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Sagem Coriolis Vibrating Gyros: A vision realized


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In the early 90's, the concepts chosen by Sagem for his future CVG (Coriolis Vibrating Gyros) developments were based upon three main key principles: • An axisymmetric resonator • A finely balanced resonator • A Whole Angle mode of control. After more than two decades of experience, these visionary choices have proven to be well-grounded. They led to continuous improvement of the company know-how for the benefit of the performances. Associated with the ever-increasing computing power of microcontrollers, it is even possible to continue to improve the performances of the early versions of the Sagem CVGs. The paper shows how these main principles have been applied to Quapason™, to HRG and more recently to advanced high performance MEMS gyro and presents the more recent tests result obtained. The high versatility of the CVG concept is shown through a description of typical applications relying on its key characteristics.
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978-1-4799-4663-1/14/$31.00 ©2014 IEEE P08
Sagem Coriolis Vibrating Gyros: a vision realized
G.Remillieux, F.Delhaye
Sagem Défense Sécurité
18/20 quai du Point du Jour
92659 Boulogne-Billancourt Cedex
Inertial Sensors and Systems 2014
Karlsruhe, Germany
In the early 90’s, the concepts chosen by Sagem for his future CVG (Coriolis Vibrating
Gyros) developments were based upon three main key principles:
· An axisymmetric resonator,
· A finely balanced resonator,
· A Whole Angle mode of control.
After more than two decades of experience, these visionary choices have proven to be
well-grounded. They led to continuous improvement of the company know-how for the
benefit of the performances. Associated with the ever-increasing computing power of
microcontrollers, it is even possible to continue to improve the performances of the early
versions of the Sagem CVGs.
The paper shows how these main principles have been applied to QuapasonTM, to HRG
and more recently to advanced high performance MEMS gyro and presents the more
recent tests result obtained.
The high versatility of the CVG concept is shown through a description of typical
applications relying on its key characteristics.
1. Introduction
When Sagem started in 1985 the development of Coriolis Vibrating Gyros, the technical
choices were rapidly based on three main principles:
· The first principle was to use an axisymmetrical resonator: these property leads
indeed to resonators exhibiting naturally good characteristics in term of Frequency
Isotropy, Damping isotropy and Balance. It allows also the use of the Whole Angle
mode of control,
· The second principle was to obtain the best tuned and balanced resonator as
possible: a very good isolation of the vibrating mode of the resonator is necessary
if one needs stable performances, independent from the environment. Even with an
axisymmetric resonator some complementary tuning and balancing is a must,
· The third principle was to use the Whole Angle mode of control: this mode
minimizes the amplitude of the forces applied for the control of the vibration and
therefore minimizes the errors caused by the electronic, the detectors and actuators
defects. Therefore, this mode leads to a very good scale factor (based on the Bryan
factor) and allows high dynamics.
Figure 1. The three main key principles choosen for CVG developments
2. The different areas of expertise
Using these principles as a basis, Sagem has built up his expertise through different
developments and applications of CVG. In order to present in the next chapters how this
principles have been applied, it is useful as illustrated in fig 2, to distinguish different areas
of expertise and to see in each area what are the lessons learnt:
The resonator itself : material, shape and size, mode of vibration, pick-offs and
actuators, process of manufacturing,
Tuning and balancing : how to reach low frequency mismatch and low mass
unbalance as needed by high performance CVG,
The control : the different types of vibration control, the defects to minimize and the
way to auto-calibrate some residual errors at the CVG control level,
The operating modes: at the system level, how to get the best from a CVG.
Figure 2. The different area of expertise
3. Resonator area of expertise
3.1. Sagem resonators
The figure 3 shows the different resonators developed by Sagem.
· The very first one was a piezo disc, about 25 mm in diameter. The vibration mode
was in the plane of the disc and the time constant was low (< 0,1second), due to
the low Q factor of the piezo material and to the relatively high frequency of the
vibrating mode (about 100 kHz). Despite this low time constant, the Whole Angle
mode of control allowed the measurement of very high angular velocities with good
accuracy as needed for spin-stabilized projectiles applications. A description of this
resonator was given during the 1994 Stuttgart Symposium [1].
· The QuapasonTM uses a four beams metallic resonator which was chosen for the
ease of manufacturing in view of medium range performances. Small piezo cells act
as pick-off and actuators. In this design, the low Q factor of the piezo material used
for the pick-off and actuators cells has little effect on the Q factor of the complete
resonator. Their effect is indeed divided by the modal mass of the resonator, which
is high, being metallic and rather massive. Therefore, with a resonance frequency of
7 kHz, this resonator exhibits a time constant of several seconds. Moreover the
pick-offs and actuators are symmetrically arranged in order to maintain optimal
mechanical insulation and therefore the best stability for gyro performance [2].
Being axisymmetric, this resonator may be used either in FTR (Force to rebalance)
or WA (Whole Angle) mode of control, which opens a wide range of applications.
Line of sight stabilization, aeronautic standby instruments and AHRS are actually
the main applications.
· The well-known HRG (Hemispherical Resonant Gyroscope) uses a fused Quartz
resonator. This material exhibits an extraordinary high Q factor and is well adapted
to high performance when associated with electrostatic pick-off and actuators.
Indeed, a thin film metallic deposit on the resonator enables the electrostatic control
of the vibration with little deterioration of the Q factor. Moreover, a Sagem patent [3]
introduces a flat electrodes design which greatly improves the simplicity of the
gyroscope and the ease of manufacturing. As a result, this type of resonator
vibrates at 7 kHz and exhibits time constants beyond 500 seconds. Therefore, when
associated with the Whole Angle mode of control, it meets the highest demanding
applications like high performance navigation ones.
· The latest Sagem resonator is a silicon MEMS one. In the view of very good
performances, Sagem first sought how to apply his principles to MEMS gyroscopes
but studies have not started until a way to accurately balance a MEMS resonator
was conceived. Finally an idea to overcome this difficulty appeared in 2011 together
with the design of a flat axisymmetric MEMS resonator [4]. From that moment, the
way was open to apply the principles already developed with the other resonators to
MEMS gyroscopes. It is particularly interesting to see that the control of an
axisymmetric MEMS is similar to that of a HRG, using electrostatic pick-off and
Figure 3. Sagem resonators
3.2. What we learnt about the resonator
· A High Q factor is highly desirable, but the real objective is to minimize the
power needed to maintain the vibration. This power is in inverse proportion to
the time constant of the resonator. As given by the formula (1), the frequency f
must also not be too high: with the same Q factor, the performance of a
resonator exhibiting a resonance frequency of 10 kHz will be ten times better
than the one with a resonance frequency of 100 KHz. It is in particular a difficulty
when one wishes to use a high harmonic mode of a resonator to design a gyro.
τ = Q/πf (1)
· The size of the resonator is not the main key factor for high performance. Unlike
the Sagnac effect optical gyros, the dimensions of the resonator are not involved
in the Scale Factor formula, only dependent to the shape of the vibration mode
through the Bryan factor [5]. Provided the resonator is well tuned, we find out
that the control defects were the main errors contributors. For example, with the
HRG, we were able to improve from 1°/h to better than 0,01°/h , while keeping
the 20mm size,
· When looking to a MEMS, the design of an axisymmetric resonator is possible,
for example like a « flat » QuapasonTM [4],
Figure 4. The design of a flat axisymmetric MEMS resonator is possible
· Finally, with a good control we find out that the small remaining errors are due to
the damping anisotropy of the resonator. That is when the damping (or the Q
factor) is not exactly the same in all directions of the vibration. This damping
anisotropy will cause some drift error because a free vibration naturally goes in
the direction where the damping is minimum. A well-balanced resonator is
required in order to minimize these errors.
4. Balancing and tuning area of expertise
4.1. Balancing and tuning necessity
We will see in the next chapter that it is possible to control the vibration even if there is
some frequency mismatch of the resonator. The bad news is that, when applying forces to
do this control, one will introduce errors due to inaccuracy of electronics or actuators.
Therefore, in view of good performances, it is useful to introduce during the manufacturing
of the resonator a specific process in order to make the resonance frequency as isotropic
as possible about the sense axis of the gyroscope: that is what we call the Tuning. The
sensitivity to a frequency mismatch is high: the figure 5 shows that a frequency mismatch
of only one millihertz requires a control accuracy of 10-5 if one look to 0,01°/h performance.
Furthermore, if the centre of mass is not motionless during the vibration, the resonator is
not well isolated. The resonator will then apply forces to its support and vibrating energy
will escape in the external structure: according to the figure 6, this will lower the real Q
factor of the resonator and will also introduce some damping anisotropy. Going the other
way, this defect will also introduce a resonator-sensitivity to external forces. For all these
reasons, a balancing process is required during the resonator manufacturing in order to
make the centre of mass motionless during the vibration.
Figure 5. Without tuning, the drift error will be high
Figure 6. Without balancing, the Q factor is lowered
4.2. What we learnt about tuning and balancing
· Removing or adding material from a resonator modifies at the same time the
stiffness and the weight distribution of the resonator. For this reason, the tuning
and balancing process are to be regarded as a whole,
· Unbalance defects will cause unwanted forces and torques at the vibration
frequency : the process has to take into account the 6 degrees of freedom,
· A tuning and balancing bench has been developed for the HRG and has
demonstrated in 2008 his ability to converge for the 6 DOF (Degrees Of
Freedom) together with the frequency tuning. Depending on the time allowed to
the process, different levels of performance may be obtained. The figure 7
shows how the 6 degrees of freedom (C1,2,3 and F1,2,3) together with the
frequency mismatch (df) converge from 800 ppm near to zero ppm during the
Figure 7. The convergence of the balancing and tuning process
· The difficulty to remove or add material to a MEMS resonator was initially seen
as the main limitation in view of high performances. Better than few degree per
hour is difficult without a tuning and balancing process. A new paradigm conduct
us to a new architecture for a MEMS resonator, enabling a dynamic tuning and
balancing based only on stiffness control (electrostatic spring). Introducing an
additional mass m0 and spring k0 (see figure 8) at a location where the
displacement is supposed to be zero allows to detect unbalance defect and to
control stiffness K1 and K2 to cancel this defect with a dynamic control loop [4],
Figure 8. Additional mass and spring allows for dynamic balancing
5. CVG control area of expertise
5.1. The basics of CVG control
According to the figure 9, controlling the vibration consists in generating harmonic forces
(that is at the vibration frequency), like F11 and F22 in order to maintain the amplitude and
the shape of the vibration to the desired value. In the case of the Force To Rebalance
mode (FTR mode), F21 forces are also needed to rebalance the Coriolis ones.
Figure 9. The harmonic forces and their effects
5.2. What we learnt about CVG control
· Phase or direction errors (pick-off, actuators and electronics) are to be avoided
because they lead to F21 forces when applying F11 or F22 ones: F21 forces will
change the direction of the vibration and the consequence will be drift errors.
Therefore, great care must be taken to design the control electronics,
· FTR Control mode is simpler to implement : it allows in particular the use of
analog components,
· WA Control mode minimizes the errors due to the defects of the pick-off and
actuators gains, phase and directions and allows very high dynamics with a very
accurate Scale Factor. As a general rule, when the force needed to rebalance
the Coriolis one is larger than the forces needed to maintain the shape and the
amplitude of the vibration, the FTR mode is less efficient :
o With a resonator exhibiting large frequency mismatch and small time
constant, FTR mode may be used until a certain dynamics ; for very large
angular velocities, the WA mode will take the lead again thanks his very
good scale factor,
o With a very low frequency mismatch and large time constant, the WA
mode is more efficient, until very, very low dynamics,
· Whatever the mode of control, with four available commands Fij, we have more
forces than necessary to control the vibration. This can be cleverly used to
minimize the residual errors [6]:
o For instance, using the force F12, it is possible to modulate the resonance
frequency and one can see with (2) that the gain of this modulation is
directly linked with the scale factor error of the FTR mode. In doing so,
one can observe and compensate this Scale Factor error.
o As a second example, using the F21 force, it is possible according to (3) to
move the direction of the vibration over a 180° interval, which is a way to
cancel the bias due to the damping anisotropy
6. “Operating modes” area of expertise
6.1. Operating modes
The CVG control acts at the gyro level using the four types of forces to minimize the
errors. At the Inertial System level, one can also take advantage of the specific CVG
features to further improve performances when other informations are available.
The principle is based on a fundamental characteristic of the residual drift errors of a CVG
in WA mode: this drift errors are due to damping anisotropy and always exhibits a very low
and stable mean value over 180° of angle.
6.2. What we learnt about operating modes
· Calibration: The damping anisotropy leads to drift errors like the red curve on the
figure 10. In the lab, this drift is easily observed using the F21 force to explore all
direction of the vibration. These drifts are then compensated at the system level
thanks to a model,
· Gyrocompass: If there is some instability in the damping anisotropy, further
refinements at the system level will overcome them. For instance, during the
gyrocompass, the direction of the vibration can be brought on well-chosen
discrete directions (two or three on the example of figure 10). The main
harmonics of these remaining errors will then be canceled and the heading
estimation will be very accurate,
· Navigation in multi-axis configuration: With more than 3 gyros, a very accurate
navigation is achieved since calibration is performed in background task.
Figure 10. Harmonic break down of damping anisotropy errors
7. How this Know-How was built up
Technical advances and associated dates provide hereinafter an overview of the building
of this Know-How:
è With the piezo disc
§ 1986: axisymmetric resonator and Whole Angle mode.
è With the Quapason
§ 1991: FTR mode,
§ 1998: Frequency mismatch tuning by material removal,
§ 2010: Auto calibrated gyro using modulation of harmonic forces (Patent),
è With the HRG
§ 1998: High Q resonator,
§ 2004: High accuracy control,
§ 2009: 6 DOF Balancing,
§ 2010: Gyrocompass with multiposition of the vibration,
§ 2011: Drift canceling through a specific operating mode,
§ 2012: Multi-axis Navigation.
è With the Sagem MEMS Gyro
§ 2011: Patent for Axisymmetric design and Dynamic balancing.
8. SAGEM CVG: A vision realized
Finally, one can say today that the original vision is now realized and the following
results just confirm that:
è Quapason
§ 100 000th QuapasonTM manufactured,
§ 500 Millions Flight hours recorded 1 Million Flight hours proven MTBF,
§ Performance: from 100 to 10°/h with auto calibration.
§ BlueNaute compass AHRS & Sterna North finder commercially available,
§ 100th HRG on order for satellite AOCS,
§ 1 Nm/h HRG based prototype IRS flight on A320,
§ 5000th HRG manufactured,
§ << 0,01°/h demonstrated with drift canceling.
è Sagem MEMS gyro
§ 2013: first results of the axisymmetric resonator: 5°/h,
§ To come : performances with dynamic balancing,
§ Sagem considers that the « lessons learnt » on QuapasonTM and HRG are
fully applicable to MEMS gyros: further improvement are expected with auto
calibration and drift canceling.
9. Conclusion
The initial vision adopted in 1985 for the development of Coriolis Vibrating Gyros has
proved to be fruitful:
§ Development activities conducted on QuapasonTM and HRG allowed to
understand the wonderful potential of axisymmetric resonant structures in the
field of gyroscopes,
§ The Know-How developed during this studies is applicable whatever the type
of axisymmetric resonators,
§ 2D axisymmetric MEMS resonator can be controlled with same or similar
principles as the HRG. This allows to design MEMS gyros able to achieve
unmatched accuracy,
§ Only few resonant structures are enough to cover the full range. Ultimately
these structures could be HRG and MEMS.
[1] A.Jeanroy, “Low Cost High Dynamic Vibrating Rate Gyro”, in Proceedings of the
Symposium Gyro Technology, Stuttgart Germany 1994
[2] P.Leger, “QUAPASONTM, a new low-cost vibrating gyroscope”, in Proceedings of 3rd
Saint Petersburg International Conference on Integrated Navigation Systems, 1996
[3] A.Jeanroy, P.Leger, HRG flat electrodes, Patent US 6474161
[4] A.Jeanroy, Capteur angulaire inertiel de type MEMS équilibré et procédé
d’équilibrage d’un tel capteur, Brevet FR2983574, 06/12/2011
[5] V.F. Zhuravlev. Oscillation Shape Control in Resonant Systems//J. Appl. Maths
Mechs, Vol. 56, No. 5, 1992 - pp. 725-735
[6] V.Ragot, G.Remillieux, “A new control mode for axisymetrical vibrating gyroscopes
greatly improving performance, in Proceedings of 18rd Saint Petersburg International
Conference on Integrated Navigation Systems, 2011
... 11 Therefore, many related studies have been carried out, among which the common ones are improving the quality factor 12,13 and matching modes through various techniques. 14, 15 Feng et al. proposed a vibration isolation structure for tuning fork resonators to eliminate the effects of weight imbalance, ultimately obtaining a Q factor of up to 3 × 10 6 . 12 Behbahani and M'Closkey reported a postmachining technique for simultaneously eliminating the frequency difference between two pairs of modes in an axially symmetric cavity. ...
A tuning fork gyroscope (TFG) with orthogonal thin-walled round holes in the driving and sensing directions is proposed to improve sensitivity. The thin walls formed by through holes produce stress concentration, transforming the small displacement of tuning fork vibration into a large concentrated strain. When piezoelectric excitation or detection is carried out here, the driving vibration displacement and detection output voltage can be increased, thereby improving sensitivity. Besides, quadrature coupling can be suppressed because the orthogonal holes make the optimal excitation and detection positions in different planes. The finite element method is used to verify the benefits of the holes, and the parameters are optimized for better performance. The experimental results show that the sensitivity of the prototype gyroscope with a driving frequency of 890.68 Hz is 100.32 mV/(°/s) under open-loop driving and detection, and the rotation rate can be resolved at least 0.016 (°/s)/Hz, which is about 6.7 times better than that of the conventional TFG. In addition, the quadrature error is reduced by 2.7 times. The gyroscope has a simple structure, high reliability, and effectively improves sensitivity, which is helpful to guide the optimization of piezoelectric gyroscopes and derived MEMS gyroscopes.
... The quality factor (Q factor) of hemispherical resonator is a critical parameter to characterize the energy loss of resonant period, and is related to the structure material and restrained conditions of the resonator [4][5][6]. Recently, the Q factor of fused silica hemispherical resonator has exceeded 25 million, which has met the application requirements of high precision gyroscopes [7][8][9]. At present, frequency splitting and Q factor nonuniformity are the main error sources, which affect the precision of hemispherical gyroscopes. ...
... In recent years, vibrating sensors have become ubiquitous [1][2][3]. This is because of their simple design (no moving parts), robustness, and continuous improvements in algorithms and electronics. ...
Conference Paper
In recent years, vibrating sensors have become ubiquitous. This is because of their simple design (no moving parts), robustness, and continuous improvements in algorithms and electronics. Nowadays, vibrating gyroscopes are replacing well-established optical technologies like ring laser and fiber optics gyroscopes. Vibrating gyroscopes are based on the Coriolis Effect. For instance, when a standing wave is excited in an axisymmetric structure (resonator) and an angular rate is applied; the Coriolis acceleration that appears on the structure causes the vibrating pattern to rotate around its symmetry axis, with a velocity proportional to the external angular rate. Non-ideal vibrating sensors suffer from a well-known effect called lock-in. For external angular velocities smaller than the lock-in rate, the standing wave does not rotate and the sensor fails to operate. For instance, Coriolis Vibrating Gyroscopes (CVGs), working in the Whole Angle Mode (WAM), have a lock-in threshold proportional to the difference between the inverse of the maximum and the inverse of the minimum values of the damping time constant. Recently, a Slow Variables (SV) method has been used to demonstrate this effect as well as to calculate the lock-in angle. In this work, using a Fast Variables (FV) method, we derive the lock-in condition without making any assumptions and/or approximations. We solve the dynamics exactly and we find equivalent conditions for the system's eigenvalues to those known for the Damped Harmonic Oscillator (DHO), i.e., angular rate decreasing to zero – over-damped dynamic, lock-in – critically damped dynamic, and free rotation – under-damped dynamic. Therefore, we can explain the lock-in effect without resorting to a nonlinear theory (SV method) but by the form of the roots of an eigenvalue problem of a linear system (FV method).
... The manufacturing technology of a hemispherical shell resonator (HSR) is the most difficult and key technology to machine a high-precision and high-reliability HRG. For ensuring stable vibration characteristics and good performances of the HSR, there are two requirements for its machining [3,4]: (1) The resonator needs to be machined as axis-symmetrical as possible, which makes it exhibit nearly perfect dynamic characteristics in terms of mass isotropy (thickness uniformity and density isotropy), stiffness isotropy, damping isotropy, vibration deformation, balance, and so on. ...
A hemispherical resonator gyroscope (HRG) is very useful for inertial sensors in the 21st century. This paper proposes a novel dynamic model of an imperfect hemispherical shell resonator (DM-IHSR) with thickness nonuniformity and an output error model of the HRG (OEM-HRG) associated with frequency split. First, the DM-IHSR is established based on the thin shell theory of elasticity, and the thickness nonuniformity is described. The differen- tial equations of vibratory motion of the IHSR are derived by leveraging Bubnov-Galerkin method, which reveals that frequency split is mainly dominated by the fourth harmonic of thickness nonuniformity. Then, by considering the characteristics of standing waves, the OEM-HRG is proposed, which discovers the effects of frequency split and the initial ori- entation angle on the HRG output error. Finally, the effect of thickness nonuniformity on the HRG output error is clarified. The quantitative relationship among the HRG output er- ror, the fourth harmonic of thickness nonuniformity, and the initial orientation angle is determined, which gives machining accuracy ranges of these variables. The above dynamic models and machining accuracy ranges are of great significance for producing and process- ing high-precision HSRs and HRGs.
In order to compensate for the hemispherical resonator gyroscope (HRG) dynamic output drift errors, a novel compensation method is presented. Through deriving the resonator motion equations and analyzing the mechanism of HRG dynamic output drift errors, it is found that the resonator defect nonuniformity is the main cause of the HRG dynamic output errors. By analyzing the mechanisms of these errors, the influence of these error sources is interacted and coupled, and it is difficult to analyze the HRG output error mechanism and establish an error model comprehensively. We proposed a compensation prediction model for the HRG dynamic output to suppress the influence of these errors comprehensively. To establish the high-precision HRG dynamic output compensation model, we proposed an improved variational mode decomposition (VMD) method to achieve an accurate HRG output. First, we used VMD to decompose the HRG output, and the optimal VMD decomposition parameters are achieved by a genetic algorithm. In order to better achieve the effective information, the decomposed components of HRG drift are classified using the sample entropy. Then, the mixed components are further processed using time–frequency peak filtering. Finally, the accurate HRG output is achieved by reconstructing all the effective components. The accurate HRG output is used to construct the training set, and the high-precision HRG dynamic output prediction model is established by long short-term memory (LSTM). The software compensation of the HRG dynamic output drift is realized by the prediction model. The experiment shows that the HRG dynamic output drift is mainly produced by the resonator nonuniformity, and it is strongly correlated with the standing wave azimuth, which verifies the correctness of the mechanism analysis. The HRG dynamic drift peak-to-peak value decreases to $5.715\times 10^{-3 \circ }$ /s, which verifies the effectiveness of the compensation method.
Hemispherical resonant gyroscopes (HRGs) are solid-state vibration gyroscopes with the highest precision and are widely used in the aerospace field. The core part of the gyroscope is the resonator, which is a thin-walled hemispherical shell. Surface error and thickness variation of a hemispherical shell causes frequency splitting, which degrades the performance of the HRG. In order to guide the mass leveling of hemispherical resonator, this paper presents a new method for scanning measurement of the surface error and thickness variation of hemispherical resonators. First, a multi-axis platform is designed for noncontact sensor scanning measurements along the meridian and latitudinal lines of the hemispherical resonator. Second, the error model of the measurement system is established. The surface error of the standard sphere is measured to calibrate and compensate for the assembly errors of the measuring device. In addition, the identification accuracy of assembly errors and the influence of assembly errors on thickness measurement are simulated by a computer. Finally, the surface error and thickness variation of the hemispherical resonators are measured. The method is experimentally demonstrated and validated with a wavefront interferometry test. The results show that the method can achieve high precision and high repeatability, which is instructive for assessment of the machining error and further evaluation of the hemispherical resonator.
Coriolis vibrating gyroscopes using axisymmetrical or near-axisymmetrical resonators, such as Sagem Quapason™, hemispherical resonator gyros, cylindrical vibrating gyros, and axisymmetrical MEMS gyros, may work in whole-angle (WA) or in force-to-rebalance (FTR) (angle-rate) mode. Although a specific industrial process is implemented, including defect identification and correction, ageing effects cannot be compensated and affect drift and scale factor stability. This paper shows how the equations governing the relations between defects, commands, and errors can be used to define a new control mode, which combines FTR and WA modes in order to greatly improve performance. The implementation of those principles to the Quapason™ gyro leads to the GVNG gyro (French acronym for Gyro Vibrant Nouvelle Génération — New Generation Vibrating Gyro), a new digitally controlled coriolis vibrating gyroscope. Its experimental results are presented in this paper. The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) for the Clean Sky Joint Technology Initiative under grant agreement no. CSJU-GAM-SFWA-2008-001.
A range of new perturbation theory problems is considered. A connection is established between different types of oscillation shape in configuration space and manifolds defined in phase space. A construction of bases on these manifolds is given, so that each basis unit vector defines one of the evolution forms of an oscillation shape under the influence of the perturbation. Algebraic properties of the local evolution basis are established. A classification of the perturbations is introduced according to the nature of the evolution induced on the oscillation shape. The control and stability problems for the oscillation shapes are solved.Similar problems include, in particular, the problem of controlling waves in uniaxial and triaxial gyroscopes, based on the inertia effect for elastic waves [1,2].
Low Cost High Dynamic Vibrating Rate Gyro
  • A Jeanroy
A.Jeanroy, "Low Cost High Dynamic Vibrating Rate Gyro", in Proceedings of the Symposium Gyro Technology, Stuttgart Germany 1994
Capteur angulaire inertiel de type MEMS équilibré et procédé d'équilibrage d'un tel capteur
  • A Jeanroy
A.Jeanroy, Capteur angulaire inertiel de type MEMS équilibré et procédé d'équilibrage d'un tel capteur, Brevet FR2983574, 06/12/2011
QUAPASON TM , a new low-cost vibrating gyroscope
  • P Leger
P.Leger, "QUAPASON TM, a new low-cost vibrating gyroscope", in Proceedings of 3 rd Saint Petersburg International Conference on Integrated Navigation Systems, 1996
HRG flat electrodes, Patent US 6474161
  • A Jeanroy
  • P Leger
A.Jeanroy, P.Leger, HRG flat electrodes, Patent US 6474161