ee 495 modern navigation systems inertial sensors monday, feb 09 ee 495 modern navigation systems...

EE 495 Modern Navigation SystemsInertial Sensors

Monday, Feb 09 EE 495 Modern Navigation Systems Slide 1 of 19

http://www.erau.edu/

Inertial Sensors

Monday, Feb 09 EE 495 Modern Navigation Systems

• As the name implies inertial sensors measure motion wrt an inertial frame Advantages: Self-contained & non-reliant on external fields

(e.g., EM radiation, Earth’s magnetic field, …) Disadvantages: Typically rate measurements & expensive

• Accelerometers measure linear acceleration Actually measure specific force, typically, in the body frame

• Gyroscopes measure angular velocity Most gyroscopes measure angular speed, typically, in the

body frame

ab b bib ib ibf

bib

Slide 2 of 19


Inertial SensorsAccelerometers


Inertial Sensors

Accelerometers

Pendulous Mass Vibratory

Closedloop

Openloop

Closedloop

Openloop

Gyroscopes

Slide 3 of 19


Inertial SensorsAccelerometer: Pendulous Mass


• The Pendulous Mass Accelerometer A mass, a suspension system,

and a sensing element Displacement applied

force resolved along thesensitive axis

Modeled as a basic 2nd order system

In steady state hence

Acc

eler

atio

n du

e to

gra

vity

Rea

ctio

n fo

rce

Mass (m)

dam

per

k

sprin

g

b

disp

lace

men

t (x

)

Sense axis

f m x bx kx

Slide 4 of 19




• Closed-loop version generates a force to null the displacement Can improve linearity and measurement range

Slide 5 of 19




• Pendulous Accelerometer Closed loop configuration

o Improved linearity

Hinge

Pendulous Arm

Restoring Coil

Permanent Magnet

Case

Excitation Coil

Pick-Off

Sensitive Input Axis

Figure: Clipp (2006)

Sen

sitiv

e ax

is

Slide 6 of 19


Inertial SensorsAccelerometer: Vibratory


• Vibratory accelerometers Vibrating Beam Accelerometers (VBA) Acceleration causes a change in resonance frequency

Mass

0f k Tension

Sen

sitiv

e ax

is

Slide 7 of 19




• MEMS Accelerometers

www.ett.bme.hu/memsedu

Slide 8 of 19

http://www.ett.bme.hu/memsedu




• MEMS Accelerometers Spring and mass from silicon and add fingers make a

variable differential capacitor Change in displacement => change in capacitance

CS1 < CS2

APPLIEDACCELERATION

SENSOR ACCELERATING

MASS

SPRING

SENSOR AT REST

FIXED

ANCHOR TOSUBSTRATE

Slide 9 of 19


Inertial SensorsGyroscopes


Inertial Sensors

Gyroscopes

Rotating Mass Sagnac Effect Coriolis Effect

Floated DTG

Flui

d Su

spen

sion

Mag

netic

Sus

pens

ion

Mec

h Su

spen

sion

Resonator Interferometer

Ring

Las

er G

yro

Fibe

r Opti

c G

yro

Hem

isph

eric

al R

eson

ator

Gyr

o

magnetohydrodynamic

Cond

uctiv

e flu

id b

ased

Mic

roel

ectr

omec

hani

cal

Accelerometers

Slide 10 of 19


Inertial SensorsGyroscopes: Rotating Mass


• Rotating Mass Gyros Conservation of Angular

Momentum The spinning mass will resist

change in its angular momentum Angular momentum

o = (Inertia * Angular velocity) By placing the gyro in a pair of frictionless gimbals it is free

to maintain its inertial spin axis By placing an index on the x-gimbal axes and y-gimbal axis

two degrees of orientational motion can be measured

Slide 11 of 19


Inertial SensorsGyroscopes: Rotating Mass

• Rotating Mass Gyros Precession

o Disk is spinning about z-axiso Apply a torque about the x-axiso Results in precession about the y-axis

x

y

z

x

y

z

Precession rate ()

H

H(t+dt)

H(t)

dt


H = Angular momentum


Inertial SensorsGyroscopes: Sagnac Effect Gyros


• Fiber Optical Gyro (FOG) Basic idea is that light travels at a

constant speed If rotated (orthogonal to the plane)

one path length becomes longer and the other shorter

This is known as the Sagnac effect Measuring path length change (over a

dt) allows to be measured

R

DetectorTransm

itter

Slide 13 of 19



• Fiber Optical Gyro (FOG) Measure the time difference betw

the CW and CCW paths CW transit time = tCW

CCW transit time = tCCW

LCW = 2R+RtCW = ctCW

LCCW = 2R-RtCCW = ctCCW

tCW = 2R/(c-R ) tCCW= 2R/(c+R ) With N turns Phase

2

2

4 Rt

c

2

4N At

c

R

Splitter

Transm

itter Detector

R

SplitterTransmitter

Detector

00

82 2 /c c

NAtf tc

c





• Ring Laser Gyro A helium-neon laser produces two

light beams, one traveling in the CW direction and the other in theCCW direction

When rotatingo The wavelength in dir of rotation

increases (decrease in freq)o The wavelength in opposite dir

decreases (increase in freq)o Similarly, it can be shown that

0

4Af

Slide 15 of 19


Inertial SensorsGyroscopes: Coriolis Effect

• Vibratory Coriolis Angular Rate Sensor Virtually all MEMS gyros are based on this effect

Linea

r mot

ion

2Corolisa v

Linea

r mot

ion

2Corolisa v




• Basic Planar Vibratory Gyro




• In plane sensing (left)• Out of plane sensing (right)

www.ett.bme.hu/memsedu


http://www.ett.bme.hu/memsedu


Inertial SensorsSummary


• Accelerometers Measure specific force of the body frame wrt the inertial

frame in the body frame coordinateso Need to remove the acceleration due to

gravity to obtain the motion induced quantity In general, all points on a rigid body do NOT experience the

same linear velocity

• Gyroscopes Measure the inertial angular velocity

o Essentially, the rate of change of orientation All points on a rigid body experience the

same angular velocity

bibf

bib

Slide 19 of 19


ee 495 modern navigation systems inertial sensors monday, feb 09 ee 495 modern navigation systems...

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