AAttttiittuuddee DDeetteerrmmiinnaattiioonn aanndd CCoonnttrrooll ((AADDCCSS)) 1166..668844 SSppaaccee SSyysstteemmss PPrroodduucctt DDeevveellooppmmeenntt SSpprriinngg 22000011 OOlliivviieerr LL.. ddee WWeecckk DDeeppaarrttmmeenntt ooff AAeerroonnaauuttiiccss aanndd AAssttrroonnaauuttiiccss MMaassssaacchhuusseettttss IInnssttiittuuttee ooff TTeecchhnnoollooggyy AADDCCSS MMoottiivvaattiioonn (cid:1) Motivation Sensors: GPS, star trackers, limb — sensors, rate gyros, inertial In order to point and slew optical — measurement units systems, spacecraft attitude control provides coarse pointing while Control Laws — optics control provides fine Spacecraft Slew Maneuvers (cid:1) pointing Euler Angles — Spacecraft Control (cid:1) Quaternions — Spacecraft Stabilization — Spin Stabilization — Key Question: Gravity Gradient What are the pointing — requirements for satellite ? Three-Axis Control — Formation Flight — NEED expendable propellant: Actuators — Reaction Wheel Assemblies — (cid:127) On-board fuel often determines life (RWAs) (cid:127) Failing gyros are critical (e.g. HST) Control Moment Gyros — (CMGs) Magnetic Torque Rods — Thrusters — OOuuttlliinnee Definitions and Terminology (cid:1) Coordinate Systems and Mathematical Attitude Representations (cid:1) Rigid Body Dynamics (cid:1) Disturbance Torques in Space (cid:1) Passive Attitude Control Schemes (cid:1) Actuators (cid:1) Sensors (cid:1) Active Attitude Control Concepts (cid:1) ADCS Performance and Stability Measures (cid:1) Estimation and Filtering in Attitude Determination (cid:1) Maneuvers (cid:1) Other System Consideration, Control/Structure interaction (cid:1) Technological Trends and Advanced Concepts (cid:1) OOppeenniinngg RReemmaarrkkss Nearly all ADCS Design and Performance can be viewed in (cid:1) terms of RIGID BODY dynamics Typically a Major spacecraft system (cid:1) For large, light-weight structures with low fundamental (cid:1) frequencies the flexibility needs to be taken into account ADCS requirements often drive overall S/C design (cid:1) Components are cumbersome, massive and power-consuming (cid:1) Field-of-View requirements and specific orientation are key (cid:1) Design, analysis and testing are typically the most (cid:1) challenging of all subsystems with the exception of payload design Need a true “systems orientation” to be successful at (cid:1) designing and implementing an ADCS TTeerrmmiinnoollooggyy : Orientation of a defined spacecraft body coordinate AATTTTIITTUUDDEE system with respect to a defined external frame (GCI,HCI) Real-Time or Post-Facto knowledge, AATTTTIITTUUDDEE DDEETTEERRMMIINNAATTIIOONN:: within a given tolerance, of the spacecraft attitude Maintenance of a desired, specified attitude AATTTTIITTUUDDEE CCOONNTTRROOLL:: within a given tolerance “Low Frequency” spacecraft misalignment; AATTTTIITTUUDDEE EERRRROORR:: usually the intended topic of attitude control “High Frequency” spacecraft misalignment; AATTTTIITTUUDDEE JJIITTTTEERR:: usually ignored by ADCS; reduced by good design or fine pointing/optical control. PPooiinnttiinngg CCoonnttrrooll DDeeffiinniittiioonnss target target desired pointing direction estimate true actual pointing direction (mean) estimate estimate of true (instantaneous) a pointing accuracy (long-term) c a s stability (peak-peak motion) k knowledge error k true c control error s aa == ppooiinnttiinngg aaccccuurraaccyy == aattttiittuuddee eerrrroorr ss == ssttaabbiilliittyy == aattttiittuuddee jjiitttteerr Source: G. Mosier NASA GSFC AAttttiittuuddee CCoooorrddiinnaattee SSyysstteemmss (North Celestial Pole) ^ Z GGCCII:: GGeeoocceennttrriicc IInneerrttiiaall CCoooorrddiinnaatteess CCrroossss pprroodduucctt GGeeoommeettrryy:: CCeelleessttiiaall SSpphheerree ^ ^ ^ Y = Z x X h g t n A r c l e dihedral (cid:3)(cid:3) (cid:1)(cid:1) ^ Y ^ VVEERRNNAALL X EEQQUUIINNOOXX (cid:1)(cid:1)(cid:2)(cid:2) IInneerrttiiaall CCoooorrddiinnaattee :: RRiigghhtt AAsscceennssiioonn (cid:3)(cid:3) SSyysstteemm :: DDeecclliinnaattiioonn X and Y are in the plane of the ecliptic AAttttiittuuddee DDeessccrriippttiioonn NNoottaattiioonnss ⋅ = { } Coordinate system ˆ Z (cid:1) A = P Vector (cid:1) (cid:1) A A = P P Position vector w.r.t. {A} P z P y ˆ P Y x A (cid:1) Px AP = P y ˆ X A P z 1 0 0 [ ] = ˆ ˆ ˆ = Unit vectors of {A} X Y Z 0 1 0 A A A 0 0 1 Describe the orientation of a body: (1) Attach a coordinate system to the body (2) Describe a coordinate system relative to an inertial reference frame RRoottaattiioonn MMaattrriixx Zˆ {A} = Reference coordinate system A Jefferson Memorial Zˆ Yˆ = B B {B} Body coordinate system Rotation matrix from {B} to {A} ˆ Y ˆ A [ ] X A A = A ˆ A ˆ A ˆ ˆ R X Y Z X B B B B B ˆ Z Special properties of rotation matrices: A Jefferson Memorial Zˆ Yˆ (1) Orthogonal: B B θ − T = T = 1 R R I, R R θ ˆ (2) Orthonormal: Y A ˆ ˆ X X = A B R 1 1 0 0 (3) Not commutative A = R 0 cos -sin B A B ≠ B A R R R R 0 sin cos B C C B EEuulleerr AAnngglleess ((11)) Euler angles describe a sequence of three rotations about different axes in order to align one coord. system with a second coord. system. ˆ α ˆ β ˆ γ Rotate about Z by Rotate about Y by Rotate about X by A B C ˆ ˆ ˆ ˆ Z ZA ZB Zˆ ZB Zˆ C C D β γ ˆ Y ˆ Y B Yˆ D B γ α ˆ Y ˆ ˆ A X ˆ X B β Y Yˆ A α C C ˆ ˆ X X ˆ ˆ X X B C C D cosα -sinα 0 cosβ 0 sinβ 1 0 0 A = α α B = C = γ γ R sin cos 0 R 0 1 0 R 0 cos -sin B C D β β γ γ 0 0 1 -sin 0 cos 0 sin cos A = A B C R R R R D B C D
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