Introduction to Attitude Control Systems MAE 155A GN/MAE155A

Determination & Attitude Control Systems (DACS) Introduction DACS Basics Attitude Determination and Representation Basic Feedback Systems Stabilization Approaches GN/MAE155A

Determination & Attitude Control Systems (DACS) Control of SC orientation: Yaw, Pitch, Roll 3 Components to DACS: Sensor: Measure SC attitude Control Law: Calculate Response Actuator: Response (Torque) Example: Hubble reqts 2x10-6 deg pointing accuracy => equivalent to thickness of human hair about a mile away! GN/MAE155A

Determination & Attitude Control Systems (DACS) Introduction DACS Basics Attitude Determination and Representation Basic Feedback Systems Stabilization Approaches GN/MAE155A

DACS Basics S/C Correction Attitude Errors Sensors Torquers Gyros Thrusters Reaction Wheels Momentum Wheels CMGs S/C Sensors Gyros Horizon Sensors Sun Sensors Correction Attitude Errors Computer Control Law GN/MAE155A

Determination & Attitude Control Systems (DACS) Spinning Spacecraft provide simple pointing control along single axis (low accuracy) Three axis stability provides high accuracy pointing control in any direction GN/MAE155A

DACS Design Considerations: Mission Reqts Disturbance Calcs DACS System Design GN/MAE155A

DACS Reqts Definition Summarize mission pointing reqts Earth (Nadir), Scanning, Inertial Mission & PL Pointing accuracy Note that pointing accuracy is influenced by all 3 DACS components Pointing accuracy can range from < 0.001 to 5 degrees Define Rotational and translational reqts for mission: Magnitude, rate and frequency Calculate expected torque disturbances Select ACS type; Select HW & SW Iterate/improve as necessary GN/MAE155A

Torque Disturbances Internal Cyclic and secular External Gravity gradient: Variable g force on SC Solar Pressure: Moment arm from cg to solar c.p. Magnetic: Earth magnetic field effects Aero. Drag: Moment arm from cg to aero center Internal Appendage motion, pointing motors- misalign, slosh Cyclic and secular Cyclic: varies in sinusoidal manner during orbit Secular: Accumulates with time GN/MAE155A

Determination & Attitude Control Systems (DACS) Introduction DACS Basics Attitude Determination and Representation Basic Feedback Systems Stabilization Approaches GN/MAE155A

SC Attitude Determination Fundamentals Attitude determination involves estimating the orientation of the SC wrt a reference frame (usually inertial or geocentric), the process involves: Determining SC body reference frame location from sensor measurements Calculating instantaneous attitude wrt reference frame Using attitude measurement to correct SC pointing using actuators (or torquers) GN/MAE155A

Basic SC Attitude Determination Sensor Data State Estimation Attitude Calculation Gyros Star/Sun Sensor Magnetometer Batch Estimators Least Squares Kalman Filtering Euler Angles DCM Quaternions Control Law Used to Determine Required Correction GN/MAE155A

Attitude Sensors Performance requirements based on mission Weight, power and performance trades performed to select optimal sensor Multiple sensors may be used GN/MAE155A

State Estimation Approaches Estimate SC orientation using data measurements Estimates typically improve as more data are collected (assuming no ‘jerk motion’) Estimation theory and statistical methods are used to obtain best values Least squares and Kalman filtering are most common approaches Least squares minimizes square of error (assumes Gaussian error distribution) Kalman filter minimizes variance GN/MAE155A

SC Attitude Representation SC frame of reference typically points SC Z axis anti-Nadir, and X axis in direction of velocity vector Relationship between SC and inertial reference frame can be defined by the 3 Euler angles (Yaw, Pitch and Roll) Note that both magnitude and sequence of rotation affect transformation between SC and inertial reference frame GN/MAE155A

SC Attitude Representation Using Euler Rotation Angles The Direction Cosine Matrix (DCM) is the product of the 3 Euler rotations in the appropriate sequence (Yaw-Pitch-Roll) DCM ~ R = R1 * R2 * R3 Ref: Brown, Elements of SC Design GN/MAE155A

Direction Cosine Rotation Matrix The DCM is given by: Note that each transformation requires substantial arithmetic and trigonometric operations, rendering it computationally intensive An alternative, and less computationally intensive, approach to using DCM involves the use of Quaternions Ref: Brown, Elements of SC Design GN/MAE155A

Quaternion Definition Euler’s theorem states that any series of rotation of a rigid body can be represented as a single rotation about a fixed axis Orientation of a body axis can be defined by a vector and a rotation about that vector A quaternion, Q, defines the body axis vector and the scalar rotation => 4 elements Q = i.q1 + j.q2 + k.q3 + q4 , where i2 = j2 = k2 = -1 GN/MAE155A

Basic Quaternion Properties Given the quaternion Q, where Q = i.q1 + j.q2 + k.q3 + q4 ; we have ij = - ji = k; jk = -kj = i; ki = -ik = j Two quaternions, Q and P are equal iff all their elements are equal, i.e., q1 = p1 ; q2 = p2 ; q3 = p3 Quaternion multiplication is order dependent, R=Q*P is given by: R = (i.q1 + j.q2 + k.q3 + q4)*(i.p1 + j.p2 + k.p3 + p4) The conjugate of Q is given by Q*, where Q* = -i.q1 - j.q2 - k.q3 + q4 The inverse of Q, Q-1 = Q* when Q is normalized GN/MAE155A

Basic Quaternion Properties The DCM can be expressed in terms of quaternion elements as: The quaternion transforming frame A into frame B is given by: VB = Qab VA (Qab)* Quaternions can also be combined as: Qac = Qbc Qab GN/MAE155A

Comparison of 3-Axis Attitude Representation Ref: Brown, Elements of SC Design GN/MAE155A

Determination & Attitude Control Systems (DACS) Introduction DACS Basics Attitude Determination and Representation Basic Feedback Systems Stabilization Approaches GN/MAE155A

Feedback Loop Systems The control loop can use either an open or closed system. Open loop is used when low accuracy is sufficient, e.g., pointing of solar arrays. Generic closed-loop system: Disturbance e = r + a Control Law, Actuators Spacecraft Dynamics Output Reference Error r a a Ref: Brown, Elements of SC Design GN/MAE155A

Basic Rotation Equations Review Angular displacement:  = 1/2  t2 = d  /dt (note ‘burn’ vs. maneuvering time) Angular speed:  =  t Angular acceleration:  = T/Iv Angular Momentum: H = Iv  => H = T t Where,  ~ rotation angle;  ~ angular acceleration T ~ torque; Iv ~ SC moment of Inertia H ~ Angular Momentum;  ~angular speed GN/MAE155A

Basic Rotation Equations Review Torque equations: T = dH/dt = Iv d /dt = Iv d2 / dt2 (Iv assumed constant) Note that the above equations are scalar representations of their vector forms (3D) Hx  Hy Spin axis precession GN/MAE155A

Determination & Attitude Control Systems (DACS) Introduction DACS Basics Attitude Determination and Representation Basic Feedback Systems Stabilization Approaches GN/MAE155A

Spin Stabilized Systems Spinning SC (spinner): resists disturbance toques (gyroscopic effect) Disturbance along H vector affects spin rate Disturbance perp. to H => Precession Adv: Low cost, simple, no propel mgmt Disadv:- Low pointing accuracy (> 0.3 deg) - I about spinning axis >> other I - Limited maneuvering, pointing Dual spin systems: major part of SC spins while a platform (instruments) is despun GN/MAE155A

SC Stabilization Systems F2 - Gravity Gradient (G2) Systems (passive): Takes adv of SC tendency to align its long axis along g vector, g = GM/r; r1<r2 => F1>F2 => Restoring Torque -Momentum Bias: Use momentum wheel to provide inertial stiffness in 2 axes, wheel speed provides control in 3rd axis r2 F1 r1 Stability condition: Ir r > (Ixx-Iyy) y Pitch axis (y) wheel SC V Nadir GN/MAE155A

SC Stabilization Systems Reaction Wheels (RW) Motor spins a small free rotating wheel aligned w. vehicle control axis (~low RPM) One wheel per axis needed, however, additional wheels are used for redundancy RW only store, not remove torques Counteracting external torque is needed to unload the stored torque, e.g., magnetic or rxn jets (momentum dumping) Speed of wheel is adjusted to counter torque GN/MAE155A

SC Stabilization Systems RW at high RPM are termed momentum wheels. Also provides gyroscopic stability Magnetic (torque) coils can be used to continuously unload wheel Wheels provide stability during periods of high torque disturbances Control Moment Gyro Gimbaled momentum wheel GN/MAE155A

SC Stabilization Systems (External): Thrusters: Used to provide torque (external) on SC Magnetic torque rods Can be used to provide a controlled external torque on SC Need to minimize potential residual disturbance torque T = M x B where M~dipole w. magnetic moment M B~Local Flux density GN/MAE155A

Reaction Wheels Magnetometers Magnetic Torquers GN/MAE155A

DACS Summary GN/MAE155A

Conclusions Examples References Discussion & Questions GN/MAE155A