Download presentation
Presentation is loading. Please wait.
Published byLester King Modified over 9 years ago
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
ASTROD 2006 2006/07/15 Outline Introduction of the Mission Simulator Controller Development Conclusion Outlook
3
ASTROD 2006 2006/07/15 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
ASTROD 2006 2006/07/15 Simulator Equations of Motion Disturbance & Environment
5
ASTROD 2006 2006/07/15 Coordinates I Heliocentric inertial frameCenter of mass of suni Earth-fixedCenter of earthe Spacecraft body-fixed frameCenter of mass of spacecraftb Sensor frame for test mass Geometrical center of sensor sens Body-fixed frame for test mass Center of mass of test masstm
6
ASTROD 2006 2006/07/15 Coordinates II FrameBase pointx directionz direction Heliocentric inertial frame Center of mass of sunAries Normal of ecliptic Spacecraft body- fixed frame Center of mass of spacecraft Parallel to symmetry axis of telescope Symmetrical axis Sensor frame for test mass Geometrical center of sensor Normal of the surface of the house nearby the telescope Normal of the upper surface of the house Body-fixed frame for test mass Center of mass of test mass Normal of the surface nearby the telescope Normal of the upper surface of test mass
7
ASTROD 2006 2006/07/15 Equations of Motion SC Translatio n SC Rotation TM Translatio n TM Rotation
8
ASTROD 2006 2006/07/15 Disturbance & Environment Gravity Field (first order--spherical) Elements of
9
ASTROD 2006 2006/07/15 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
ASTROD 2006 2006/07/15 Disturbance & Environment Coefficient of reflection Unit vector Effective area of SC Solar mean momentum flux / Solar pressure Solar Pressure
11
ASTROD 2006 2006/07/15 Solar Pressure deterministic part Solar pressure at 1AU 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
12
ASTROD 2006 2006/07/15 Coupling between SC&TM Translation coupling Rotation coupling
13
ASTROD 2006 2006/07/15 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
ASTROD 2006 2006/07/15 Simulator
15
ASTROD 2006 2006/07/15 Controller Design Structure of Controller Requirements of controller Synthesis Closed loop Analysis
16
ASTROD 2006 2006/07/15 Structure of Controller DFACS 3 Sub-system SensorActuator SC-Attitude (3DOF) Star-Sensor Gyroscope (??) FEEP Drag-Free (3DOF-translation) EPSFEEP TM-Suspension (3DOF-rotation) EPS ( Electrostatic Positioning/ Measurement System ) EPS
17
ASTROD 2006 2006/07/15 Requirements of Controller SC-Attitude (3DOF) Drag-Free (3DOF-translation) TM-Suspension (3DOF-rotation) (????) It depends on the cross-talking between rotation and translation DOFs of test mass. It also need to meet the requirements of laser interferometer(not too big anglar velocity).
18
ASTROD 2006 2006/07/15 Synthesis I With the LQR method we can derive the optimal gain matrix K such that the state-feedback law minimizes the quadratic cost function Given following linear system : Just as the kalman filter we can get the minimum steady-state error covariance LQR: Linear-Quadratic-Regulator
19
ASTROD 2006 2006/07/15 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
ASTROD 2006 2006/07/15 LQG Design Plant
21
ASTROD 2006 2006/07/15 Controller Standard LQR used here is MIMO PD controller. It ’ s feedback is proportion (position, angle ) and derivative (velocity and angular velocity) of outputs of system. Feed forward part can cancel the static error.
22
ASTROD 2006 2006/07/15 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? w ith 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
ASTROD 2006 2006/07/15 Closed loop analysis Transfer function & PSD of Simulation Data Pointing accuracy :
24
ASTROD 2006 2006/07/15 Test mass position
25
ASTROD 2006 2006/07/15 Transfer function analysis
26
ASTROD 2006 2006/07/15 PSD analysis
27
ASTROD 2006 2006/07/15 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 (LQR+KF) was developed which can meet the requirements of the mission.
28
ASTROD 2006 2006/07/15 Outlook Detailed model Based on SC design –Inertial sensor : Cross-coupling between DOFs –Star sensor : Sample 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
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.