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Calibration and Applications of a rotational sensor Calibration and Applications of a rotational sensor

Calibration and Applications of a rotational sensor - PowerPoint Presentation

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Calibration and Applications of a rotational sensor - PPT Presentation

ChinJen Lin George Liu Institute of Earth Sciences Academia Sinica Taiwan Outlines Calibration of the following rotational sensors R1 R2 Two applications to find true north Attitude ID: 180878

north rotation calibration frequency rotation north frequency calibration sensor attitude deviation response frame angle rate allan azimuth earth resolution

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Slide1

Calibration and Applications of a rotational sensor

Chin-Jen Lin, George Liu

Institute of Earth Sciences, Academia

Sinica

, TaiwanSlide2

Outlines

Calibration

of the following rotational sensors

R-1 R-2Two applications to find true northAttitude Estimator (inertial navigation)North Finder

2Slide3

Various technologies

of a rotational sensor

MEMS

(Micro Electro-Mechanical System)FOG (Fiber Optic

G

yroscope)

RLG (Ring Laser Gyroscope)MET (Molecular Electronic Transducers)R-1R-2

Commercial

and aerospace

use

Observatory stage only to date

DC-response

Band-pass response

3Slide4

Specification and Calibration

Self-Noise Level

High

frequency Low frequency

Frequency Response

Sensitivity

LinearityCross-effectLinear-rotation

Rotation-rotation

Nigbor

, R. L., J. R. Evans and C. R. Hutt (2009). Laboratory and Field Testing of Commercial Rotational Seismometers, Bull. Seis. Soc. Am., 99, no. 2B, 1215–1227.

--- PSD (power spectrum density)

--- Allan Deviation

R-2

R-1

The R-2 is the second generation of

R-1.The R-2 improvements:

increased

clip level

lower

pass-band

differential output

Linearity

MHD calibration electronics

4Slide5

Self-noise (PSD)

A good way to test sensor noise at

high frequency

Noise comparison at

high frequency band

:

MET

> FOG >

MEMS

R-2 does not improve resolution over the R-1.

R-1 and R-2

are corrected

for instrument response.

5

MEMS

FOG

MET

R-2

R-1Slide6

Aerotech

TM

Rotation Shaker

reference sensor

FOG (VG-103LN)

(DC~2000 Hz)

Frequency Response

R-1

(20s~30 Hz)

6

Swept sine!Slide7

Frequency Response

5 R-1s

and 2 R-2s were tested

R-2

R-1

Phase response

of

the R-1

TM

is not normalized

; these particular R-2s

TM are improved.

7Slide8

Shaker

VS

Coil-calibration (R-2)

Blue

: via shake table

Green

: via coil-calibration

At low frequency

, both results are almost identicalAt high frequency, the results from the shake table are systematically higher

8

R-2 #A201701

R-2 #A201702Slide9

Linearity

R-2

R-1

6 % error, input below 8

mrad

/s

9

2

%

error, input below 8

mrad/s

Linearity of R-2 is improved!

9

Frequency responses under various input

amplitude (

0.8 ~ 8

mrad

/s) Slide10

R-1: Aging problem (1 of 2)

Apr-12

Jan-13

difference (%)

#A201504

46.1

45

-2.4%

47.2

48

1.7%

46

43.8-4.8%

#A20150552.9

51.3-3.0%

43.643.2

-0.9%

55.8

51.7

-7.3%

#A201506

59.2

57.4

-3.0%

60.2

57.1

-5.1%

55.4

54.1

-2.3%

Sensitivity decreases…

3 R-1 samples

10Slide11

R-1: Aging problem (2 of 2

)

After a half-year deployment:

amplitude differs about +/- 0.5 dB

phase differs about +/- 2.5

11Slide12

Conclusions (Calibration)

Both R-1 and R-2 can provide useful data, however:

R-1

Frequency response is not flatSensitivity is not normalizedHas aging problem (needs regular calibration)Linearity is about 6% (under 8 mrad/s input)R-2

Instrument noise is somewhat higher than the R-1

Sensitivity and frequency response are not normalized

The pass-band is flatter than R-1Linearity is improved (2%, under 8 mard/s input)Self calibration works well at low frequency but not high12Slide13

Applications for Finding True north

Attitude Estimator

Trace orientation in three-dimension (inertial navigation)

North Finder

Find

true

north13Slide14

Attitude

Estimator

(track the sensor’s orientation)

Euler angle-rates

Rotational measurements

(sensor frame)

14

Euler angles

composed of:

Roll

Pitch

Yaw

Reference frame

Sensor frame

displacement

for

translation

Lin, C.-J., H.-P. Huang, C.-C. Liu and H.-C. Chiu (2010). "Application of Rotational Sensors to Correcting Rotation-Induced Effects on Accelerometers."

Attitude equation

14

Euler angles

for

rotation

6 degree-of-freedom motionSlide15

Compare with AHRS …

15

(

 Attitude Heading Reference System)

Xens

MTI-G-700-2A5G4

SN: 07700075

Attitude Estimator

FOG3-axis VG-103LN

Dynamic Roll and pitch are within 0.5

∘Dynamic Yaw is within 2∘Slide16

The attitude estimator can …

t

rack orientation of sensor frame

guide sensor frame from one orientation to another oneEx., plot perpendicular line or parallel line on the groundSlide17

North Finder

~(

find azimuth angle)North-finding is important, especially for:

tunnel engineering

inertial navigation

Missile navigationSubmarine navigationseismometer deploymentmobile

robot navigationNorth can

be found by several techniques:

Magnetic compassSun compass

AstronomicalGPS compassG

yro compass

17Slide18

Magnetic compass

Advantage

: very easy to useDisadvantage

:

Subject to large

error sources from local ferrous material, even a hat rim or belt buckleNeed to

correct for magnetic declination

18Slide19

Tiltmeter

Determine

tilt angle

from

a projection of the gravity

g

0.5g

30

o

g

tilt

= g*sin

θ

19

North

Finder

Determine

azimuth angle

from

projection of Earth’s rotation vector

Principle?Slide20

Earth rotation axis

equator

gyro

Principle

Earth’s

rotation-rate

projection

of

Earth’s

rotation-rate

Gyro frame

20

latitude

azimuth angle

ω

e

: earth

rotation rate

ω

e

1

: local projection of earth

rotation rate

φ

:

latitude

θ

: azimuth angle

ω

x

:earth rotation rate about X-axis of gyro

ω

y

:earth rotation rate about X-axis of gyroSlide21

Resolution …

Resolution is related to the

accuracy

of the mean value

How much

time

it takes to determine the mean value with most accuracy

??

Allan Deviation Analysis

is the

proper way to evaluate accuracy

21Slide22

Allan Deviation Analysis (1 of 2)

22

A quantitative way to measure

the accuracy of the

mean value

resolution

for any given

averaging time

AVAR: Allan variance

AD: Allan deviation

τ

: average time

y

i

: average value of the measurement in bin i

n: the total number of bins

resolution

average timeSlide23

Bias stability

copied

from Crossbow

Technology

~VG700CA

TM

,

made

by

Crossbow

TM

Allan

Deviation Analysis (2 of 2

)Slide24

Experiments

SDG-1000

made by

Systron

Donner (USA)

MEMS

bias stability: <3.7E-4

deg

/s

angle random walk: <1.7E-3

deg

/s

TRS-500

made by

Optolink

(Russia)

Fiber

Optic

G

yro

bias stability: <1.4E-4

deg

/s

angle random walk: <1.7E-4

deg

/s

24Slide25

SDG-1000

TRS-500

Resolution 0.14

°

Projection of

the Earth’s rotation rate

3.7E-3 °/s

(latitude

25°)

25

1000 s

Resolution

2

°

20 s

Allan Deviation AnalysisSlide26

Other challenges…

rotation

Two fixed points

DC offset

sensitivity

26Slide27

Mechanical

misalignment

Sensor frame

Platform frame

Find true north…

~ from sun compass

These two orientation lines were made from sun compass

50 cm

Maximum error

0.1 cm

50 cm

40.1

40.2

Theodolite

&

GPS

Need a reference of true north

27

error =

0.11

°Slide28

Work on seismic station

Station

data

Existing

azimuth*

Deviation**

TWKB

2011/10/3

359.0

-1MASB

2011/10/3359.8

-0.2

SBCB2011/5/11

358.8-1.2

WUSB2011/6/22

New station0

VWDT

2011/6/23

New station

0

NACB

2011/7/14

0.3

0.3

YULB

2011/7/18

357.7

-2.3

TPUB

2011/7/20

359.0

-1

CHGB

2011/7/22

359.8

-0.2

YHNB

2011/9/07

359.4

-0.6

ANPB

2011/9/20

1.9

1.9

NNSB

2011/9/27

2.3

2.3

TDCB

2011/9/27

1

1

VDOS

2011/12/7

358

-2

Danda

station (central Taiwan)

*previous north direction is found by

sun compass

(BATS,

B

roadband

A

rray in

T

aiwan for

S

eismology)

28

**standard deviation is

1.3

°Slide29

conclusions

North finder

and

attitude

estimator

can be and are implemented by

DC-type gyro.

An efficient way to find the true north is:First, use a north finder

to find arbitrary azimuth angleSecond, rotate that azimuth angle with an attitude estimator

29Slide30

Thank you!

Your comments and questions are greatly appreciated!

30