ICRA ’07 Space Robotics Workshop A Form Based Control Algorithm for Reducing the Complexity of an...

ICRA ’07 Space Robotics Workshop

A Form Based Control Algorithm for

Reducing the Complexity of an Attitude Control System

at

ICRA 2007 Space Robotics Workshop

April 14, 2007

Cleveland State University / Industrial Space Systems Lab

Northrop Grumman Space Technology

Brian Fast Dr E.

[email protected]


Problem Description• System Characteristics and ObjectiveSystem Characteristics and Objective

– Investigation complexity related to a Investigation complexity related to a flywheel based power/attitude control flywheel based power/attitude control system system

• System Architecture ConsiderationsSystem Architecture Considerations– Hardware constraintsHardware constraints

• Packaging limitationsPackaging limitations• Mounting tolerancesMounting tolerances

– Software constraintsSoftware constraints• Computation complexityComputation complexity

• Performance MetricsPerformance Metrics– Complexity of the systemComplexity of the system

• Algorithm & tuningAlgorithm & tuning– Development timeDevelopment time The focus of this work is to demonstrate that The focus of this work is to demonstrate that

a well designed control algorithm can a well designed control algorithm can dramatically reduce: the hardware dramatically reduce: the hardware

constraints, the time to test and debug, and constraints, the time to test and debug, and the cost to develop a system.the cost to develop a system.


Benefits & ObjectivesBenefits & Objectives• Increased life time Increased life time

compared to batteriescompared to batteries• Improved system Improved system

characteristics characteristics – state of chargestate of charge

• Increased charge and Increased charge and discharge capabilitiesdischarge capabilities

• Dual use system Dual use system – power and attitude power and attitude

controlcontrol• Reduces the need for Reduces the need for

propellant propellant for attitude controlfor attitude control

NASA-GRC


A Three Degree of Freedom Satellite Attitude Control System

• Four reaction wheels Four reaction wheels mounted in a tetrahedron mounted in a tetrahedron configurationconfiguration

• Assumptions: Assumptions: – Imaging spacecraftImaging spacecraft– Camera is mounted at the Camera is mounted at the

bottom of the spacecraftbottom of the spacecraft– Global reference frame is Global reference frame is

at the bottom of the at the bottom of the satellitesatellite

– Reaction wheels are not Reaction wheels are not mounted in the global mounted in the global reference framereference frame


The Systems Mathematical Description

4321 TTTTTTKE p

Tpppp wIwT2

1

zyxpw

IzzIyzIxz

IyzIyyIxy

IxzIxyIxx

I p

Tnnnn wIwT2

1

1111 4

2

2

3

2

2

2

2zyxw

222 2

2

2

2zyxw

33334

2

4

6

2

2zyxw

zyxw 44

4,3,2,1;

00

00

00

n

C

B

A

I

n

n

n

n


The Systems Mathematical Description

0

xd

dT

4*4

3*3

2*2

1*1

** 2

2

2

2

2

2

A

A

A

A

A

A

A

A

A

Ixz

A

Ixyzyx

0

yd

dT

3*3

1*1

** 4

6

2

6

B

B

B

B

B

Ixz

B

Ixyzxy

0

zd

dT

3*3

2*2

1*1

** 4

2

2

2

2

2

C

C

C

C

C

C

C

Iyz

C

Ixzyxz

MIMO Cross

Coupling Terms


A General Form of a Problem

The ability to systematically design a control algorithm to account for complex The ability to systematically design a control algorithm to account for complex system dynamics will dramatically speed up the development time and reduce system dynamics will dramatically speed up the development time and reduce

the number of hardware constraints. By approximating the system dynamics the the number of hardware constraints. By approximating the system dynamics the algorithm is capable of compensating for unknown and time-varying parameters, algorithm is capable of compensating for unknown and time-varying parameters,

nonlinearities, and the cross coupling terms in MIMO systems. nonlinearities, and the cross coupling terms in MIMO systems.

)()()(

tbutfdt

tydn

n

)()(

)( tbudt

tydtf

n

n

)()()()(

tbutwtgdt

tydn

n


Form Based Control Algorithm

• Observer: Approximates Observer: Approximates immeasurable signalsimmeasurable signals

• Observer Gains: Observer Gains: Determines the Determines the performance of the performance of the observerobserver

• Observer Outputs: Observer Outputs: – Filtered measurementFiltered measurement– Approximation of the Approximation of the

dynamicsdynamics• Control AlgorithmControl Algorithm

– Inner loop compensates Inner loop compensates for the system dynamicsfor the system dynamics

– Output loop dictates Output loop dictates tracking performancetracking performance

b

uz

b

ufu n

ˆˆ

ˆ00

)( zyLBuAzz

1122110 ...)( nn zkzkzRku

)( 1zyLy

uBAzz

0,...,0,,2 32

21 noo llll

0,...,0,0, 321 nc kkkk


Simulation Results3DOF Satellite Attitude Control

0 2 4 6 8 10 12 14-50

0

50

100Angular Position

x [d

eg]

0 2 4 6 8 10 12 14-50

0

50

100

y [d

eg]

0 2 4 6 8 10 12 14-50

0

50

100

Time [s]

z [d

eg]

0 2 4 6 8 10 12 14-2

0

2

4Position Error

x E

rror

0 2 4 6 8 10 12 14-2

0

2

4

y E

rror

0 2 4 6 8 10 12 14-2

0

2

Time [s]

z E

rror


Simulation Results3DOF Satellite Attitude Control

0 2 4 6 8 10 12 14-50

0

50

100Angular Position

x [d

eg]

0 2 4 6 8 10 12 14-50

0

50

100

y [d

eg]

0 2 4 6 8 10 12 14-50

0

50

100

Time [s]

z [d

eg]

2 4 6 8 10 12

1000

1500

2000

Wheel Velocity

w1

[rpm

]

2 4 6 8 10 12

-1000

-500

0

w2

[rpm

]2 4 6 8 10 12

0

1000

2000

w3

[rpm

]

0 2 4 6 8 10 12 141498

1500

1502

Time [s]

w4

[rpm

]


Algorithm Summary & Conclusions

• Generates a good approximation of the system Generates a good approximation of the system dynamicsdynamics– Approximates unknown parameters, states, Approximates unknown parameters, states,

disturbances, and coupling between MIMO systemsdisturbances, and coupling between MIMO systems• Requires minimal information about the plantRequires minimal information about the plant• Mathematically elegantMathematically elegant

– Increased confidence in the designIncreased confidence in the design– Good for computationally starved systems or Good for computationally starved systems or

systems which require a large control frequency systems which require a large control frequency – Parallel nature allows multiple processes to be Parallel nature allows multiple processes to be

controller simultaneously controller simultaneously • Constraints Constraints

– The available control effort is large enough to The available control effort is large enough to perform the desired operationperform the desired operation

– The system does not have a large time delayThe system does not have a large time delay


Problem Summary & Conclusions

• Flexibility when designing the system architectureFlexibility when designing the system architecture– More flexibility packaging the system by not More flexibility packaging the system by not

having to be as concerned about the specific having to be as concerned about the specific alignmentalignment

• Decreased development timeDecreased development time– Less system parameters to identifyLess system parameters to identify– Accounts for cross coupling termsAccounts for cross coupling terms– Systematic approach to improving the Systematic approach to improving the

performanceperformance• Minimal computational overheadMinimal computational overhead

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