Content uploaded by Fabrice Delhaye
Author content
All content in this area was uploaded by Fabrice Delhaye on May 11, 2018
Content may be subject to copyright.
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
FRANCE
Inertial Sensors and Systems 2014
Karlsruhe, Germany
Abstract
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
actuators.
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
process.
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.
(2)
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
(3)
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.
è HRG
§ 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.
References
[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
