IMU for Radar Antenna Drive Control

Dr. Ahmed Bassyouni IEEE Meeting-Syracuse

IMU & GPS Sensors Integrated to

Antenna Drive Control Loop

Dr. Ahmed Bassyouni

Consultant Engineer

Systems and Sensors

[email protected]

1


Azimuth and Elevation Errors of Radar Antenna

Antenna’s Radar may suffer from poor accuracy in Azimuth and

Elevation angular motion due to External and Internal sources of

errors.

• External Error Sources

• Surface Deflections due to thermal effects and force of wind

• Disturbance of motion due to Gust and Wind

• Additional weights due to accumulated snow and dust

• Internal Error Sources

• Changes in the control loop parameters due to aging or misuse.

• Poor reliability due to undetected errors of HW and SW designs

or installation

2

Dr. Ahmed Bassyouni IEEE Meeting-Syracuse 3

These Sources are:

1. Forces OF WIND AND GHUST applied to the antenna

2. Fluctuating and systematic errors in the drive control

3. Environmental effects that may cause vibrations

4. Geometrical structure of the antenna, spacing of radiators,

5. Channels mismatch due to the errors of phase shifters output



We can model the beam Pointing Error as

δӨ = δӨΦ + δӨT + δӨa + δӨw

Where

δӨΦ pointing error due to phase shifters

δӨT Pointing error due to temperature effect

δӨa pointing error due to antenna structure

δӨw Pointing error due to forces of wind

Trades analysis and control techniques are developed

for these models

Today we focus only to model the wind effect



The force on the antenna due to wind with velocity V is given by

Where is the static air density, CD is Drag Coefficient and A is the projected

antenna area.

This equation is valid for both steady and time-varying wind gusts. The wind

velocity V is composed of a mean velocity Vm and a gust component Vg.

2

2

1AVCF DD

Modeling of Wind Applied to Antenna Surface

gm VVV


The projected area A is related to the array face area A0 by the azimuth

angle of the array relative to wind and the antenna tilt back angle by

)Tiltcos()AZcos(AA 0


The antenna deflection due to wind is proportional to force F, such that

we may write

2V)AZcos(K

The constant K depends on the antenna design and mechanical structure;

it is the transfer coefficient that relates the wind velocity to the deflection at

particular antenna azimuth angle .


For a rotating antenna with constant rotation rate Ω, we then have

2)t(VV)tcos(K)t( gm


where t is time and is shown explicitly to emphasize the time varying

nature of the deflection due to wind variability and antenna rotation.


A proposed antenna controller consists of the estimator, the PI

controller, and the flexible mode controller.

The antenna state –space model(A,B,C) includes the disturbances v

and the measurement noise w

x Ax Bu v

y Cx w

The disturbances (predominantly wind gusts) have covariance V. The

measurement noise has covariance W. It is assumed additionally that the

input and output noises are not correlated. This assumption is equivalent

to independence of their sources. Indeed, the measurement noise is

independent of the wind disturbances.

Controller Model for Disturbed Antenna


The purpose of the estimator is to evaluate the antenna dynamic

states using the rate input, u, and the encoder output, y, of the

antenna. The estimated state vector is denoted , and the error

between the actual encoder output and the estimated output is

defined as

ˆ ˆy Cx y y

The estimated state is obtained from the following equation:

ˆ ˆex Ax Bu K



Antenna

Flexible mode Controller

Estimator

PI Controller

+

+

+

y

v w

r

_

+

eupI

u

++

ufu

++

x̂

Controller Modules



Electronic sensors to determine forces acting on a body

* Accelerometers * Gyros (Angular Rate Sensors

Limitations that System Engineer has to overcome:

Inherent errors in position and velocity due to integration of sensor

error and sensor drift and Kalman Filter Latency

Uncertain dynamics may cause sudden errors that

decrease the Azimuth and Elevation accuracy

The System Engineer has to resolve the problem

applying advanced technology and creative ideas

11

Improve the Azimuth and Elevation Accuracy


GPS position and velocity are blended with the inertial data. Otherwise, if the GPS data is not available, the system will operate without any GPS aiding.

The inertial navigator computes position, velocity and orientation of the IMU.

The Kalman filter estimates the errors in the inertial navigator along with IMU, distance


The IMU consists of three accelerometers and three gyroscopes (gyros) so that accelerations along specific axis and angular rotations can be measured. From the IMU angular rotations and acceleration along its axis are used to calculate roll, pitch and yaw angles.

The IMU feeds its data into KF

IMU

Angular RateAccelerationTime

GPS

PositionVelocityTime

PositionVelocityAccelerationAngular RateTime

Kalman Filter

High short term

P, V accuracy

High Long term

P,V accuracy

High long term and

short term accuracy

Advantage of Integrating IMU and GPS




Standard Kalman Filter Loop


1k k k kx x v

k k k kz H x w

KF is built to estimate the

random process 1kx

Strap downINS

ProcessorIMU

Error ControllerAlgorithm

Kalman Filter Algorithm

GPS AzMeasure

GPSRx2

GPSRx1

Output

Position

Filter Correction Estimated Error

GPS Observables

Integrated IMU and GPS for Accurate Positioning




Difference between the position form the IMU and GPS is processed

In KF (typically @ 10Hz) to estimate the slowly growing position error

In the IMU.

Since this error is a function of Azimuth error (as modeled in the

differential equations in KF) , observing the inertial position errors

means the orientation errors and IMU sensor errors can also be

estimated.


System Accuracy Process

sin .cos sin .sin

cos cosN E D AzimuthAz

, ,N E D Orientation errors w r to North, East, and Down axis

Azimuth Offset angle between IMU and GPS

AntennaSystem

AzimuthDrive

IMU&GPSIntegrated Algorithms

PositionController

External/Internal

Disturbance

Desired

Azimuth

Actual

Azimuth

IMU& GPS integrated to Antenna Position Control Loop




IMU Accuracy

Inertial error sources can be divided into stationary errors like the

random constant part of the gyro drift, and on-stationary errors like

the accelerometer scale factor.

Kalman Filter

The estimation accuracy depends on the a priori information of the

system and measurement models, as well as the noise statistics.

A well-designed Kalman filter will attenuate the initial state errors, and

smooth the effects of system and measurement errors through the

averaging process.

Factors Influence the Measurements Accuracy

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The ACU has the following operational modes:

• Shutdown (no power to motors, brakes set)

• Standby (motor power on, brakes set)

• Velocity (rate loop driving of axes from local handset)

• Encoder (drive so encoders equal commanded position)

• Autonomous (drive so bore-sight equals commanded position)

• Preset (same as Autonomous with limited velocity and acceleration)

• Stow (drive to stow position).

To Achieve Reliable and Repeatable positioning data



Questions ?

Thank You

Documents

IMU for Radar Antenna Drive Control