5/1/19 1 Seminar 11 Project Management & System Design Spacecraft Guidance Robert Stengel FRS 148, From the Earth to the Moon Princeton University Copyright 2019 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/FRS.html 1 Project Management & Spacecraft Design Fundamentals of Space Systems, Ch 1 NASA-SP-2016-6105 Spacecraft Guidance: Understanding Space Sec 12.3 Systems Engineering and Management Pisacane, V., Fundamentals of Space System Design, Ch. 1 § Introduction § Fundamentals of System Engineering § Concepts in Systems Engineering § Project Development Process § Management of the Development of Space Systems § Organization 2
Transcript
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Seminar 11Project Management & System Design
Spacecraft GuidanceRobert Stengel
FRS 148, From the Earth to the MoonPrinceton University
Copyright 2019 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/FRS.html
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Project Management & Spacecraft DesignFundamentals of Space Systems, Ch 1
NASA-SP-2016-6105Spacecraft Guidance:Understanding Space
Sec 12.3
Systems Engineering and Management
Pisacane, V., Fundamentals of Space System Design, Ch. 1
§ Introduction§ Fundamentals of System Engineering§ Concepts in Systems Engineering§ Project Development Process§ Management of the Development of Space Systems
§ Organization
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Systems Engineering
Pisacane, V., Fundamentals of Space System Design, Ch. 1 3
Product Development
Pisacane, V., Fundamentals of Space System Design, Ch. 1
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NASA-2016-6105 5
NASA-2016-61056
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Spacecraft Mission Objectives and Requirements
Fortescue
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Requirements Definition• What must the system accomplish?• Why must it be done?• How do we achieve the design goal?• What are the alternatives?• What sub-systems perform what functions?• Are all functions technically feasible?• How can the system be tested to show that
it satisfies requirements?
Wertz and Larson 8
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Program Management: Gantt Chart
• Project schedule• Task breakdown and dependency• Start, interim, and finish elements• Time elapsed, time to go
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Program Evaluation and Review Technique (PERT) Chart• Milestones• Path descriptors• Activities, precursors, and successors• Timing and coordination• Identification of critical path• Optimization and constraint
• Power and Propulsion–Solar cells–�Kick� motor/ payload assist module (PAM)–Attitude-control–orbit-adjustment–station-keeping–Batteries, fuel cells–Pressure tanks–De-orbit systems
•Electronics–Payload–Control–Radio transmitters and receivers–Radar transponders–Antennas
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Functional Requirements of Spacecraft Subsystems
1. Payload must be pointed in the right direction2. Payload must be operable3. Data must be communicated to the ground4. Desired orbit for the mission must be maintained5. Payload must be held together and mounted on
the spacecraft structure6. Payload must operate reliably over some specified
period7. Adequate power must be provided
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Typical Satellite Mass Breakdown
• Satellite without on-orbit/de-orbit propulsion• �Kick� motor/ PAM can add significant mass
LADEE
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Communications Satellite Mass Breakdown
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Recommended Mass Growth Margins
Pisacane, V., Fundamentals of Space System Design, Ch. 1 19
Guidance, Navigation, and Control
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Guidance, Navigation, and Control
• Navigation: Where are we?• Guidance: How do we get to our destination?• Control: What do we tell our vehicle to do?
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First Apollo Program Contract MIT Instrumentation Laboratory
August 9, 1961
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Components of Apollo CSM Primary Navigation Guidance and Control
System (“PNGCS”)
Mindell, D., Digital Apollo, Ch. 5 23
Landmark Tracking for Apollo Guidance
Mindell, D., Digital Apollo, Ch. 524
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Mindell, D., Digital Apollo, Ch. 5
IMU Alignment and State Update
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Apollo Guidance Computer
• Parallel processor• 16-bit word length (hexadecimal)• Memory
– 36,864 words (fixed)– 2,048 words (variable)
• 1st operational solid-state computer• Identical computers in CSM and LM
– Different software (with many identical subroutines)
Impulse– CSM/IMU Align– Final Phase– First Abort Burn
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A Little AGC Digital Autopilot Code
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Apollo GNC Software Testing and Verification
• Major areas of testing– Computational accuracy– Proper logical sequences
• Testing program– Comprehensive test plans– Specific initial conditions and operating sequences– Performance of tests– Comparison with prior simulations, evaluation, and re-testing
• Levels of testing– 1: Specifications coded in higher-order language for non-flight hardware
(e.g., mainframe then, PCs now)– 2: Digital simulation of flight code– 3: Verification of complete programs or routines on laboratory flight
hardware– 4: Verification of program compatibility in mission scenarios– 5: Repeat 3 and 4 with flight hardware to be used for actual mission– 6: Prediction of mission performance using non-flight computers and
laboratory flight hardware 33
Lunar Module Navigation, Guidance, and Control Configuration
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Lunar Descent Guidance
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Lunar Module Transfer Ellipse to Powered Descent Initiation
• Reference (nominal) trajectory, rr(t), from target position back to starting point (Braking Phase example)– Calculated before mission– Three 4th-degree polynomials in time– 5 points needed to specify each polynomial
�
rr(t) = rt + vt t + a tt 2
2+ jt
t 3
6+ st
t 4
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�
r(t) =x(t)y(t)z(t)
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
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Coefficients of the Polynomials
�
rr(t) = rt + vt t + a tt 2
2+ jt
t 3
6+ st
t 4
24• r = position vector• v = velocity vector • a = acceleration vector• j = jerk vector (time
derivative of acceleration)• s = snap vector (time
derivative of jerk)
�
r =xyz
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
v = drdt
=!x!y!z
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥=
vxvyvz
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
a = dvdt
=axayaz
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
j = dadt
=jxjyjz
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
s = djdt
=sxsysz
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
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Corresponding Reference Velocity and Acceleration Vectors
�
vr(t) = vt + a t t + jtt 2
2+ st
t 3
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�
a r(t) = a t + jt t + stt 2
2• ar(t) is the reference control vector
– Descent engine thrust / mass = total acceleration
– Vector components controlled by orienting yaw and pitch angles of the Lunar Module 43
• If initial conditions, dynamic model, and thrust control were perfect, ar(t) would produce rr(t)
ar (t) = at + jtt + stt 2
2⇒
rr (t) = rt + v tt + att 2
2+ jt
t 3
6+ st
t 4
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• ... but they are not• Therefore, feedback control is
required to follow the reference trajectory
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Guidance Law for the Lunar
Module Descent
acommand (t) =ar (t)+KV vmeasured (t)− v r (t)[ ]+KR rmeasured (t)− rr (t)[ ]
• Nominal acceleration profile is corrected for measured differences between actual and reference flight paths
• Considerable modifications made in actual LM implementation (see Klumpp�s paper on Blackboard)
KV :velocity error gainKR :position error gain
Linear feedback guidance law (real time
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LM Manual Control Response During Simulated Landing
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Simulated LM Manual Control Response To Rate Command
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Next Time:The Future of Space Flight
Telemetry, Communications & Tracking
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Supplemental Material
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Apollo GNC Software Specification Control
• Guidance System Operations Plan (GSOP)– NASA-approved specifications document for mission software– Changes must be approved by NASA Software Control Board
• Change control procedures– Program Change Request (NASA) or Notice (MIT)– Anomaly reports– Program and operational notes
• Software control meetings– Biweekly internal meetings– Joint development plan meetings– First Article Configuration Inspection– Customer Acceptance Readiness Review– Flight Software Readiness Review
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Apollo GNC Software Documentation and Mission Support
• Documentation generation and review– GSOP: 1: Prelaunch 2: Data links 3: Digital autopilots 4:
of procedures– Computer listing of flight code– Independently generated program flowchart– Users� Guide to AGC– NASA program documents: Apollo Operations Handbook, Flight Plans
and Mission Rules, various procedural documents• Mission support
– Pre-flight briefings to the crew– Personnel in Mission Control and at MIT during mission
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Ascent (Launch) Guidance
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Gravity-Turn Flight Path
• “Oberth’s Synergy Curve”• Gravity-turn flight path is
function of 3 variables– Initial pitchover angle (from
vertical launch)– Velocity at pitchover– Acceleration profile, T(t)/m(t)• Gravity-turn program closely approximated by
tangent steering laws
Hermann Oberth
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Tangent Steering Laws Approximate Gravity Turn
• Neglecting surface curvature
tanθ(t) = tanθo 1−ttBO
⎛⎝⎜
⎞⎠⎟
• Accounting for effect of Earth surface curvature on burnout flight path angle
• �Open-loop� command, i.e., no feedback of vehicle state
tanθ(t) = tanθo 1−ttBO
− tanβ ttBO
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢
⎤
⎦⎥
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Feedback Guidance Law Errors due to disturbances and modeling errors corrected by feedback control with damping
Thrust Angle(t) = cθ θc(t)−θ(t)[ ]− cqq(t)q = dθ
dt= pitch rate
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Phases of Ascent Guidance
• Vertical liftoff• Roll to launch azimuth• Pitch program to
atmospheric �exit�– Jet stream penetration– Booster cutoff and staging
• Explicit guidance to desired orbit– Booster separation– Acceleration limiting– Orbital insertion
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Jet Stream Profiles • Launch vehicle must able
to fly through strong wind profiles
• Design profiles assume 95th-99th-percentile worst winds and wind shear
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Thrust Vector Control During Launch
• Attitude control– Attitude and rate
feedback• Drift-minimum control
– Attitude and accelerometer feedback
– Increased loads• Load relief control
– Rate and accelerometer feedback
– Increased drift
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Explicit Guidance Law~Lunar Module Ascent, Space Shuttle Launch (Brand, Brown, Higgins, and Pu, CSDL, 1972)• Initial conditions
– End of pitch program, outside atmosphere
• Final condition– Insertion in desired orbit
• Initial inputs– Desired radius– Desired velocity magnitude– Desired flight path angle– Desired inclination angle– Desired longitude of the
ascending/descending node• Continuing outputs
– Unit vector describing desired thrust direction
– Throttle setting 59
Guidance Program Initialization• Thrust acceleration estimate• Mass/mass flow rate• Acceleration limit (~ 3g)• Effective exhaust velocity• Various coefficients• Unit vector normal to desired
orbital plane, iq
�
iq =sinid sinΩd
sinid cosΩd
cosid
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
id:desired inclination angle
Ωd :desired longitude of descending node60
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Guidance Program Operation: Position and Velocity
• Thrust acceleration estimate, aT, from guidance system
• Compute corresponding mass/flow rate and throttle setting, δT
• Position
• Velocity
�
ryz
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
=r
rsin−1 ir • iq( )open
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
�
˙ r ˙ y ˙ z
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
=vIMU • irvIMU • iqvIMU • iz
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ v IMU :velocity estimate in IMU frame
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Guidance Program: Velocity and Time to Go
• Effective gravitational acceleration
• Velocity to be gained
• Time to go prediction (prior to acceleration limiting)
vgo =
!rd − !r( )− geff tgo / 2− !y!zd − !z
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
�
tgo = m˙ m
1− e−vgo / ceff( )
�
geff = − µr2
+r × v 2
r3
• Time to go (to burnout)
�
tgonew = tgoold −Δt Δt :guidance interval
ceff : effective exhaust velocity62
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Guidance Program Commands • Guidance law produces required radial and
cross-range accelerations
�
aTr = aT A + B t − to( )[ ] − geffaTy = aT C + D t − to( )[ ]
• Guidance coefficients, A, B, C, and D are functions of
�
rd ,r, ˙ r , tgo( )y, ˙ y ,tgo( )
plus ceff ,m !m, acceleration limit
aT = net available acceleration, accounting for limit
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Guidance Program Commands • Required thrust direction, iT (i.e., vehicle
orientation in (ir, iq, iz) frame
• Guidance philosophy• Force spacecraft into desired
orbital plane• Climb toward desired 2-D orbit• Achieve orbital velocity
