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EP-4737850-A1 - SCALE FACTOR CALIBRATION METHOD FOR MICROELECTROMECHANICAL GYROSCOPES

EP4737850A1EP 4737850 A1EP4737850 A1EP 4737850A1EP-4737850-A1

Abstract

A calibration method (100) of a gyroscope (11) that is microelectromechanical, including a movable mass (12), a movable sensing electrode (13) of the movable mass (12), a fixed sensing electrode (17) capacitively coupled to the movable sensing electrode (13) and a bias terminal (19) of the movable mass (12) includes: applying, to the bias terminal (19), a sequence of forcing signals (S F ) having a forcing time (T F ) and being determined by signals that are variable over time superimposed on respective forcing bias voltages (V D ) selected in a range; acquiring a sequence of sense signals (V S ) indicative of a damped oscillation of the movable mass (12) along a sense direction (Y) caused by respective forcing signals (S F ) consecutively to respective forcing times (T F ); from the sense signals (V S ), estimating a sequence of respective natural sense frequencies (f S ), each dependent on the corresponding forcing bias voltage (V D ); and estimating a sense gap (g), indicative of a distance at rest between the movable sensing electrode (13) and the fixed sensing electrode (17), starting from the sequence of natural sense frequencies (f S ).

Inventors

  • GUERINONI, LUCA
  • BERNABUCCI, DAVIDE
  • YALLICO SANCHEZ, Gianfranco Javier
  • Quartiroli, Matteo

Assignees

  • STMicroelectronics International N.V.

Dates

Publication Date
20260506
Application Date
20251016

Claims (17)

  1. A calibration method (100) of a microelectromechanical gyroscope (11) comprising a movable mass (12), a movable sensing electrode (13) of the movable mass (12), a fixed sensing electrode (17) capacitively coupled to the movable sensing electrode (13) of the movable mass (12) and a bias terminal (19) of the movable mass (12), the calibration method (100) comprising a first procedure (110) comprising: - applying, to the bias terminal (19) of the movable mass (12), a sequence of forcing signals (S F ), each forcing signal (S F ) having a forcing time (T F ) and being determined by a signal that is variable over time superimposed on a respective forcing bias voltage (V D ) selected in a range of forcing bias voltages (V D ); - acquiring a sequence of sense signals (V S ), each sense signal (V S ) being indicative of a damped oscillation of the movable mass (12) along a sense direction (Y) caused by a respective one of the forcing signals (S F ) consecutively to the respective forcing time (T F ); - from the sense signals (V S ), estimating a sequence of respective natural sense frequencies (f S ), each dependent on the forcing bias voltage (V D ) of the corresponding forcing signal (S F ); and - estimating a reference sense gap (g TRIM ), indicative of a distance at rest between the movable sensing electrode (13) of the movable mass (12) and the fixed sensing electrode (17), starting from the sequence of natural sense frequencies (f S ).
  2. The calibration method (100) according to claim 1, further comprising: - causing the movable mass (12) to oscillate, along a drive direction (X) perpendicular to the sense direction (Y), at a natural drive frequency (f D ); - measuring the natural drive frequency (f D ); and - starting from the estimate of a reference natural sense frequency (f S_BS ) of the sequence of natural sense frequencies (f S ) for which the corresponding forcing bias voltage (V D ) coincides with a sense bias voltage (V BS ) of the fixed sensing electrode (17), calculating a reference frequency mismatch (f M_TRIM ) according to: f M _ TRIM = f S _ BS − f D wherein: - f M_TRIM is the reference frequency mismatch (f M_TRIM ); - f S_BS is the reference natural sense frequency (f S_BS ) estimated in the first procedure (110); and - f D is the natural drive frequency (f D ) measured in the first procedure (110).
  3. The calibration method (100) according to the preceding claim, further comprising performing a best fitting of a curve (170) of the sequence of natural sense frequencies (f S ) against the forcing bias voltages (V D ) of the sequence of forcing signals (S F ) by means of the formula: f S g TRIM = f D + 1 2 π 2 πf M _ TRIM 2 − k g TRIM 3 V D − V BS 2 wherein: - g TRIM is the reference sense gap (g TRIM ); - f S (g TRIM ) indicates the dependence of the sequence of natural sense frequencies (f S ) on the reference sense gap (g TRIM ); - k is an electromechanical constant that depends on electrical and mechanical parameters of the gyroscope (11) along the sense direction (Y); - V D are the forcing bias voltages (V D ); and - V BS is the sense bias voltage (V BS ) of the fixed sensing electrode (17), and wherein estimating the reference sense gap (g TRIM ) comprises solving an optimization problem starting from said formula.
  4. The calibration method (100) according to the preceding claim, wherein estimating the reference sense gap (g TRIM ) comprises employing a least squares method: min g TRIM f S g TRIM 2 2
  5. The calibration method (100) according to any of claims 2 to 4, further comprising a second procedure (210) performed subsequently to the first procedure (110) and comprising: - applying, to the bias terminal (19) of the movable mass (12), the sequence of forcing signals (S F ); - acquiring a sequence of sense signals (V S ), each sense signal (V S ) being indicative of a damped oscillation of the movable mass (12) along the sense direction (Y) caused by a respective one of the forcing signals (S F ) consecutively to the respective forcing time (T F ); - from the sense signals (V S ), estimating a sequence of respective natural sense frequencies (f S ), each dependent on the forcing bias voltage (V D ) of the corresponding forcing signal (S F ); and - estimating a set-up sense gap (g FIELD ), indicative of a distance at rest between the movable sensing electrode (13) of the movable mass (12) and the fixed sensing electrode (17), starting from the sequence of natural sense frequencies (f S ).
  6. The calibration method (100) according to the preceding claim, further comprising: - causing the movable mass (12) to oscillate along the drive direction (X) at a natural drive frequency (f D ); - measuring the natural drive frequency (f D ); and - starting from the estimate of a reference natural sense frequency (f S_BS ) of the sequence of natural sense frequencies (f S ) for which the corresponding forcing bias voltage (V D ) coincides with the sense bias voltage (V BS ) of the fixed sensing electrode (17), calculating a set-up frequency mismatch (f M_FIELD ) according to: f M _ FIELD = f S _ BS − f D wherein: - f M_FIELD is the set-up frequency mismatch (f M_FIELD ); - f S_BS is the reference natural sense frequency (f S_BS ) estimated in the second procedure (210); and - f D is the natural drive frequency (f D ) measured in the second procedure (210).
  7. The calibration method (100) according to the preceding claim, further comprising performing a best fitting of a curve (270) of the sequence of natural sense frequencies (f S ) against the forcing bias voltages (V D ) of the sequence of forcing signals (S F ) by means of the formula: f S g FIELD = f D + 1 2 π 2 πf M _ FIELD 2 − k g FIELD 3 V D − V BS 2 wherein: - g FIELD is the set-up sense gap (g FIELD ); - f S (g FIELD ) indicates the dependence of the sequence of natural sense frequencies (f S ) on the set-up sense gap (g FIELD ); - k is an electromechanical constant that depends on electrical and mechanical parameters of the gyroscope (11) along the sense direction (Y); - V D are the forcing bias voltages (V D ); and - V BS is the sense bias voltage (V BS ) of the fixed sensing electrode (17), and wherein estimating the set-up sense gap (g FIELD ) comprises solving an optimization problem starting from said formula.
  8. The calibration method (100) according to the preceding claim, wherein estimating the set-up sense gap (g FIELD ) comprises using a least squares method: min g FIELD f S g FIELD 2 2
  9. The calibration method (100) according to any of claims 6 to 8, further comprising estimating a variation of a scale factor (DSF) of the gyroscope (11) on the basis of the reference sense gap (g TRIM ) estimated in the first procedure (110), the set-up sense gap (g FIELD ) estimated in the second procedure (210), the reference frequency mismatch (f M_TRIM ) calculated in the first procedure (110) and the set-up frequency mismatch (f M_FIELD ) calculated in the second procedure (210) according to: DSF % = g TRIM 2 g FIELD 2 ⋅ f M _ TRIM f M _ FIELD ⋅ 100 and using the estimated variation of the scale factor (DSF) to correct a measurement (Ω M ) of angular velocity of a rotary movement (Ω) of the gyroscope (11) around a rotation direction (Z) perpendicular to the drive direction (X) and the sense direction (Y).
  10. The calibration method (100) according to any of claims 5 to 9, wherein the first procedure (110) is performed in a factory calibration step of the gyroscope (11) and wherein the second procedure (210) is performed in a set-up calibration step of the gyroscope (11).
  11. The calibration method (100) according to any of the preceding claims, wherein each forcing signal (S F ) comprises a voltage step signal, or voltage pulse signal, or a sinusoidal signal having an average value corresponding to the forcing bias voltage (V D ).
  12. The calibration method (100) according to any of the preceding claims, wherein the gyroscope (11) is at rest during applying the sequence of forcing signals (S F ) and estimating the sequence of natural sense frequencies (f S ).
  13. A system (10) for sensing angular velocity comprising a microelectromechanical gyroscope (11) and an electronic processing unit (21) coupled to the gyroscope (11), the gyroscope (11) comprising: - a movable mass (12); - a movable sensing electrode (13) of the movable mass (12); - a fixed sensing electrode (17), capacitively coupled to the movable sensing electrode (13) of the movable mass (12); and - a bias terminal (19) of the movable mass (12), the electronic processing unit (21) comprising: - a signal generator (28), configured to apply, to the bias terminal (19) of the movable mass (12), a sequence of forcing signals (S F ), each forcing signal (S F ) having a forcing time (T F ) and being determined by a signal that is variable over time superimposed on a respective forcing bias voltage (V D ) selected in a range of forcing bias voltages (V D ); - an analog-to-digital converter (22), configured to acquire a sequence of sense signals (V S ), each sense signal (V S ) being indicative of a damped oscillation of the movable mass (12) along a sense direction (Y) caused by a respective one of the forcing signals (S F ) consecutively to the respective forcing time (T F ); - a sampler (26), configured to estimate a sequence of respective natural sense frequencies (f S ) from the sense signals (V S ), each natural sense frequency (f S ) being dependent on the forcing bias voltage (V D ) of the corresponding forcing signal (S F ); and - an estimator (29), configured to estimate a sense gap (g), indicative of a distance at rest between the movable sensing electrode (13) of the movable mass (12) and the fixed sensing electrode (17), starting from the sequence of natural sense frequencies (f S ).
  14. The system (10) according to claim 13, wherein the electronic processing unit (21) further comprises: - a drive module (15), coupled to a drive structure (16) of the movable mass (12) of the gyroscope (11) and configured to cause the movable mass (12) to oscillate along a drive direction (X), perpendicular to the sense direction (Y), at a natural drive frequency (f D ); and - a frequency meter (18), configured to measure the natural drive frequency (f D ) of the movable mass (12), and wherein the estimator (29) is further configured to calculate, starting from the estimate of a reference natural sense frequency (f S_BS ) of the sequence of natural sense frequencies (f S ) for which the corresponding forcing bias voltage (V D ) coincides with a sense bias voltage (V BS ) of the fixed sensing electrode (17), a frequency mismatch (f M ) according to: f M = f S _ BS − f D wherein: - f M is the frequency mismatch (f M ); - F S_BS is the reference natural sense frequency (f S_BS ); and - f D is the natural drive frequency (f D ).
  15. The system (10) according to the preceding claim, wherein the estimator (29) of the electronic processing unit (21) is further configured to perform a best fitting of a curve (170, 270) of the sequence of natural sense frequencies (f S ) against the forcing bias voltages (V D ) of the sequence of forcing signals (S F ) by means of the formula: f S g = f D + 1 2 π 2 πf M 2 − k g 3 V D − V BS 2 wherein: - g is the sense gap (g); - f S (g) indicates the dependence of the sequence of natural sense frequencies (f S ) on the sense gap (g); - k is an electromechanical constant that depends on electrical and mechanical parameters of the gyroscope (11) along the sense direction (Y); - V D are the forcing bias voltages (V D ); and - V BS is the sense bias voltage (V BS ) of the fixed sensing electrode (17), and wherein the estimator (29) is configured to estimate the sense gap (g) by solving an optimization problem starting from said formula.
  16. The system (10) according to the preceding claim, wherein the estimator (29) is configured to estimate the sense gap (g) using a least squares method: min g f S g 2 2
  17. The system (10) according to any of claims 14 to 16, wherein the electronic processing unit (21) further comprises a digital compensator (27) configured to: - receive at input, from the estimator (29), the estimated sense gap (g) and the calculated frequency mismatch (f M ); - estimate a variation of the scale factor (DSF) of the gyroscope (11) on the basis of a variation of the sense gap (g) and a variation of the frequency mismatch (f M ); and - use the estimated variation of the scale factor (DSF) to correct a measurement (Ω M ) of angular velocity of a rotary movement (Ω) of the gyroscope (11) around a rotation direction (Z) perpendicular to the drive direction (X) and the sense direction (Y).

Description

Technical Field The present invention relates to a scale factor calibration method for microelectromechanical gyroscopes, and in particular to an estimation method of the variation of the scale factor and a correction method thereof. Background As is known, microelectromechanical (MEMS) inertial sensors, such as for example MEMS gyroscopes, generally comprise a support body and at least one movable mass, suspended on and coupled to the support body through flexures. The flexures are configured so as to allow the movable mass to oscillate with respect to the support body according to one or more degrees of freedom. The movable mass is coupled to the support body generally in a capacitive manner and forms, with the support body, capacitors of variable capacitance. In particular, the movement of the movable mass with respect to fixed electrodes on the support body, due to the action of forces acting thereon, modifies the capacitance of these capacitors; the displacement of the movable mass with respect to the support body is sensed by this capacitive variation and the external force that caused the displacement is calculated starting from the sensed displacement. Among MEMS inertial sensors, gyroscopes have a complex electromechanical structure that may comprise, for example, at least two movable masses, each having one or at most two degrees of freedom with respect to the support body, or a single movable mass provided with at least two degrees of freedom. In all cases, capacitive coupling occurs through fixed and movable actuation (or driving) electrodes and through fixed and movable sensing electrodes. In the implementation with a single movable mass, for example, the movable mass is coupled to the support body so as to be movable with respect to the latter with two independent degrees of freedom, and precisely one degree of freedom for actuation and one degree of freedom for sensing. The latter may envisage a movement along the plane of the movable mass ("in-plane" movement) or perpendicular to the plane ("out-of-plane" movement). An actuation or driving device maintains the movable mass in controlled oscillation according to the degree of freedom for actuation. The movable mass moves based on the degree of freedom for sensing in response to the rotation of the support body, due to the Coriolis force. A principle diagram of a single movable mass gyroscope is shown in Figure 1, showing in broad terms the mechanical sense structure of a gyroscope 1. Here, the gyroscope 1 comprises a movable mass 2 supported by a support structure 3 (shown schematically) through a first and a second flexure system 4, 5, also shown only schematically and each represented through a respective elastic element 41, 51 (having respective elastic constants kx and ky) and a respective damping element 42 and 52 (having respective damping constants rx and ry). In Figure 1, the first flexure system 4 allows the movement of the movable mass 2 in a first direction, parallel to a first axis of a Cartesian reference system (here the X axis) and therefore referred to as the drive direction X, and the second flexure system 5 allows the movement of the movable mass 2 in a second direction, parallel to a second axis of the Cartesian reference system (here the Y axis) and therefore referred to as the sense direction Y. In Figure 1, driving electrodes not shown cause the oscillation of the movable mass 2 in the drive direction X. In the presence of a rotary movement Ω of the gyroscope 1 around an axis parallel to the Z axis (which is therefore a rotation direction Z), the Coriolis force causes an oscillatory movement of the movable mass 2 in the sense direction Y, in a known manner. This movement determines a variation in the distance, or "gap", between the movable mass 2 (or a movable electrode integral thereto in the sense direction Y) and a fixed electrode 7 of the gyroscope 1 and may be sensed on the basis of the resulting capacitive variation ΔC. As indicated, real MEMS gyroscopes have a complex structure and often have non-ideal electromechanical interactions between the movable mass and the support body, for example due to manufacturing defects, environmental conditions (temperature and humidity) and/or assembly in packaging (thermomechanical stresses) and aging that modify the gyroscope scale factor, i.e. the ratio between the gyroscope output signal (capacitive variation ΔC) and the angular velocity Ω to be sensed. In fact, such conditions may give rise to a disturbance that acts in the sense direction Y, increasing or decreasing the elongation of the movable mass 2 caused by the Coriolis force in the sense direction Y and/or varying the distance between the movable mass 2 and the fixed electrode 7 and therefore giving rise to different capacitive variations between the same movable mass and the fixed electrode, causing a variation of the scale factor. This fact may also be demonstrated mathematically starting from the definition of the