Dynamics Modeling and First Design of DragFree Controller for ASTROD I

1
Dynamics Modeling and First Design of Drag-Free
Controller for ASTROD I

• Hongyin Li, W.-T. Ni
• Purple Mountain Observatory, Chinese Academy of
  Sciences
• S. Theil, L. Pettazzi,
• M. S. Guilherme

ZARM University of Bremen, Germany
2
Outline

• Introduction of the Mission
• Simulator
• Controller Development
• Conclusion
• Outlook

3
Mission Introduction

• Science goal
• Solar-system gravity mapping relativistic
  gravity test
• Orbit
• Heliocentric orbit, 0.5AU-1AU
• Orbit launch in 2015 ?
• SC configuration
• Cylinder 2.5 (diameter)m 2 m covered by
  solar panels.
• FEEP(Field Emission Electric Propulsion)
• Star Sensor, Gyroscope (??)
• EPS(Electrostatic Positioning/ Measurement
  System)
• 1 test mass

4
Simulator

• Equations of Motion
• Disturbance Environment

5
Coordinates I
6
Coordinates II
7
Equations of Motion
8
Disturbance Environment

• Gravity Field (first order--spherical)

Elements of
Elements of
9
Disturbance Environment

• Gravity Field (second order )
• One of the Science goal of ASTROD I is to test
  the gravity field parameter of the solar gravity.
  So, It must be included in the further
  model.

10
Disturbance Environment

• Solar Pressure

11
Solar Pressure

• Solar pressure at 0.5 AU is 4 times that of
  1AU
• A low-pass filter is used to get the
  stochastic part with a white noise passed

deterministic part
Solar pressure at 1AU
12
Coupling between SCTM
Translation coupling
Rotation coupling
13
Sensors and actuators

• Star-Sensor
• EPS-position measurement
• EPS-attitude measurement
• EPS-attitude suspension
• FEEP-force
• FEEP-torque
• White noise ? shaped noise
• Need to consider sample frequency, nonlinearity
  in the future model.

14
Simulator
15
Controller Design

• Structure of Controller
• Requirements of controller
• Synthesis
• Closed loop Analysis

16
Structure of Controller

• DFACS 3 Sub-system

17
Requirements of Controller
18
Synthesis I
LQR Linear-Quadratic-Regulator
Given following linear system

• With the LQR method we can derive the optimal
  gain matrix K such that the state-feedback law
  minimizes the quadratic cost function

Just as the kalman filter we can get the minimum
steady-state error covariance
19
Synthesis II

• LQG LQR KF
• Linear-Quadratic-Gaussian
  Linear-quadratic-regulator kalman
  filter(Linear-quadratic-filter)
• With DC disturbance need feed forward

DC disturbance
20
LQG Design Plant
21
Controller
Standard LQR used here is MIMO PD controller.
Its feedback is proportion (position, angle )
and derivative (velocity and angular velocity) of
outputs of system. Feed forward part can cancel
the static error.
22
Synthesis III

• What does feed forward do to the frequency
• Response of the controller?
• Improve the performance in low frequency
  range.(integral )
• but reduce the stability of the closed loop
  ,need to trade-off
• Stability of the closed loop system?
• with some weight gains, there is still some
  poles on the right phase because the negative
  stiffness. So we need to chose the weight gain
  carefully. Try and tuning to get better
  performance as well as a stable system.

23
Closed loop analysis

• Transfer function PSD of Simulation Data
• Pointing accuracy

24
Test mass position
25
Transfer functionanalysis
26
PSD analysis
27
Conclusion

• A model for ASTROD I is built. However it is
  simple, the structure is established and each
  subsystem can be extended to get a more detailed
  model.
• LQG (LQRKF) was developed which can meet the
  requirements of the mission.

28
Outlook

• Detailed model Based on SC design
• Inertial sensorCross-coupling between DOFs
• Star sensorSample frequency,data fusion of two
  sensors.
• Gyroscope to help the attitude estimate.
• FEEP nonlinearity,frequency response.Location of
  FEEP clusters.
• Advanced control strategy
• Loop-Shaping with weighted LQR
• Decoupling of controllers and DOFs
• Robust Control method