velocity Ω.

[0087] We will now focus more specifically on the processing of these signals by the electronic processing circuit 7.

[0088] The treatment performed includes (with reference to Figure 3):

[0089] - a phase estimation branch of 100,

[0090] - a servo control branch with an amplitude of 200,

[0091] - a quadrature control branch 300, and - an angle estimation branch 400.

[0092] The frequency control branch 100 is arranged to provide a CF signal from a phase estimation error X q having undergone a correction to obtain a compensated error in phase estimation X q .

[0093] The X phase estimation error q is obtained from the quadrature components of the measurement signals by a calculation function 101 applying the following formula:

[0094]

[0095] A correction function 102 then calculates the compensated error of phase estimation X q based on the X phase estimation error q by applying the following formula:

[0096]

[0097] The compensated error in X-ray phase estimation q is then amplified by means of an amplification function 103 having a gain GF(P) whose output corresponds to the control signal CF. The CF signal feeds a voltage-controlled oscillator 104 (or VCO) to provide a phase reference signal $ and a quadrature reference signal Q.

[0098] The phase and quadrature reference signals are used in particular to demodulate the measurement signals in order to extract the phase component x and the quadrature component x3 of the first measurement signal and the phase component x2 and the quadrature component x4 of the second measurement signal.

[0099] The phase and quadrature reference signals are also used, as will be seen later, to remodulate the feed signals of the actuator transducers 6.1, 6.2.

[0100] The amplitude control branch 200 is arranged to provide an AC control signal derived from an amplitude control error that depends on an amplitude X p controlled to an amplitude control setpoint a0 and which has undergone a correction to provide a compensated amplitude control error X p — a0.

[0101] The AC control signal has the function of powering the actuator transducers 6.1, 6.2 to maintain the amplitude of the vibration in such a way that this amplitude is constant.

[0102] The amplitude X p is obtained from the phase components of the measurement signals by a calculation function 201 applying the following formula:

[0103]

[0104] A correction function 202 then calculates the compensated amplitude X p based on the amplitude X pby applying the following formula:

[0105]

[0106] The compensated amplitude X p is then compared to the amplitude control setpoint a0 to provide the amplitude control error X p — a0. The compensated amplitude control error X p — a0 is then amplified by means of an amplification function 203 having a gain G (P ) whose output corresponds to the control signal AC.

[0107] The quadrature control branch 300 is arranged to provide a CQ control signal derived from a quadrature control error Y q having undergone a correction to obtain a compensated quadrature servo error Y q The CQ control signal has the function of powering the actuator transducers 6.1, 6.2 to cancel the spatial quadrature.

[0108] The quadrature control error Y q is obtained from the quadrature components of the measurement signals by a calculation function 301 applying the following formula:

[0109] Y q = -x3sinθ̂ + x4cosθ̂

[0110] A correction function 302 then calculates the compensated quadrature control error Y q from the quadrature control error Y q by applying the following formula:

[0111]

[0112] The compensated error of the quadrature control system Y q is then amplified by means of an amplification function 303 having a gain G q (p) whose output corresponds to the CQ control signal.

[0113] The angle estimation branch 400 is arranged to provide a CT output signal derived from an angle estimation error Y phaving undergone a correction to provide a compensated quadrature servo error Y p The output signal C allows us to obtain the 0 estimate of the electric angle in the modal frame.

[0114] The error in estimating angle Y p is obtained from the phase components of the measurement signals by a calculation function 401 applying the following formula:

[0115]

[0116] A correction function 402 then calculates the compensated error in angle estimation Y p based on the error in estimating angle Y p by applying the following formula:

[0117]

[0118] The compensated error in angle estimation Y pis then amplified by means of an amplification function 403 having a gain G(p) whose output corresponds to the output signal CT. The output signal C represents the rotational speed of the vibration Ô e and allows us to obtain, after applying an integration function 404, the estimate 0 of the electric angle 0 e .

[0119] To obtain the rotational speed, called i r applied to the angular sensor and the angle, called, in which the angular sensor is located around the central axis of the resonator 2, it suffices to multiply, by a correction function 405, the estimated angular velocity Ω̂ := θ̂̇ and the angle estimated by -1 / a (i.e. the inverse of the form coefficient a of the resonator 2, this form coefficient being for example determined during a calibration operation known in itself).

[0120] The processing here further includes a precession control branch 500 arranged to provide a precession control signal C p applied to the actuator transducers 6.1 and 6.2 to create a force maintaining the vibration orientation (or electrical angle) at a predetermined value. This force, being proportional to the angular velocity applied along the sensor's sensitive axis, constitutes a measurement of said velocity. In this operating mode, the angular measurement process thus comprises the steps of applying a precession command to control the vibration orientation to a set angular value and determining an angular measurement from the precession command.

[0121] The precession control branch 500 includes a subtractor 501 receiving on its positive input an electrical angle setpoint θ cand on its negative input the estimation θ̂ of the electric angle to provide the precession error θ at the output c — θ̂ which is then amplified by an amplification function 502 with a gain Gp (p) to obtain the precession control signal C P .

[0122] The CA, CQ and CP control signals applied to the actuator transducers 6.1, 6.2 are then subjected to trigonometric processing 10 and then to remodulation 20. More specifically, the quadrature control signal CQ is:

[0123] - on the one hand multiplied by —sinθ̂ by application of the trigonometric function 11 before being remodulated by the reference signal in phase $ and applied to an adder 30.1 supplying the actuator transducer 6.1;

[0124] - on the other hand multiplied by cosθ̂ by application of the trigonometric function 12 before being remodulated by the reference signal in phase $ and applied to an adder 30.2 supplying the actuator transducer 6.2.

[0125] The AC and CP control signals are:

[0126] - on the one hand multiplied by cosd and -sind respectively by application of the trigonometric function 13 (C A cosθ̂ — C P sinθ̂) before being remodulated by the quadrature reference signal Q and applied to the adder 30.1 supplying the actuator transducer 6.1;

[0127] - on the other hand, multiplied by sinθ̂ and +cosθ̂ respectively by application of the trigonometric function 14 (C A sinθ̂ — C P cosθ̂) before being remodulated by the phase reference signal $ and applied to an adder 30.2 supplying the actuator transducer 6.2.

[0128] Apart from the calculation of compensated errors, the operation of the angular sensor is identical to that of document FR-A-2749394 and will therefore not be detailed further here.

[0129] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

[0130] In particular, the invention is applicable to any type of inertial angular sensors, regardless of the shape of the axisymmetric resonator and its vibration modes.

[0131] The present invention is described in a specific case where only two detectors and two actuators are used, but the invention applies to the more general case where there are more transducers. Alternatively, the same transducers can successively act as detectors and actuators.

[0132] The transducers can be attached to the housing and the resonator, or only to the resonator.

[0133] The sensor can be a pure gyrometer or a pure gyroscope. The electronic processing circuit can be implemented using one or more processors, microprocessors, microcontrollers, FPGAs, etc.

[0134] The functions can be performed digitally or analogically.

[0135] The treatment of the X phase estimation error q is optional. Indeed, in some applications, the phase estimation error is negligible.

[0136] Alternatively, as shown in Figure 4, the electronic processing circuit 7 is arranged to perform compensation on the components x1, x2, x3, x4 of the measurement signals, via a compensation function 1234 implemented upstream of the calculation functions 101, 201, 301, 401. The compensated errors can then be calculated as follows:

[0137]

[0138]

Claims

DEMANDS 1. Angular sensor comprising: a resonator 2 ( ) capable of exhibiting a vibration mode, radial with respect to an axis of symmetry of the resonator (2); transducers (5.1, 5.2, 6.1, 6.2) to provide a first measurement signal and a second measurement signal of a deformation of the resonator (2) respectively along a first and a second direction orthogonal to each other of a reference frame of the vibration mode and to apply a force on the resonator (2) along these two orthogonal directions; and an electronic processing circuit (7) electrically connected to the transducers (5, 6) and arranged so as to determine from the measurement signals an estimate Ω̂ of an angular velocity applied to the angular sensor and to emit control signals of the transducers ( 6.1, 6.2).2) to generate and maintain a vibration of the resonator (2) at a frequency corresponding approximately to a theoretical natural frequency <u0et avec une amplitude a sensiblement constante et une composante en quadrature q sensiblement nulle, en traitant une erreur d' asservissement en amplitude X. p — where X p is an amplitude controlled by a setpoint of amplitude a0, a quadrature control error Y q and an error in estimating angle Y p characterized in that the electronic processing circuit (7) is arranged to perform compensation making said errors insensitive to a variable angular velocity of the sensor by taking into account the theoretical natural frequency ω0 and the estimation of the angle of the angular sensor.

2. Sensor according to claim 1, wherein the electronic processing circuit (7) is arranged to generate and maintain the vibration of the resonator (2) while also processing a phase estimation error X q .

3. Sensor according to claim 2, wherein the electronic processing circuit (7) is arranged such that the The treatment includes a phase of calculating compensated errors X p , Ÿ q , Ÿ p X q used for subsequent treatment and such as:

4. Sensor according to claim 1 or 2, wherein each measurement signal has an in-phase component (x1, x2) and a quadrature component (x3, x4) and the electronic processing circuit (7) is arranged to perform compensation on the components (x1, x2, x3, x4) of the measurement signals.

5. Sensor according to claim 4, wherein:

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

7. A sensor according to any one of the preceding claims, wherein the amplitude control error X p is obtained using the following formula: where 9 is an estimate of an angle of deformation in the modal reference frame, x1 is a phase component of the first measurement signal and x2 is a phase component of the second measurement signal.

8. A sensor according to any one of the preceding claims, wherein the quadrature control error Y q is obtained using the following formula: — x3sin9 + x4cos0 where 9 is an estimate of an angle of deformation in the modal reference frame, x3 is a quadrature component of the first measurement signal and x4 is a quadrature component of the second measurement signal.

9. Sensor according to any one of the preceding claims, wherein the angle estimation error Y p is obtained using the following formula: x2cosθ — x1sinθ where 9 is an estimate of an angle of deformation in the modal reference frame, x1 is a phase component of the first measurement signal and x2 is a phase component of the second measurement signal.

10. Sensor according to any one of claims 2, 3 and 4 to 9 depending on claim 2, wherein the phase estimation error X q is obtained using the following formula: x3cos9 + x4sin9 where 9 is an estimate of an angle of deformation in the modal reference frame, x3 is a quadrature component of the first measurement signal and x4 is a quadrature component of the second measurement signal.

11. Sensor according to any one of the claims previous, in which the electronic processing circuit (7) is arranged to determine a precession command (C P ) by difference between an angle command and an estimate θ̂ of an angle of the deformation in the modal reference frame.

Images