SNAP Attitude Control: SNAP Attitude Control Mechanical Engineering Dep’t University of California Berkeley


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


Phase Zero Goals: Phase Zero Goals Vehicle Dynamics Simulation Control Sensor simulation


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


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


Sensor Simulation: Sensor Simulation Star sensors only Attitude computation Data format for control


Coordinate Systems used: 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


Coordinate Systems used: 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


Near-Rigid Modeling: 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


Issues in Near Rigid Simulation: 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


Near Rigid Modeling Results: Near Rigid Modeling Results


Near Rigid Results: Near Rigid Results


Near Rigid Error Results: Near Rigid Error Results


Treetops Modeling: 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


Slide15: 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 Treetops Modeling


Treetops Modeling: Treetops Modeling Inertial coordinate body coordinate Position Sensor (relative to inertial coordinate) Moment generator Hinge (between inertial and body coordinate)


Tracking Control implementation with Treetops and Near Rigid Body Method: 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)


Tracking Control implementation with Treetops and Near Rigid Body Method: 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)


Sensor Simulation: Star sensor - principle Sensor Simulation photons


Sensor Simulation: Star sensor - identifying satellite attitude Sensor Simulation Sensor ‘sees’ star Satellite position known in initial coordinates


Sensor Simulation: Role within the ACS Sensor Simulation Desired heading Control unit Actuator Simulation Simulation of sensors Simulation of dynamics feedback


Sensor Simulation: 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


Sensor Simulation: Validation For zero noise – i.e. zero standard deviation and no satellite motion: input = output Sensor Simulation !


Sensor Simulation: Validation Sensor Simulation Noise (blue) and true data (red) are identical


Sensor Simulation: Results – CCD surface Sensor Simulation Rotation speed = 0 °/s Sample time = 1/30 s Simulation time = 1 s CCD surface


Sensor Simulation: Results – 3D graphics - still satellite Sensor Simulation The noise- (blue) and the star -(red) vector on the CCD surface CCD surface


Current Status: 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


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