Attitude Determination and Control by nikeborome

VIEWS: 27 PAGES: 42

									Attitude Determination and
          Control




              Dr. Andrew Ketsdever
                        MAE 5595
                                  Outline
•   Introduction
     –   Definitions
     –   Control Loops
     –   Moment of Inertia Tensor
     –   General Design
•   Control Strategies
     – Spin (Single, Dual) or 3-Axis
•   Disturbance Torques
     –   Magnetic
     –   Gravity Gradient
     –   Aerodynamic
     –   Solar Pressure
•   Sensors
     –   Sun
     –   Earth
     –   Star
     –   Magnetometers
     –   Inertial Measurement Units
•   Actuators
     –   Dampers
     –   Gravity Gradient Booms
     –   Magnetic Torque Rods
     –   Wheels
     –   Thrusters
INTRODUCTION
               Introduction
• Attitude Determination and Control
  Subsystem (ADCS)
  – Stabilizes the vehicle
  – Orients vehicle in desired directions
  – Senses the orientation of the vehicle relative
    to reference (e.g. inertial) points
• Determination: Sensors
• Control: Actuators
• Controls attitude despite external
  disturbance torques acting on spacecraft
                    Introduction
• ADCS Design Requirements and Constraints
  – Pointing Accuracy (Knowledge vs. Control)
       • Drives Sensor Accuracy Required
       • Drives Actuator Accuracy Required
  –   Rate Requirements (e.g. Slew)
  –   Stationkeeping Requirements
  –   Disturbing Environment
  –   Mass and Volume
  –   Power
  –   Reliability
  –   Cost and Schedule
Introduction
     Z

          Nadir




                           Y




            X


         Velocity Vector
                                  Control Loops
      Disturbance Torques

Desired                                                                                    Actual
Attitude                                          Commands
                                    Attitude                            Attitude           Attitude
                                    Control       e.g. increase         Actuators
e.g. +/- 3 deg                                                                             e.g. – 4 deg
Ram pointing
                                     Task         Wheel speed
                                                                                           Ram pointing
                                                  100rpm

                                    Attitude                 Attitude
                 Estimated        Determination              Sensors
                 Attitude             Task
                 e.g. – 3.5 deg
                 Ram pointing                                             Spacecraft Dynamics
                                                                           - Rigid Body
                                                                           - Flexible Body (non-rigid)
           Mass Moment of Inertia
                                  
                              H  I
where H is the angular momentum, I is the mass moment of inertia
tensor, and  is the angular velocity

             H x   I xx                  I xy       I xz   x 
                                                           
        H   H y    I yx               I yy        I yz   y 
             H z    I zx
                                         I zy       I zz    z 
                                                               
 where the cross-term products of inertia are equal (i.e. Ixy=Iyx)
       Mass Moment of Inertia
• For a particle     O



                                     IO  r m     2
                         r

                                 m




                     O

• For a rigid body
                     O

                                     I   r 2 dm   r 2 dm
                         r
                             dm                       m



                             m            I   r 2  dV
                     O                        V
                             Mass MOI
           
I xx   y  z dm
                2        2
                             
I yy     x   2
                    z   2
                             dm   Rotational Energy:


I zz     x
            2
                    y   2
                             dm           1
                                        E  I ij i  j
                                           2
I xy    xy dm

I xz    xz dm

I yz    yz dm
                Mass MOI
• Like any symmetric
  tensor, the MOI            I x   0    0
  tensor can be              0
                          I       Iy   0 
  reduced to diagonal
  form through the
  appropriate choice of      0
                                   0    Iz 
                                            
  axes (XYZ)
• Diagonal components              
  are called the
  Principle Moments of
                               H  I
  Inertia
                   Mass MOI
• Parallel-axis theorem: The moment of
  inertia around any axis can be calculated
  from the moment of inertia around parallel
  axis which passes through the center of
  mass.
  O
           m
                   CM
                        r’
       d                     I  I  md   2



               r


  O
ADCS Design
ADCS Design
ADCS Design
ADCS Design
ADCS Design
Control Strategies
    Gravity Gradient Stabilization
• Deploy gravity
  gradient boom
• Coarse roll and
  pitch control
• No yaw control
• Nadir pointing
  surface
• Limited to near
  Earth satellites
                     Best to design such that Ipitch > Iroll > Iyaw
         Spin Stabilization
• Entire spacecraft
  rotates about
  vertical axis
• Spinning sensors
  and payloads
• Cylindrical
  geometry and solar
  arrays
               Spin Stability
UNSTABLE                    STABLE
      S

                                   S


                                        T


           T




   IS                           IS
      1                           1
   IT                           IT
            Satellite Precession
• Spinning Satellite
• Satellite thruster is fired to
  change its spin axis
• During the thruster firing, the
  satellite rotated by a small
  angle Df                                   Dy H
                                                    F
• Determine the angle Dy                        



     2 FR(Dt )      Df                  Df
Dy            ; 
        I          Dt
                                         R
     2 FR(Df )
Dy 
        I 2                        F
          Dual Spin Stabilization
• Upper section does not
  rotate (de-spun)
• Lower section rotates to
  provide gyroscopic
  stability
• Upper section may rotate
  slightly or intermittently to
  point payloads
• Cylindrical geometry and
  solar arrays
           3-Axis Stabilization
• Active stabilization of all three
  axes
   – Thrusters
   – Momentum (Reaction) Wheels
      • Momentum dumping
• Advantages
   – No de-spin required for
     payloads
   – Accurate pointing
• Disadvantages
   – Complex
   – Added mass
Disturbance Torques
              External Disturbance Torques
                                      NOTE: The magnitudes of the torques is
                                      dependent on the spacecraft design.
                 Drag
Torque (au)




                        Gravity
                                                                        Solar
                                                                        Press.

                                          Magnetic

               LEO                                          GEO

                              Orbital Altitude (au)
   Internal Disturbing Torques
• Examples
  – Uncertainty in S/C Center of Gravity (typically
    1-3 cm)
  – Thruster Misalignment (typically 0.1° – 0.5°)
  – Thruster Mismatch (typically ~5%)
  – Rotating Machinery
  – Liquid Sloshing (e.g. propellant)
  – Flexible structures
  – Crew Movement
Disturbing Torques




            
           I
    T H
      
    T  r F
Gravity Gradient Torque
       3                                   z
  Tg     3
            I z  I y sin 2 
       2R
   where:
                                                 y
Tg  maximum gravity gradient
  Earth's gravitational parameter
R  orbit radius
I y , I z  S/C mass moments of inertia
  maximum deviation away from vertical 
              Magnetic Torque
                       Tm  m xB
where:
            Tm  magnetic disturbance torque
                                                
             m  S/C residual magnetic dipole Amp  m 2   
             B  strength of Earth's magnetic field
                M
                 3
                    for points above the equator
                R
                2M
               3 for points above the poles
                 R
                                            
            M  Earth's magnetic moment 7.96  1015 tesla  m 3   
            R  orbit radius meters

*Note value of m depends on S/C size and whether on-board compensation is used
     - values can range from 0.1 to 20 Amp-m2
     - m = 1 for typical small, uncompensated S/C
Aerodynamic Torque
             Ta  F c pa  c g 
                   1
where:          F  C D Av 2
                   2
   Ta  aerodynamic disturbance torque
     atmospheric density
   C D  coefficient of drag typical S/C values are 2 - 2.5
   A  cross- sectional area
   v  velocity
   C pa  center of atmospheric pressure
   Cg  center of gravity
         Solar Pressure Torque
                Tsrp  F c ps  c g 

                            As 1    cosi
                         Fs
where:
                      F
                         c
         Tsrp  solar radiation presuredisturbance torque
         c ps  center of solar radiation pressure
         c g  center of gravity
                                 W
         Fs  solar flux density  2 
                                 m 
         c  speed of light
         As  area of illuminate d surface
           reflectance factor 0    1, typical value 0.6 for S/C
         i  sun incidence angle
FireSat Example
                  Disturbing Torques
• All of these disturbing torques
  can also be used to control the
  satellite
   –   Gravity Gradient Boom
   –   Aero-fins
   –   Magnetic Torque Rods
   –   Solar Sails
Sensors
        Attitude Determination
• Earth Sensor (horizon sensor)
  – Use IR to detect boundary between deep space &
    upper atmosphere
  – Typically scanning (can also be an actuator)
• Sun Sensor
• Star Sensor
  – Scanner: for spinning S/C or on a rotating mount
  – Tracker/Mapper: for 3-axis stabilized S/C
     • Tracker (one star) / Mapper (multiple stars)
• Inertial Measurement Unit (IMU)
  – Rate Gyros (may also include accelerometers)
• Magnetometer
  – Requires magnetic field model stored in computer
• Differential GPS
     Attitude Determination



     Earth Horizon Sensor            Sun Sensor         Star Tracker



   Sensor                          Accuracies               Comments
    IMU                     Drift: 0.0003 – 1 deg/hr      Requires updates
                             0.001 deg/hr nominal
 Star Sensor                  1 arcsec – 1 arcmin      2-axis for single star
                             (0.0003 – 0.001 deg)      Multiple stars for map
 Sun Sensor                      0.005 – 3 deg                Eclipse
                               0.01 deg nominal
Earth Sensor
       GEO                     < 0.1 – 0.25 deg                    2-axis
       LEO                       0.1 – 1 deg
Magnetometer                     0.5 – 3 deg                 < 6000 km
                                                         Difficult for high i
Actuators
                Attitude Control
• Actuators come in two types
  – Passive
    •   Gravity Gradient Booms
    •   Dampers
    •   Yo-yos
    •   Spinning
  – Active
    •   Thrusters
    •   Wheels
    •   Gyros
    •   Torque Rods
                      Actuators
Actuator              Accuracy           Comment
Gravity Gradient      5º                2 Axis, Simple
Spin Stabilized       0.1º to 1º       2 Axis, Rotation
Torque Rods           1º                High Current
Reaction Wheels       0.001º to 0.1º   High Mass and Power,
                                         Momentum Dumping
Control Moment Gyro   0.001º to 0.1º   High Mass and Power
Thrusters             0. 1º to 1º      Propellant limited,
                                         Large impulse
Attitude Control

								
To top