# Presentation: 349348

## SNAP Attitude Control

- Mechanical Engineering Dep’t
- University of California
- Berkeley

## Participants

- Jong Hak Kim – graduate student
- Andy Jennings – undergraduate student
- Anuscheh Nawaz – visiting student (Stuttgart)
- David Auslander – faculty

- SNAP - Attitude Control System

- April 4th, 2003

## Phase Zero Goals

- Vehicle Dynamics Simulation
- Control
- Sensor simulation

- SNAP - Attitude Control System

- April 4th, 2003

## Vehicle Dynamics

- Two methods
- Near-Rigid Body, Discrete
- Treetops (NASA software)
- Rigid body model
- Coordinate systems

- SNAP - Attitude Control System

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## Control

- Attitude representation
- Angles
- Vectors
- Rotation matrix
- Axis-by-axis control
- Multi single-loop control
- Profiled moves

- SNAP - Attitude Control System

- April 4th, 2003

## Sensor Simulation

- Star sensors only
- Attitude computation
- Data format for control

- SNAP - Attitude Control System

- April 4th, 2003

## Coordinate Systems used

- 1-Inertial Coordinate System
- Origin: Center of earth
- x: towards vernal equinox
- z: perpendicular to equatorial plane
- y: completes the right hand system
- _vernal equinox_: one of the
- crossing points of ecliptic and
- celestial equator

- z

- x

- y

- SNAP - Attitude Control System

- April 4th, 2003

## Coordinate Systems used

- 2-Body fixed Coordinate System
- Origin: Satellite Center of Mass
- x: direction light strikes the focal plane
- z: along satellite axis
- y: completes the right hand system

- Z

- X

- Y

- CM

- SNAP - Attitude Control System

- April 4th, 2003

## Near-Rigid Modeling

- Principles
- Use only point masses
- Connect (constrain) masses with springs/dampers
- Springs/dampers very stiff but NOT rigid
- Why?
- System equations only need Newton’s laws- not Euler
- Not complexity limited – interacting components
- Fit well with object-oriented computing

- SNAP - Attitude Control System

- April 4th, 2003

## Issues in Near Rigid Simulation

- Stiff, high-order differential equations
- Error control
- ODE solver artifacts – conventional error estimates don’t seem to work
- Model fidelity – measure and control errors associated with constraint stiffness
- Representation of modal shapes

- SNAP - Attitude Control System

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## Near Rigid Modeling Results

- SNAP - Attitude Control System

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## Near Rigid Results

- SNAP - Attitude Control System

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## Near Rigid Error Results

- SNAP - Attitude Control System

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## Treetops Modeling

- Node

- Actuator

- Node

- Hinge

- Body

- Inertial Frame

**Sensor**

- Treetops –
- have tree structure as an interconnected set of individual bodies, sensors and actuators
- Rigid, flexible and Nastran body modeling is possible

- SNAP - Attitude Control System

- April 4th, 2003

## Body – stand-alone basis without regard to the rest of the bodies in the tree. for FEM         
              analysis, Nastran model can be generated.

Hinges -  defines the kinematic variables of the multi-body system
                hinge variables define the relative motion between bodies

Actuators –reaction wheel model in Treetops can be reprogrammable
                    user can design new reaction wheel model

Sensors -  have no dynamics associated with them
                 Using the user defining code allows a lot of flexibility to include user 
                 defined models into Treetops

-               analysis, Nastran model can be generated.
- Hinges -  defines the kinematic variables of the multi-body system
-                 hinge variables define the relative motion between bodies
- Actuators –reaction wheel model in Treetops can be reprogrammable
-                     user can design new reaction wheel model
- Sensors -  have no dynamics associated with them
-                  Using the user defining code allows a lot of flexibility to include user
-                  defined models into Treetops

**Treetops Modeling**

- SNAP - Attitude Control System

- April 4th, 2003

## Treetops Modeling

**Inertial coordinate **

**body coordinate **

**Position Sensor (relative to inertial coordinate)**

**Moment generator**

**Hinge (between inertial and body coordinate)**

- SNAP - Attitude Control System

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## Tracking Control implementation with Treetops and Near Rigid Body Method

- Satellite is following a object
- moving 14.644 arcsec/s in the
- inertial coordinate system
- represented with a spherical
- coordinate system

- Control algorithm  - PD controller
- ( using decoupled, linearized and
-  simplified satellite dynamic
-  model)

- SNAP - Attitude Control System

- April 4th, 2003

## Tracking Control implementation with Treetops and Near Rigid Body Method

- Applied torque from the actuator in X axis
- for Tracking control in Treetops and Near rigid method

- Error level in tracking control
- (position error between observed star vector and z axis of satellite – angle in
- YZ plane)

- SNAP - Attitude Control System

- April 4th, 2003

## Star sensor - principle

**Sensor Simulation**

- photons

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## Star sensor - identifying satellite attitude

**Sensor Simulation**

- Sensor ‘sees’ star

- Satellite position known in initial coordinates

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## Role within the ACS

**Sensor Simulation**

- Desired heading

- Control unit

- Actuator Simulation

- Simulation of sensors

- Simulation of dynamics

- feedback

- SNAP - Attitude Control System

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## Simulation of the star sensor

**Sensor Simulation**

- Noise model according to Study Aurélia Secroun, Michael Lampton and Michael Levi as function of time

- simulation

- star position

- SNAP - Attitude Control System

- April 4th, 2003

## Validation

For zero noise – i.e. zero standard deviation     
and no satellite motion:

				input = output

- For zero noise – i.e. zero standard deviation
- and no satellite motion:
- 				input = output

**Sensor Simulation**

- !

- SNAP - Attitude Control System

- April 4th, 2003

## Validation

**Sensor Simulation**

- Noise (blue) and true data (red) are identical

- SNAP - Attitude Control System

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## Results – CCD surface

**Sensor Simulation**

- Rotation speed = 0 °/s
- Sample time = 1/30 s
- Simulation time = 1 s

**CCD surface**

- SNAP - Attitude Control System

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## Results – 3D graphics - still satellite

- Results – 3D graphics - still satellite

**Sensor Simulation**

- The noise- (blue) and the star -(red) vector on the CCD surface

**CCD surface**

- SNAP - Attitude Control System

- April 4th, 2003

## Current Status

- Verifying the compatibility between Treetops and near-rigid model software
- have identical result from both simulation
- Understanding the structure of Treetops software
- Further implementation of noise model and sensor model
- Adding sun sensor and gyro to the sensor simulation

- SNAP - Attitude Control System

- April 4th, 2003

## Next Steps

- Model reaction wheel actuators
- Add additional attitude sensors
- Validate sensor noise model
- Sensor noise filtering
- Characterize vehicle vibration modes
- Assess controller performance

- SNAP - Attitude Control System

- April 4th, 2003