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· Satellite Attitude Control System Design Using Reaction Wheels

Bhanu Gouda Brian Fast Dan Simon

Aerospace Power & Electronics Simulation Workshop 2004

Outline

1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. Conclusion

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ADCS

·ADCS: Attitude Determination and Control subsystem ·Attitude Determination Using sensors ·Attitude Control - Using actuators

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Disturbance torques

· Aerodynamic · Gravity gradient · Magnetic · Solar radiation · Micrometeorites

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Attitude control modes

·Orbit insertion ·Acquisition ·Slew ·Contingency or Safe

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Spacecraft control type

· Passive control

- Gravity gradient control

- Spin control

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Spacecraft control type

· Active control (Actuators) - Reaction wheels

- Momentum wheels - Control - moment gyros - Magnetic torquers - Gas Jets or Thrusters

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Tetrahedron configuration of Reaction wheels

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Outline

1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. Conclusion

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Problem formulation

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Mathematical model

Angular momentum of each disk M = Mass of the space craft mi = mass of the reaction wheel wi= angular velocity of the wheel

1 H1 = I1w1 = mr 2 + md 2 [- w1 ] 2

1 H 2 = I 2 w2 = mr 2 + md 2 [w2 ] 2

Moment with respect to the space craft

= Angular position of space craft

r = radius of the wheel I= moment of inertia

I = Mr + 2Md

2 2

··

(

)

··

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Mathematical model

Conservation of angular momentum

·· d [H 1 + H 2 ] = I dt

·· d 1 2 1 2 2 2 2 2 2 mr + md (- w1 ) + 2 mr + md (w2 ) = Mr + 2 Md dt

(

)

d M ·· (- w1 + w2 ) = 2. . dt m

· (- w1 + w2 ) = M + c

2

m

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Outline

1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. Conclusion

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Control Scheme

Two types of controllers are investigated - Modified PI Controller - Active Disturbance Rejection Controller

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Simplorer

· Simplorer

· · · ·

Circuit element models Electric machine models Data analysis tools Interfaces with Matlab / Simulink

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Outline

1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. Conclusion

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Modified PI Controller

· This controller is used as the baseline controller · Only one tuning parameter · Generalized 2 DOF control structure is proposed

Reference: A Robust Two-Degree-of-Freedom Control Design Technique and its Practical Application -Robert Miklosovic, Zhiqiang Gao

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des

kis-1

Plant transfer function

act

ki c ( des - act ). - k p . act = ( des - act ). - 2.c . act S S

2

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kp

Motion profiling

·The desired trajectories as the command input in the closed loop control ·In this case, a profile generator is used to produce desired angle to the system ·Motion profile is used instead of step.

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Simulation Results

Plant Model

w1

act

theta_de

w1

w2

theta theta_dot

GAIN

Motion_profi

tY GAIN GAIN

error in theta control signal

Theta Actual

w2

GAIN

theta_dot_de

t_des_de

deg_rad

Motion profile

Modified PI Controller

SUM5

RANDOM

Disturbanc

CONST

Random_Nois

Random Noise

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Plant Model

GAIN3

10

GAIN

w1

10

theta_do

GAIN

10

w2

GAIN4 SUM4

I

10

Modified PI Controller

10 10

I GAIN

theta

error_in_the

INTG

GAIN

disturbance

GAIN

10

10

GAIN2

theta_actu

(- w1 + w 2 ) = · + c

2

2

( des

k - act ). i - k p . act = ( des - act ). c - 2. c . act S S

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Simulation Results

Theta Actual & desired

0.1k 80 60 40 20 -10 0 2 4 6 8 10 t [s] t_des_ theta_d

0.1k 80 60 40 20 -10 0 2 4 6 8 10 t [s] t_des_ theta_d

Noise amplitude: 0.07 - 0.1

Noise interval: 2 sec

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Simulation Results

control inputs w1 and w2

7

8 7 6 5 4 3 2 1 0 2 4 6 8 10 t [s] w1.VAL w2.VAL

w1.VAL w2.VAL

5 4 3 2 0 0 2 4 6 8 10 t [s]

Noise amplitude: 0.07 - 0.1

Noise interval: 2 sec

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Outline

1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. Conclusion

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Active Disturbance Rejection Controller

·New digital controller to motion control problems · Disturbances are estimated using extended state observer (ESO) and compensated in each sampling period. ·Dynamic compensation reduces motion system to a double integrator which can be controlled using a nonlinear PID controller

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Extended State Observer

· It is a unique nonlinear observer · Proper Selection of the gains and functions are critical to the success of the observer · Once ESO is properly setup, the performance of the observer is quite insensitive to plant variations and disturbances

· - 2 z o ·1 = 2 z 2 - o 1 z1 bo z + 0 0 2 2o u o2 y

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Simulation Results

Plant Model

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Simplorer and Matlab

Define Simplorer inputs and outputs in the property dialog of the SiM2SiM component

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Matlab/Simulink Model

Inputs to the simplorer

Outputs from the Simplorer

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Simulation Results

Theta Actual and Theta desired

0.1k 80 60 40 20

-10 0.1k 80 60 40 20

t_des_d GAIN1. theta_d

t_des_ theta_

-10 0 0.2 0.4 0.6 0.8 1.1 t [s]

00.2

0.6

1 1.2 1.7 t [s]

Noise amplitude: 0.05 Noise Interval: 0.5 sec

30

Aerospace Power & Electronics Simulation Workshop 2004

Simulation Results

w1 and w2

12 8 6 4 2 -2 0 0.2 0.4 0.6 0.8 1.1 t [s] w1.VA w2.VA

15 5 0 -5 -10 -20 0

w1.VA w2.VA

0.4 0.8 1 1.2 1.7 t [s]

Noise amplitude: 0.05 Noise Interval: 0.5 sec

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Conclusion and Future work

·

· · ·

The simulation of Modified PI and ADRC showed that ADRC worked well for the system 1 DOF problem will be extended to 3 degrees of freedom problem Implementation of the controller design in microcontroller/FPGA microchip. Comparisons with other controllers

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