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Seminar 10 !Project Management & System Design!
Spacecraft Guidance!Robert Stengel!
FRS 112, From the Earth to the Moon!Princeton University, 2015!
"
Copyright 2015 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"
Sec 1.1 – 1.6""GOES N Series Data Book!Ch 1, 2, 8, 9, 11, 12, 13"
"
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!
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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"
4!
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Spacecraft Mission Objectives and Requirements"
Fortescue"
5!
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 specified functions?"•# Are all functions technically feasible?"•# How can the system be tested to show that it
satisfies requirements?"
Wertz and Larson" 6!
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Spacecraft Subsystems"
Numbers refer to mission functions in Fortesque et al, Spacecraft Systems Engineering"7!
Satellite Systems "•#Structure"
–#Skin, frames, ribs, stringers, bulkheads"
–#Propellant tanks"–#Heat/solar/ micrometeoroid shields, insulation"
–#Articulation/ deployment mechanisms"
–#Gravity-gradient tether"
–#Re-entry system (e.g., sample return)"
•# Power and Propulsion"–#Solar cells"–# Kick motor/ payload assist module"
–#Attitude-control/orbit-adjustment/station-keeping thrusters"
–#Batteries, fuel cells"
–#Pressurizing bottles"
–#De-orbit/ graveyard
systems"
•#Electronics"–#Payload"–#Control computers"–#Control sensors and actuators"
–#Control flywheels"–#Radio transmitters and receivers"
–#Radar transponders"
–#Antennas"
8!
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Functional Requirements of Spacecraft Subsystems"
1.# Payload must be pointed in the right direction"2.# Payload must be operable"3.# Data must be communicated to the ground"4.# Desired orbit for the mission must be maintained"5.# Payload must be held together and mounted on the
spacecraft structure"6.# Payload must operate reliably over some specified
period"7.# Adequate power must be provided"
9!
Typical Satellite Mass Breakdown "
•# Satellite without on-orbit/de-orbit propulsion"•# Kick motor/ PAM can add significant mass"
LADEE"
10!
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Communications Satellite Mass Breakdown "
11!
Recommended Mass Growth Margins "
Pisacane, V., Fundamentals of Space System Design, Ch. 1" 12!
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Satellite Buses "•#Standardization of common components for a variety of missions"
Modular Common Spacecraft Bus"Lander Congiguration"
LADEE Bus Modules"
13!
Hine et al" 14!
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15!
Geostationary Operational Environmental Satellite (GOES-NOP)"
16!
GOES Expanded View"
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17!
GOES Weather Watch System"
18!
GOES Communication Sub-System"
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GOES Telemetry and Command Sub-System"
19!
20!
GOES Electric Power Sub-System"
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21!
GOES Attitude Control Sub-System"
22!
GOES Propulsion Sub-System"
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GOES Thermal Control Sub-System"
23!
Guidance, Navigation, and Control!
24!
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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?"
25!
First Apollo Program Contract !MIT Instrumentation Laboratory !
August 9, 1961"
Charles Stark Draper"(1901-1987)"
BUT … Lunar landing technique was not decided until July, 1962"26!
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Components of Apollo CSM Primary Navigation Guidance and Control
System (“PNGCS”)"
Mindell, D., Digital Apollo, Ch. 5" 27!
Landmark Tracking for Apollo Guidance"
Mindell, D., Digital Apollo, Ch. 5"28!
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Mindell, D., Digital Apollo, Ch. 5"
IMU Alignment and State Update"
29!
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)"
http://klabs.org/history/build_agc/" 30!
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Apollo Guidance Computer (AGC) vs. iPhone 5S"
!# 16-bit Processor"!# Storage: 36,864 words (fixed)"!# 2,048 words (variable)"!# Clock speed: 1 million “ticks” per sec"!# Weight: 70 lb"!# 1st operational solid-state computer"!# Separate Inertial Measurement Unit"
!# 64-bit Processor"!# Storage: 16-64 Gbytes"!# 1 Gbyte RAM"!# Clock speed: 1,300 million
“ticks” per sec"!# Weight: 1/4 lb"!# Plus accelerometers
angular rate gyros, …."31!
Apollo Guidance Computer Magnetic Core Memory Ropes"
1 Kiloword Memory Bank"1 core = 1 bit "
!# No built-in redundancy"!# No redundant computers"!# No failures"!# Mean time between failures = $"
32!
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Apollo Lunar Module Radars"•# Landing radar"
–# 3-beam Doppler radar altimeter"
–# LM descent stage "
•# Rendezvous radar"–# continuous-wave
tracking radar"–# LM ascent stage !
33!
Apollo Guidance Computer Commands"•# Display/Keyboard (DSKY)"•# Sentence"
–# Subject and predicate"–# Subject is implied"
•# Astronaut, or"•# GNC system"
–# Sentence describes action to be taken employing or involving an object"
•# Predicate"–# Verb = Action"–# Noun = Variable or Program
(i.e., the object)"
See http://apollo.spaceborn.dk/dsky-sim.html!
And http://www.ibiblio.org/apollo/ for simulation"
34!
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Numerical Codes for Verbs and Nouns in Apollo Guidance
Computer Programs"Verb Code !Description ! !Remarks!01 !Display 1st component of !Octal display of data
! ! ! !on REGISTER 1!02 !Display 2nd component of !Octal display of data
! ! ! !on REGISTER 1!03 !Display 3rd component of !Octal display of data
! ! ! !on REGISTER 1!
Noun Code !Description ! !Scale/Units!01 ! !Specify machine address !XXXXX!02 ! !Specify machine address !XXXXX!03 ! !(Spare)!04 ! !(Spare)!05 ! !Angular error ! !XXX.XX degrees!06 ! !Pitch angle ! !XXX.XX degrees!
! !Heads up-down ! !+/- 00001!07 ! !Change of program or major mode!11 ! !Engine ON enable!
35!
Verbs and Nouns in Apollo Guidance Computer Programs"
•# Verbs (Actions)"–# Display"–# Enter"–# Monitor"–# Write"–# Terminate"–# Start"–# Change"–# Align"–# Lock"–# Set"–# Return"–# Test"–# Calculate"–# Update"
•# Selected Nouns (Variables)"
–# Checklist"–# Self-test ON/OFF"–# Star number"–# Failure register
code"–# Event time"–# Inertial velocity"–# Altitude"–# Latitude"–# Miss distance"–# Delta time of burn"–# Velocity to be
gained"
•# Selected Programs (CM)"
–# AGC Idling"–# Gyro Compassing"–# LET Abort"–# Landmark Tracking"–# Ground Track
Determination"–# Return to Earth"–# SPS Minimum
Impulse"–# CSM/IMU Align"–# Final Phase"–# First Abort Burn"
36!
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A Little AGC Digital Autopilot Code"
http://www.ibiblio.org/apollo/assembly_language_manual.html!37!
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" 38!
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Lunar Module Navigation, Guidance, and Control Configuration"
39!
Lunar Descent Guidance!
40!
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Lunar Module Transfer Ellipse to Powered Descent Initiation"
41!
Lunar Module Powered Descent"
42!
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Lunar Module Descent Events"
43!
Lunar Module Descent Targeting Sequence"
•# Braking Phase (P63)"•# Approach Phase (P64)"•# Terminal Descent Phase (P66)! 44!
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Characterize Braking Phase By Five Points"
45!
Lunar Module Descent Guidance Logic (Klumpp, Automatica, 1974)"
•# 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
24
r(t) =x(t)y(t)z(t)
!
"
# # #
$
%
& & &
46!
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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
!
"
####
$
%
&&&&
47!
Corresponding Reference Velocity and Acceleration Vectors"
vr(t) = vt + a t t + jtt 2
2+ st
t 3
6
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 ! 48!
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Guidance Logic Defines Desired Acceleration Vector"
•# 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
24
•# ... but they are not"•# Therefore, feedback control is
required to follow the reference trajectory !
49!
Guidance Law for the Lunar Module Descent"
acommand (t) =ar (t)+KV vmeasured (t)! vr (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 original paper on Blackboard) !
KV :velocity error gainKR :position error gain
Linear feedback guidance law (real time !
50!
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LM Manual Control Response During Simulated Landing"
51!
Simulated LM Manual Control Response To Rate Command"
52!
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Next Time:!Commercial Space Flight"
Augustine’s Laws, Ch 1, 8, 26, 36, 37, 40; 1986 (On-Line Copy in Princeton University
Library)" "
Commercial Space Transportation: !Industry Trends, Government Challenges, and
International Competitiveness Issues, GAO 12-836T, 2013 "
"Telemetry, Communications & Tracking"[Understanding Space] Sec 13.1, "15.1 ""
53!
Supplemental Material!
54!
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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"
55!
Apollo GNC Software Documentation and Mission Support"
•# Documentation generation and review"–# GSOP: 1: Prelaunch 2: Data links 3: Digital autopilots 4:
Operational modes 5: Guidance equations 6: Control data"–# Functional description document: H/W-S/W interfaces, flowcharts 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"
56!
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Ascent (Launch) Guidance!
57!
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"
58!
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Tangent Steering Laws Approximate Gravity Turn "
•# Neglecting surface curvature "
tan!(t) = tan!o 1"ttBO
#$%
&'(
•# Accounting for effect of Earth surface curvature on burnout flight path angle "
•# Open-loop command, i.e., no feedback of vehicle state "
tan!(t) = tan!o 1"ttBO
" tan# ttBO
$%&
'()
*
+,
-
./
59!
Feedback Guidance Law "Errors due to disturbances and modeling errors
corrected by feedback control with damping "
Thrust Angle(t) = c! !c(t)"!(t)[ ]" cqq(t)q = d!
dt= pitch rate
60!
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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 "
61!
Jet Stream Profiles "•# Launch vehicle must able
to fly through strong wind profiles"
•# Design profiles assume 95th-99th-percentile worst winds and wind shear"
62!
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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"
63!
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" 64!
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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 sin!d
sinid cos!d
cosid
"
#
$ $ $
%
&
' ' '
id:desired inclination angle
!d :desired longitude of descending node65!
Guidance Program Operation: Position and Velocity "
•# Thrust acceleration estimate, aT, from guidance system"
•# Compute corresponding mass/flow rate and throttle setting, #T"
•# Position"
•# Velocity"
ryz
!
"
# # #
$
%
& & &
=r
rsin'1 ir • iq( )open
!
"
# # #
$
%
& & &
˙ r ˙ y ˙ z
!
"
# # #
$
%
& & &
=vIMU • irvIMU • iqvIMU • iz
!
"
# # #
$
%
& & & v IMU :velocity estimate in IMU frame
66!
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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 !"t !t :guidance interval
ceff : effective exhaust velocity
67!
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
68!
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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"
aT =
aTraTy
what's left over
!
"
####
$
%
&&&&
; iT =aTaT
69!