2. Gyroscope sensors: Basic Specifications
• Gyroscope sensor has the following basic specifications:
– Measurement range
– Number of sensing axes
– Nonlinearity
– Working temperature range
– Shock survivability
– Bandwidth
– Angular Random Walk (ARW)
– Bias
– Bias Drift
– Bias Instability
3. Gyroscope sensors: Basic Specifications
• Measurement range
– This parameter specifies the maximum angular speed with which the sensor can
measure, and is typically in degrees per second (˚/sec).
• Number of sensing axes
– Gyroscopes are available that measure angular rotation in one, two, or three axes.
– Multi-axis sensing gyros have multiple single-axis gyros oriented orthogonal to one
another.
– Vibrating structure gyroscopes are usually single-axis (yaw) gyros or dual-axis gyros.
– Rotary and optical gyroscope systems typically measure rotation in three axes.
5. Gyroscope sensors: Basic Specifications
• Nonlinearity
– Gyroscopes output a voltage proportional to the sensed angular rate.
– Nonlinearity is a measure of how close to linear the outputted voltage is proportional to
the actual angular rate.
– Not considering the nonlinearity of a gyro can result in some error in measurement.
– Nonlinearity is measured as a percentage error from a linear fit over the full-scale range,
or an error in parts per million (ppm).
6. Gyroscope Performance Specifications
• The specifications and test procedures for rate gyroscopes are outlined in the IEEE
Standard Specification Format Guide and Test Procedure for Coriolis Vibratory Gy- ros [2].
The following is a summary of important specifications and definitions from IEEE Standard
for Inertial Sensor Terminology [3].
• Scale factor:
– The ratio of a change in output to a change in the input intended to be measured, typ- ically specified
in mV/◦/sec, and evaluated as the slope of the least squares straight line fit to input-output data. Scale
factor error specifications include:
• Linearity error: The deviation of the output from a least-squares linear fit of the input-
output data. It is generally expressed as a percentage of full scale, or percent of output.
• Nonlinearity: The systematic deviation from the straight line that defines the nominal
input-output relationship.
• Scale factor temperature and acceleration sensitivity: The change in scale factor
resulting from a change in steady state operating temperature and a constant accel- eration.
• Asymmetry error: The difference between the scale factor measured with positive input
and that measured with negative input, specified as a fraction of the scale factor measured
over the input range.
• Scale factor stability: The variation in scale factor over a specified time of continuous
operation. Ambient temperature, power supply and additional factors pertinent to the
particular application should be specified.
7. • Bias (zero rate output):
• The average over a specified time of gyro output measured at specified operating
conditions that has no correlation with input rotation. Bias is typically expressed in◦/sec
or ◦/hr.
• The zero-rate output drift rate specifications include:
• Random drift rate: The random time-varying component of drift rate. Random drift
rate is usually defined in terms of the Allan variance components:
• a) Angle Random Walk: The angular error buildup with time that is due to white
noise in angular rate, typically expressed in ◦/ hr or ◦/s/ hr.
8. MEMS Gyroscope Sensor
• …..
Sense
Circuit
Electrostatic
Drive Circuit
Proof
Mass
Digital
Output
Rotation
induces
Coriolis
acceleration
12. • A generic MEMS implementation of a linear vibratory rate gyroscope. A proof-
mass is suspended above a substrate using a suspension system comprised of
flexible beams, anchored to the substrate. One set of electrodes is needed to excite
the drive-mode oscillator, and another set of electrodes detects the sense-mode
response.
13. • The overall dynamical system becomes simply a two degrees-of-freedom (2-DOF)
mass- spring-damper system.
• For a generic z-Axis gyroscope, the proof mass is required to be free to oscil- late
in two orthogonal directions:
– the drive direction (x-Axis) to form the vibratory oscillator,
– and the sense direction (y-Axis) to form the Coriolis accelerometer.
15. Typical MEMS vibratory gyroscope
• MEMS Vibratory Gyroscope is designed to measure the angular velocity of the
body about the z axis of the ground reference frame.
• The main principle of MEMS gyros is: The transfer of energy between two modes
of vibration , the drive and the sense modes, through the Coriolis acceleration
16. model of vibrating gimbaled gyroscope
• A simplified two-dimensional model of a vibrating gimbaled gyroscope is shown
• The suspensions provide appropriate elastic stiffness and constraints such that
the central proof mass relative to the frame may only move in the x direction
(sense mode)
• On the other hand the frame relative to the chip may only move in the y direction
(drive mode).
17. Structure of a MEMS Gyroscope
Gyroscope structure free to move, except at anchors
• Comb Drive Transducers used to drive proof masses
• Sense electrodes used to detect rotation
Sense
electrodes
Proof mass
Proof mass
18. Drive Mode
• Structure made to vibrate at natural frequency
• Vibration of proof mass provides necessary velocity for Coriolis
Acceleration
Drive Mode Vibration
19. Sense Mode
• When rotation is applied, Coriolis force causes proof mass direction to
change.
• Coriolis Acceleration
Vac ×Ω= 2
Sense Mode Vibration
In the y-direction
20. Vibrating Gyroscope Topologies:
• Single Spring Mass with Translational Drive
– Subscript d is drive mode
– Subscript s is sense mode
21. Vibrating Gyroscope Topologies:
• Dual Mass Spring (tuning Fork) with translational drive
– Subscript d is drive mode
– Subscript s is sense mode
27. Coriolis Effect
• Consider an object travelling from the center point (point O) towards P on the
edge of a rotating disc.
• It takes time ∆t when travelling at speed v, so the distance OP equals v. ∆t
• However, after a time ∆t, P will have moved from its original position (P') to a new
position (P).
• The angle POP’ equals t times the speed of rotation of the disc in radians per
second.
• If the distance “d” is short, then
• d -> v ∆t2 Ω (with tan approximation)
• That sideways distance d is traveled in
• time t
• resulting from a sideways acceleration “a”
28. Coriolis effect
• In the inertial frame of reference (upper part of the picture), the black ball moves
in a straight line.
• However, the observer (red dot) who is standing in the rotating/non-inertial frame
of reference (lower part of the picture) sees the object as following a curved path
due to the Coriolis and centrifugal forces present in this frame.
29.
30. Coriolis effect
• Coriolis effect : is an inertial force described by the 19th-century French engineer-
mathematician Gustave-Gaspard Coriolis in 1835. Coriolis showed that, if the
ordinary Newtonian laws of motion of bodies are to be used in a rotating frame of
reference, an inertial force--acting to the right of the direction of body motion for
counterclockwise rotation of the reference frame or to the left for clockwise
rotation--must be included in the equations of motion.
• The effect of the Coriolis force is an apparent deflection of the path of an object
that moves within a rotating coordinate system. The object does not actually
deviate from its path, but it appears to do so because of the motion of the
coordinate system
31. The Coriolis effect
• The Coriolis effect is most apparent in the path of an object moving longitudinally.
• On the Earth an object that moves along a north-south path, or longitudinal line,
will undergo apparent deflection to the right in the Northern Hemisphere and to
the left in the Southern Hemisphere.
• There are two reasons for this phenomenon: first, the Earth rotates eastward; and
second, the tangential velocity of a point on the Earth is a function of latitude (the
velocity is essentially zero at the poles and it attains a maximum value at the
Equator).
• Thus, if a cannon were fired northward from a point on the Equator, the projectile
would land to the east of its due north path. This variation would occur because
the projectile was moving eastward faster at the Equator than was its target
farther north. Similarly, if the weapon were fired toward the Equator from the
North Pole, the projectile would again land to the right of its true path. In this
case, the target area would have moved eastward before the shell reached it
because of its greater eastward velocity. An exactly similar displacement occurs if
the projectile is fired in any direction
32. Rotating Reference Frame
• A rotating frame of reference is a special case of a non-inertial reference frame
that is rotating relative to an inertial reference frame
