aircraft control lecture 15

7/29/2019 aircraft control Lecture 15

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16.333: Lecture#15

InertialSensorsComplementaryfilteringSimpleKalmanfiltering


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Fall2004 16.333152


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Image removed due to copyright considerations.

Image removed due to copyright considerations.

Fall2004 16.333156


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Fall2004 16.333157

Fibre Coil

Lens

Spatial

Filter

LaserSource

Splitters

Sagnac0

Phase Shift

Lens

Fringe Pattern

Detector

Polariser Beam

Optical Intensity

Phase Shift

Proportional to


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Fall2004 16.333159


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Examples of Estimation Filters

from Recent Aircraft Projects at MIT

November 2004

Sanghyuk Park and Jonathan How


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Complementary Filter(CF)Often, there are cases where you havetwodifferent measurement sourcesforestimatingonevariable and the noise properties of the two measurementsare such that one source gives good information only in low frequency regionwhile the other is good only in high frequency region.

You can use a complementary filter !

accelerometer rate gyro

g

outputaccel.sin 1

- not good in long termdue to integration

- only good in long term

- not proper during fast motionLow Pass Filter

High Pass Filter

dtrate)(angular

est

Example: Tilt angle estimation using accelerometer and rate gyro

+

=1

1

s

+

= examplefor,1s

s


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Complementary Filter(CF) Examples

CF1. Roll Angle Estimation

CF2. Pitch Angle EstimationCF3. Altitude Estimation

CF4. Altitude Rate Estimation


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CF1. Roll Angle Estimation

High freq. : integrating roll rate (p) gyro output

Low freq. : using aircraft kinematics

- Assuming steady state turn dynamics,

roll angle is related with turning rate, which is close to yawrate (r)

=

sin

sin

r

mgL

mVL

r

g

V

CF setup 1s

HPF

LPFVg

RollRate

Gyro

YawRate

Gyro

+

+

Roll

angle

estimat

p

r


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CF2. Pitch Angle Estimation

High freq. : integrating pitch rate (q) gyro output

Low freq. : using the sensitivity of accelerometers to gravity direction- gravity aiding

In steady state

cos

sin

gA

gA

Z

X

=

=

=

z

x

A

A1tan

outputsteraccelerome, ZX AA

Roll angle compensation is needed

CF setup

estmeasq cos

= est

z

xss

AA costan 1

measqest

xA

zAest

s1

LPF

HPF

++ est


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CF3. Altitude Estimation

Motivation : GPS receiver gives altitude output, but it has ~0.4 seconds of delay.In order of overcome this, pressure sensor was added.

Low freq. : from GPS receiver

High freq. : from pressure sensor

CF setup & flight data

KFGPSfromh LPF

HPF

++ esth

SensorPressurefromh


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CF4. Altitude Rate Estimation

Motivation : GPS receiver gives altitude rate, but it has ~0.4 seconds of delay.In order of overcome this, inertial sensor outputs were added.

Low freq. : from GPS receiver

High freq. : integrating acceleration estimate in altitude directionfrom inertial sensors

CF setup

KFGPSfromh

za

ya

xa

Angular Transform

estest , s1

LPF

HPF

++

ha

esth

outputsteraccelerome, zx AA

[ ][ ]

=

gA

A

A

a

a

a

estest

z

y

x

z

y

x

0

0

:note

[ ] [ ] matricestiontransformaangular:, estest


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Kalman Filter(KF) Examples

KF1. Manipulation of GPS Outputs

KF2. Removing Rate Gyro Bias Effect


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KF 1. Manipulation of GPS Outputs

Background & Motivation

Stand-alone GPS receiver gives position and velocity

position pseudo-ranges velocity Doppler effect

These are obtained by independent methods :

and are certainly related )( vx=

Kalman filter can be used to combine them !

Motivation :

Position ~30 m

Velocity ~0.15 m/s

Typical Accuracies

Many GPS receivers provide high quality velocity information

Use high quality velocity measurement to improve position estimate

KF 1 K l Filt S t


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KF 1. Kalman Filter Setup

2+=vvmeas

avdt

d=

1=jdt

d

Measurements Filter Dynamics

measx 1+= xxmeas

measv jadt

d=

vx

dt

d=

est

x

estv

esta

NorthEast

Down

a

v

jii ,

x : velocity

: acceleration : jerk

: position

: white noises

:esta

noisy, but not biased combined with rate gyros in removing the gyro biases (KF2)

KF 2. Removing Rate Gyro Bias Effect


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KF 2. Removing Rate Gyro Bias Effect

Background & Motivation

In aircraft control, roll anglecontrol is commonly used in inner-loop to create requiredlateral accelerationwhich is commanded from guidance outer-loop

Biased roll angle estimate can cause steady-state error in cross-track

1s

HPF

LPFVg

Roll

RateGyro

Yaw

RateGyro

+

+

Rollangle

estimat

p

r

Drawback : biased estimate

Complementary filter with roll & raw gyros (CF1)Single-Antenna GPS Based

Aircraft Attitude Determination- Richard Kornfeld, Ph.D. (1999)

Drawback : sampling rate limit (GPS),typical filter time constant ~0.5 sec.

rVgas p

KF 2 Kalman Filter Setup


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KF 2. Kalman Filter Setup

sa

V

ii ,r

: velocity

: acceleration in sideways direction

: roll rate : yaw rate

: bank angle

: white noises

2++= pmeas biaspp

2=pdt

d

3=pbiasdtd

Measurement Equations Filter Dynamics

measp

estpbias( )estsa 1+=gas

3 ++= rmeas biasV

grmeasr

4=rbias

dt

d

1 += pdt

d

estp

( )estrbias

estfrom Rate Gyros

from GPS Kalman Filter


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KF 2. Simulation Result

Simulation for 10 degree bank angle holdRoll rate gyro bias=0.03 rad/s, yaw rate gyro bias = 0.02 rad/swere used in simulation

References


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References

Applied Optimal EstimationEdited by Arthur Gelb, MIT Press, 1974

Fundamentals of Kalman Filtering A Practical Approach

Paul Zarchan& Howard Musoff, Progress in Astronautics and Aeronautics Vol. 190

Avionics and Control System Development for Mid-Air Rendezvous of Two Unmanned Aerial VehiclesSanghyuk Park, Ph.D. Thesis, MIT, Feb. 2004

Fundamentals of High Accuracy Inertial Navigation

Averil Chatfield, Progress in Astronautics and Aeronautics Vol. 174

Applied Mathematics in Integrated Navigation SystemsR. Rogers, AIAA Education Series, 2000

The Impact of GPS Velocity Based Flight Control on Flight Instrumentation Architecture

Richard Kornfeld, Ph.D. Thesis, MIT, Jun. 1999

Autonomous Aerobatic Maneuvering of Miniature HelicoptersValdislavGavrilets, Ph.D. Thesis, MIT, May 2003

aircraft control lecture 15

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