Attitude Determination and Control Dr. Andrew Ketsdever MAE 5595

Outline Introduction Control Strategies Disturbance Torques Sensors 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 Spacecraft Dynamics - Rigid Body Attitude Control Task Actuators Commands e.g. increase Wheel speed 100rpm Desired e.g. +/- 3 deg Ram pointing Sensors Determination Actual e.g. – 4 deg Estimated e.g. – 3.5 deg Spacecraft Dynamics - Rigid Body - Flexible Body (non-rigid)

Mass Moment of Inertia where H is the angular momentum, I is the mass moment of inertia tensor, and W is the angular velocity where the cross-term products of inertia are equal (i.e. Ixy=Iyx)

Mass Moment of Inertia For a particle For a rigid body

Mass MOI Rotational Energy:

Mass MOI Like any symmetric tensor, the MOI tensor can be reduced to diagonal form through the appropriate choice of axes (XYZ) Diagonal components are called the Principle Moments of 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.

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

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 Determine the angle Dy Dy H F w Df R 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 Advantages 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

Gravity Gradient Torque z y q where:

Magnetic Torque where: *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 where:

Solar Pressure Torque where:

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

Actuators

Attitude Control Actuators come in two types Passive Active 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 High Mass and Power Thrusters 0. 1º to 1º Propellant limited, Large impulse

Attitude Control