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Spacecraft Control Toolbox User's Guide V3.0

1. Simulation Table 11 1 Attitude Simulation Functions State Space Support oe Model pares Functions Output Tree Topological tree TreeAdd TreeH TreeInit TreePlot TreePrnt VIModel Body with time varying inertia WireFRB Deployable wire model WireDMch WireH Wirelnit WirePlot WireC Deployable wire model WireDMch employing kinematic con WireH straints Wirelnit WirePlot models are represented with two functions one that has only the dynamics such as RBModel and the other which appends quaternion kinematics to the equations of motion You can get linearized models of those that don t directly output state space equations by using the Jacobian function A simple rigid body attitude simulation can be embodied in the function xDot ASim x t inertia torque xDot QITOBDot x 1 4 x 5 7 RBModel x 5 7 inertia torque The first four elements of x form the quaternion from the inertial frame to the body frame The last three elements of x are the inertial body rates measured in the body frame t is not used in ASim This would be called by the script 11 4 Dynamics Models CHAPTER 11 Simulation Initializing xPlot speeds up the script considerably Notice the use of brack Listing 11 1 Rigid Body Attitude Simulation dT 0 01 nSimSteps 1000 inertia 3000 0 0 0 1000 0 0 0 1000 torque 0 0 0 xPlot zeros 7 nSimSteps tPlot zeros 1 nSimSteps x 1 0 0 0 1 0 0
2. The next listing shows an unloading momentum entry Fuel Budget Unloading momentum Unloading momentum Budgets Listing 13 7 k k 1 event k type event k description event k aCSThruster event k dVThruster event k dVTotal event k dHTotal event k dTControl event k nPulses event k duration event k regulated event k cM Listing 13 8 Event 4 k k 1 event k type event k description event k aCSThruster event k dVThruster event k dVTotal event k dHTotal event k dTControl event k disturbance event k nPulses event k duration event k regulated event k cM 13 6 Fuel Budgets delta h Delta H L2 3 ANS 6 28 9 10 LT 22 CHAPTER 13 Budgets Listing 13 9 Fuel Budget Using ACS thrusters Event 5 Using thrusters for ACS k k 1 event k type acs event k description ACS Disturbance event k aCSThruster 123456789 10 11 12 event k dVThruster A event k dVTotal event k dHTotal 7 event k dTControl 1 event k disturbance 03170 event k nPulses event k duration 10000 event k regulated 0 event k cM 0 0 0 The next listing shows an example of firing a few pulses Listing 13 10 Fuel Budget Firing a few pulses Event 6 Firing a few pulses k k 1 event k type pulsed event k
3. the List UI Element that creates a list of checkboxes EditPM CHAPTER 8 UlElements DataStructureList DataStructureList is implemented as shown in Listing 8 1 on page 17 Listing 8 4 DataStructureList d a rand 3 3 d b rand 5 1 d c rand 1 4 d d struct x rand 2 2 y rand 3 3 z Mike h dataStructureList UIElement parent h fig height 40 position 155 5 200 200 width 180 style datastructurelist datastructure d This will create a list of any data structure List List is implemented as shown in Listing 8 1 on page 17 The list property is Listing 8 5 List s One Two Three Four Five Six Seven EBight for k 1 length s for j 1 4 c k j string Col num2str j s k style edit end end h list UIElement parent h fig style list width 130 position 360 5 135 200 list an n by m list of uicontrols Any uicontrol can be included 8 18 DataStructureList CHAPTER 8 UlElements ListWithButton ListWithButton is implemented as shown in Listing 8 1 on page 17 This cre Listing 8 6 ListWithButton h listWithButton UIElement parent h fig style listwithbutton position 5 5 145 100 buttonstring Pick One hS get h listWithButton userdata set hS list string One Two Three ates a listbox with a pushbutton Either clicking on an ele
4. Enter your user id and password and click ok The same dialog will appear Enter the data again You will then see the upgrades list 1 6 Background CHAPTER 1 Installing The Spacecraft Control Toolbox Figure 1 4 Last modified 23 Jun 99 08 46 Nd May 99 16 22 WHtay 77 10 30 tafe os Upgrades 4 Anue Gdad d Back forward Renai Home Search Wetscape majes Prit Securiy Stoo Size Description 21 Dao 98 14 44 2 9 2i 14 Zi Deo 70 14 7 E Princeton SATELLITE FITE Poa nome PrAducl m omanan Lonlacl of Tiai 0s What s Hew ObjsetAgent Oreduct Documentation Discussion Bourg Sobtware Updates deb Opportunities Poo Amire amp Pagers apace Data Links All of the files are stored in archives The files and their types are listed in Table 1 1 Archives File Macintosh Windows UNIX Toolbox Functions SC sit SC zip SC tar gz mat Files SCMat sit SCMat zip SCMat tar gz Table 1 1 on page 7 Download all of the files in the appropriate column Your net browser should decompress the files You need version 5 1 of the Stuffit decompression Background utility on the Macintosh to decompress the sit files 1 7 CHAPTER 1 Installing The Spacecraft Control Toolbox Included Files The files listed in Table 1 2 on page 8 Table 1 2 Files included in the Spacecraft Control Toolbox Files Explanation SC Directory of toolbox directories catalog pdf Ca
5. t 0 for k 1l nSimSteps xPlot k x tPlot k t zI0 1 3 4 0 0 0 x RK4 ASim x dT t inertia torque t t dT end Plot2D tPlot xPlot Time sec Q1 Q2 03 Q4 Wx Wy Wz Rigid Body ets in x to make the script easier to read The results are shown in the follow ing figure Figure 11 1 Dynamics Models Rigid body simulation Body Rates Body Rates n T L 10 20 30 40 50 60 Time sec CHAPTER 11 Simulation Wire Model The wire model simulates a spacecraft with deployable wires Two models are included One includes the extensional dynamics modeling the stretching of the wire The second applies kinematic constraints to control the length between wire nodes The former can introduce very high frequency dynamics into the simulation but is useful if you expect the wire to stretch The latter is useful for most scientific satellites with copper or aluminum wires Either model can simulate deployment and both account for system center of mass motion A spacecraft can have any number of wires The configuration is illus trated below Figure 11 2 Wire model 11 6 Core Attach Point Node Reference Point Wire Model CHAPTER 11 Simulation The following script illustrates the use of the model Listing 11 2 Wire Simulation Header This script demonstrates the deployment of the wire from the spacecraft
6. called All of the actions come about when you click buttons on the window You run GUIPlugin by typing GUIPlugin If a GUIPlugin window already exists it will bring it to the front 9 26 Writing Your Own GUI Function CHAPTER 9 GUI Plug Ins The CreateGUI subfunction draws the window and initializes all the plug Writing Your Own GUI Function 9 27 CHAPTER 9 GUI Plug Ins ins Listing 9 2 CreateGUI function CreateGUI The figure window AP ol 5 5 760 480 h fig figure name GUIPlugInDemo Units pixels Position 40p 4 600 p 3 4 resize off NumberTitle off tag GUI PlugIn Demo CloseRequestFcn CreateCallback quit xe Buttons v parent h fig units pixels fontunits pixels r p 1 p 3 h run uicontrol v Position r 205 10 60 20 callback CreateCallback run string Run h quit uicontrol v Position r 140 10 60 20 callback CreateCallback quit string QUIT h help uicontrol v Position r 75 10 60 20 callback CreateCallback help string HELP Initialize the plugins 2 2 cB GUIPlugiIn changed h orbitDisplayTag OrbitDisplayPlugIn initialize h fig 5 250 290 185 El yy h plotPlugInTag PlotPlugin initialize h fig 5 10 290 235 h timePlugInTag TimePlugin initialize h fig 300420450
7. 0 L ji L L L L L L L 0 5 10 15 20 25 30 35 40 45 50 Torque microNm The specific impulse assumes very short pulses Control Ackerman s pole placement formula can be used to critically damp a double integrator Ackerman s formula should be used with caution for higher order systems a l 0 1 0 0 r b 0 1 p Sort 2 2 1 j 1 j k Acker a b p k 1 00000000000000 1 41421356237310 eig a b k ans 0 70710678118655 0 707106781186551 0 70710678118655 0 707106781186551 In the following example we use a lead lag compensator to compensate a dou ble integrator The double integrator plant is as follows 4 8 Example Functions CHAPTER 4 Basic Functions a 0 1 0 0 b 0 1 C 1 Oly Create a lead network with 60 deg of phase lead at 1 rad sec aC bC cC dC LeadLag 1 60 1 The following demonstrates automatic plotting LeadLag 1 60 1 Figure 4 4 LeadLag Input 1 to Output 1 D a Magnitude db s a 8 T T T a T o D i Angle deg nN ao D a Oo oO oO Oo T T T T L L we 10 10 10 Frequency rad sec Bo Generate the closed loop system aT bT cT dT CLoopS a b c aC bC CC dc The closed loop eigenvalues eig aT ans 1 72303339062007 3 41662654402684i 1 72303339062007 3 41662654402684i1 0 28598402632875 Example Functions 4 9 CH
8. Customization Pane The first four buttons are the names of functions the propagator should call The default names in the GUI are default functions When you hit initialize the function will display an initialization GUI The Noise Function returns the plant noise matrix q for the covariance propa gation pDot f p p f q where f is the matrix of partials of the right hand side of the orbit The initial mass is the mass of the spacecraft The next two parameters relate to the integration accuracy Rel Tolerance gives the relative error tolerance The estimated error in each integration step satisfies Using the Graphical User Interface 6 41 CHAPTER 6 Orbit Propagation e i lt max RelTol abs y i Tol i Integration Tolerance gives the absolute error tolerance which applies to all components of the solution vector The next two checkboxes allow you to select planetary perturbations and or to propagate the covariance When you select planetary perturbations you will get the moon and the sun if the earth is selected as the center through the elements pane or the earth and the sun if the moon is selected as the center If you select other planets or moons you will not get any perturbations When you select Propagate Covariance the initial covariance input will be enabled You should enter the initial state covariance into the box You need only enter upper or lower triangular information The propagator automatica
9. On the central body force 0 0 0 On the central body Create the wires You can have as many wires as you like Each column repre sents one wire If you are using the constrained equations you can ignore the spring and damping constants Listing 11 5 Wire Simulation Initialization of the wire model 11 8 The wire model Each column is one wire oe nNodes 3 3 rWireBase 0 0 0 6 0 6 0 0 1WireMax 0 04 0 08 massWire 0 4 0 4 kSpring 30 3 0 cSpring 0 5 0 5 cDeploy cSpring nodeDeploying 0 0 vDeploy 0 001 0 001 m sec Initialize the wire data structure oe wireDS x WireInit nNodes mass massWire Used only by WireFRB Used only by WireFRB Used only by WireFRB To start undeployed set these to 3 lWire cSpring vDeploy cDeploy nodeDeploying rWireBase r r0 inertia gGOn Wire Model ax kSpring ECI V ECI q omega CHAPTER 11 Simulation Alpha is a constraint torque gain mu determines the damping omega the con straint stiffness The number of iterations is generally less than 2 Listing 11 6 Wire Simulation Kinematic constraints oe If using the kinematic constraints oe penalty alpha 1le6 penalty mu 1 penalty omega 10 penalty nIts a Initialize the plotting arrays Listing 11 7 Wire Simulation Initialization of plotting Wire Model Plotting arrays xPlot
10. Spacecraft Control Toolbox User s Guide V3 0 This software described in this document is furnished under a license agreement The software may be used copied or translated into other languages only under the terms of the license agreement Spacecraft Control Toolbox User s Guide April 1999 Copyright 1996 1999 by Princeton Satellite Systems Inc All rights reserved Any provision of Princeton Satellite System Software to the U S Government is with Restricted Rights as fol lows Use duplication or disclosure by the Government is subject to restrictions set forth in subparagraphs a through d of the Commercial Computer Restricted Rights clause at FAR 52 227 19 when applicable or in sub paragraph c 1 ii of the Rights in Technical Data and Computer Software clause at DFARS 252 227 7013 and in similar clause in the NASA FAR Supplement Any provision of Princeton Satellite Systems documentation to the U S Government is with Limited Rights The contractor manufacturer is Princeton Satellite Systems Inc 33 With erspoon Street Princeton New Jersey 08542 MATLAB is a registered trademark of The MathWorks Inc Macintosh is a registered trademark of Apple Computer Inc Silicon Graphics is a registered trademark os Silicon Graphics Adobe Acrobat and FrameMaker are trademarks of Adobe Systems Incorporated All other trademarks are the property of their respective holders All other brand or product names are trad
11. When you change anything in a plug in the following code is executed Listing 9 6 Update GUIPlugin function Update Get the simulation data oP ol ty I GetH im n Update the spacecraft state 2 o o if isfield Sit evoke Vr QLVLH QLVLH sim orbit r else QLVLH 1 0 0 0 end amp isfield sim orbit v GetSimData h sim orbit v h g body 1 bHinge q QPose qLVLH if isfield sim orbit r h g rECI else h g rECI end h g qLVLH qLVLH DrawSCPlugin update spacecraft h scWindowTag h g sim time h orbitDisplayTag OrbitDisplayPlugin clear plot DrawSCPlugin update planet PutH h h scWindowTag sim orbit r sim orbit el 1 0 0 jDEpoch sim orbit planet sim orbit planet This function gets the data from the elements and time plug ins Listing 9 7 function sim GetSimData h Get the data from the plug ins 2 2 sim orbit ElementsPlugIn sim time TimePlugIn get get Writing Your Own GUI Function Get data from the plug ins h elementsPlugInTag h timePlugInTag 9 31 CHAPTER 9 GUI Plug Ins The following are utility functions for getting data from the figure handle put ting data into the figure handle and creating uicontrol callback strings Listing 9 8 Utilities Put the data into the figure handl functio
12. 0 2 0 2 lo oO io t fo O lo Ove 8 0 8 0 3 0 OD 25 8 09 0 8 20 0 8 8 0 8 0 8 0 0 1522 0 0 0 0 I 1 i 1 0 0 0 0 13 3 CHAPTER 13 Budgets In the next listing the thruster performance data is collected into data struc tures Listing 13 3 o for k riseT fallT u 20 12 ime ime systemID I3 lt 16 iSP thrust riseT fallT u Ha ime ime systemID Fuel Budget Thruster performance data 2 07 100 100 10 Collect thruster data into the data structures 1 iSP thrust See REA m for definition of this array 0 016 0 016 u k r k Odd k li 6 3S REA m for definition of this array In seconds r r 1 You can have as many fuel systems as you 100 250 10 0 828e 0 016 0 016 u k r k Odd k 6 In this case just multiplying this by pressure r r 1 The next listing has general spacecraft data Listing 13 4 oe Fuel Budget General spacecraft data Sys Sys Sys pre pre dry fue thr con xx x xe KM KM MM KM M temTemp temVol temFuel ssurantMass ssurantR ass 1Density usterData trolDT 13 4 Fuel Budgets Assemble general spacecraft data regulatedPressure 250 250 6895 298 298 1 6505e 01 1 6505e 01 1 1789e 02 1 1789e 02 1 8372e 01 1 8372e 01 Mo
13. Simulation 9 1 Table 11 1 Figure 11 1 Listing 11 1 Figure 11 2 Listing 11 2 Listing 11 3 Listing 11 4 Listing 11 5 Listing 11 6 Listing 11 7 Listing 11 8 Listing 11 9 Figure 11 3 Listing 11 10 Figure 11 4 Listing 11 11 Listing 11 12 Listing 11 13 Listing 11 14 Listing 11 15 Figure 11 5 Listing 11 16 Listing 11 17 Listing 11 18 Attitude Simulation Functions 9 3 Rigid body simulation 9 5 Rigid Body Attitude Simulation 9 5 Wire model 9 6 Wire Simulation Wire Simulation Wire Simulation Wire Simulation Wire Simulation Wire Simulation Wire Simulation Wire Simulation Wire simulation Wire Simulation Header 9 7 Initialization 9 7 Spacecraft properties 9 8 Initialization of the wire model 9 8 Kinematic constraints 9 9 Initialization of plotting 9 9 Simulation loop plotting 9 10 Dynamics model 9 10 Results 9 11 Plotting 9 11 Topological Tree 9 12 Tree Simulation Tree Simulation Tree Simulation Tree Simulation Tree Simulation Tree Simulation Tree Simulation Tree Simulation NORAD m 9 16 Orbit Propagation 19 Figure 12 1 Table 12 1 Table 12 2 Table 12 3 Table 12 4 Figure 12 2 Orbit Propagatio Element sets 23 Initialization 9 13 Adding bodies 9 13 A hinge acceleration 9 13 A low earth orbit 9 14 Initialization 9 14 One of several plots 9 15 The simulation loop 9 15 Plotting 9 15 n GUI 21 Stopping Conditions 26 PropagateOrbitPlugin API 29 Plugin Fu
14. This model assumes that the center of mass of the spacecraft does not move as the wires deploy The simulation models the wire as a string of masses connected by springs Orbit dynamics and gravity gradient are included JP oP X Copyright 1997 Princeton Satellite Systems Inc All rights reserved JP oP oP oN Clean up the workspace A ol close all clear all Constants ct Hh K o c He 0u 0 ot m SA These parameters manage the script kConst determines whether the con strained model is to be used Listing 11 3 Wire Simulation Initialization Simulation parameters tSim 120 0 dT 0 125 nSim tSim dT nPlot min tSim dT 200 nPMax floor nSim nPlot nPlot floor nSim nPMax gGOn false kConst true Print the time to go message every nTTGo steps Go 1000 4 Time statistics function oe ol tToGoMem ratioRealTime zeros 1 3 0 The core body information The model includes orbit dynamics Wire Model 11 7 CHAPTER 11 Simulation Listing 11 4 Wire Simulation Spacecraft properties Spacecraft properties mass 800 kg ro 0 0 0 inertia 104 0 0 0 107 8 0 0 0 125 4 Orbital elements a i Ww e M 0 j 7000 0 0 0 0 0 3 98600436e5 muEarth Initial rigid body state oP ol rECI vECI El2RV el omega 0 0 0 5 pi 30 q 1 0 0 0 torque 0 0 0
15. description Short Pulse event k aCSThruster 1 2 event k dVThruster 7 event k dVTotal E event k dHTotal A event k disturbance R event k nPulses Won t use any fuel this way event k pulsewidth 0 05 event k duration A event k regulated 0 event k cM 0 0 0 Listing 13 11 Fuel Budget Example Fuel Budgets FBudget event x Generates the following results in TestBudget Propellant budget 19 Sep 1997 Item Description Tota 1 Initial State 1190 2 Delta V Continuous 1153 3 Delta V Off Pulse 1099 4 Delta H 1099 5 ACS Disturbance 1087 6 Short Pulse 1087 1 Fuel Remaining Fuel Used 117 89 117 8 0 000 0 000 2 99 36 99 36 18 525 18 525 2 72 02 72 02 27 346 27 346 1 72 02 72 02 0 001 0 001 1 66 16 66 16 5 862 5 862 1 66 16 66 16 0 000 0 000 1 6 pt type Pressure 4e 06 2 4e 06 4e 06 2 4e 06 7et 06 1 7e 06 2e 06 1 2e 06 2e 06 1 2e 06 2e 06 1 2e 06 ACS Isp 0 00 100 02 100 00 100 41 100 39 100 50 13 7 CHAPTER 13 Budgets For east west stationkeeping the delta V required because of longitude drift due to the earth s tesseral gravitational harmonics is computed by dVEW dTEW DVLDrift box scLon where the first number is the size of the stationkeeping box in degrees and the second is the spacecraft longitude DVLDrift outputs the delta V required per maneuver and the time between maneuvers For north south st
16. force is in the LVLH frame FAero Computes aero forces in the ECI frame FSolar Computes solar forces in the ECI frame FPlantNoise The Q matrix in the covariance propagation equation FAtmDensity Atmospheric density The baseline model is Jacchia J70 Each model supplied with the toolbox has its own GUI These popup when you hit the Initialize button next to each function s name 6 44 Plugin Functions CHAPTER 6 Orbit Propagation Figure 6 2 FEngine GUI The FEngine model allows you to enter a constant force in the ECI frame and a constant mass change rate Figure 6 3 FAero GUI Plugin Functions 6 45 CHAPTER 6 Orbit Propagation The FAero model assumes a flat plate spacecraft with the plate always normal to the velocity vector The input is the product of the drag coefficient and plate area Figure 6 4 FSolar GUI Solar Force Model Initialization Absorbed Coefficient _ a a T The FSolar model is a flat plat model in which the plate is always normal to the sun vector 6 46 Plugin Functions CHAPTER 6 Orbit Propagation Figure 6 5 FPlantNoise GUI FPlantNoise function assumes a constant plant noise covariance matrix The inputs are the uncertainty in body accelerations Plugin Functions 6 47 CHAPTER 6 Orbit Propagation The FAtmDensity GUI gives inputs for the Jacchia J70 model Listing 6 1 FAtmDensity GUI O S Atmospheric Dens
17. xPlot wPlot X Z Spin Axis and Target Plot2D tPlot ePlot radToDeg Time sec Roll deg Pitch deg Attitude Errors Figure 10 2 on page 13 shows the results of Plot V It shows the spin axis unit vector It starts as 0 0 1 the highest point on the plot and as the spacecraft acquires picks up y and x components until it traces out a circle in the xy plane Figure 10 2 TMAPSim Motion of the unit vector Using the Spacecraft Control Toolbox 10 13 CHAPTER 10 A Worked Design Example Figure 10 3 TMAPSim Precession of the unit vector Summary 10 14 Precession Angle T Precession Angle deg a T i 5 i L L L 0 500 1000 1500 2000 2500 3000 3500 4000 Time sec As can be seen from the plots the control system successfully acquires and tracks the target The overall pointing accuracy is better than 0 2 deg All of the plots were generated using Spacecraft Control Toolbox functions All of the design functions and simulated functions fit in a single MATLAB script The second plot shows the unit vector for the spin axis of the spacecraft in three dimensional space Initially it is aligned with the z axis so its x and y compo nents are zero After acquisition the x and y axes trace out a circle in the xy plane and the z value is constant The control system presented here is only part of the overall control architec ture that includes not onl
18. zeros length x nPlot hPlot zeros 1 nPlot tPlot zeros 1 nPlot nP 0 kP 0 t 0 Initialize the status message function 2 2 oe ee ratioRealTime tToGoMem TimeToGo nSim 0 tToGoMem 0 aT CHAPTER 11 Simulation The simulation loop The first part shows the plotting functions Listing 11 8 Wire Simulation Simulation loop plotting for k 1 nSim Print the status message dP 0 if floor k nTTGo k nTTGo ratioRealTime tToGoMem TimeToGo nSim k tToGoMem ratioRealTime dT end Plotting if nP kP kP 1 xPlot kP x hPlot kP WireH x wireDS tPlot kP t nP nPMax 1 else nP nP 1 end This is the simulation Wi reDMch simulates the deployment mechanism It just assigns a nonzero extensional rate to the innermost wire segment Listing 11 9 Wire Simulation Dynamics model Choos ither th xtensional stiffness or constrained wire models oA o if kConst true x RK4 WireC x dT t wireDS muEarth torque force penalty i else x RK4 WireFRB x dT t wireDS muEarth torque force end t t dT wireDS x WireDMch wireDS x t end 11 10 Wire Model CHAPTER 11 Simulation The following listing shows the plotting code Listing 11 10 Wire Simulation Plotting Output domega xPlot 11 xPlot 11 1 xPlot 12 xPlo
19. Listing 10 5 TMAPSim ACS design Attitude Loops zeta 0 7071 Damping ratio wN 0 53 Closed loop undamped natural frequency wR 4 0 Rate filter break frequency tau 50 Integrator time constant aRoll bRoll cRoll dRoll PIDMIMO inr 1 1 zeta wN tau wR tSamp Delta aPitch bPitch cPitch dPitch PIDMIMO inr 2 2 zeta wN tau wR tSamp Delta Listing 10 6 on page 6 gives the yaw rate loop that will maintain the MAP spin rate This uses the same PI controller as the reaction wheels but with a slower time constant Listing 10 6 TMAPSim Rate loop Rate Loops oe zeta 1 0 Damping ratio wN 0 5 Closed loop undamped natural frequency aYaw bYaw cYaw dYaw PIDesign zeta wN inr 3 3 tSamp Delta Now that the controller design is complete it is time to run a simulation to test the system Of course we should also do frequency domain analysis of the entire controller Even though we used SISO design techniques this is really a MIMO design The controller has fast inner loops to control the wheels and slower outer loops to control the attitude Several tools exist in SCT for analyz ing such systems 10 6Using the Spacecraft Control Toolbox CHAPTER 10 A Worked Design Example The first step is to initialize the control system We ve turned off the momen tum management system Listing 10 7 TMAPSim Initialize the control system Initialize t
20. Stability 4 7 MagTComp 4 8 LeadLag 4 9 Torque transmission 4 10 Nichols plot 4 11 Bode Plot 4 11 AtmDens1 4 13 AtmDens2 4 14 A sine wave using Plot2D 4 15 Pivot Mechanism 4 15 Elliptical orbit 4 16 Blowdown curve 4 17 Earth Albedo 4 17 Data Structures 5 1 Table 5 1 Table 5 2 Figure 5 1 Listing 5 1 Object oriented design terms 5 4 Classes 5 5 Second order response 5 6 Example of using the statespace class 5 6 Coordinate Transformations 6 1 Using the CAD Functions 7 1 Table 7 1 Figure 7 1 Listing 7 1 Figure 7 2 Table 7 2 Table 7 3 Table 7 4 Listing 7 2 Figure 7 3 Table 7 5 Figure 7 4 Table 7 6 Figure 7 5 Table 7 7 Build3DSC actions 7 2 Build3DSC 7 3 Adding a component by defining faces and vertices 7 4 Geometry of a component 7 5 Predefined surfaces 7 5 Geometric primitives 7 6 Component properties 7 7 Example body data structure 7 9 Topological tree 7 10 DrawSC Modes 7 10 DrawSC 7 11 Disturbance 7 12 Disturbance display 7 13 CAD File Importing 7 13 Chapter 8 Chapter 9 Chapter 10 UlElements 15 Figure 8 1 UIElementDemo 16 Listing 8 1 EditPM 17 Listing 8 2 EditScroll 17 Listing 8 3 CheckBoxList 17 Listing 8 4 DataStructureList 18 Listing 8 5 List 18 Listing 8 6 ListWithButton 19 GUI Plug Ins 21 Figure 9 1 GUIPlugIn on starting 22 Figure 9 2 GUIPlugIn after changing inputs 23 Figure 9 3 GUIPlugIn with the earth as center 23 Figure 9 4 Selecting planets
21. be defined either as an RGB vector m faceColor 1 0 0 0 0 0 m edgeColor 1 0 0 0 0 0 m specularStrength 2 m diffuseStrength 0 5 m specularExponent 10 m specularColorReflectance 0 for red or using a name Unless you are very picky about the image it is not necessary to specify anything except the faceColor Table 7 2 Predefined surfaces Surfaces Ug lleue e eudlil Building a Spacecraft Model 7 5 CHAPTER 7 Using the CAD Functions Table 7 2 Predefined surfaces Surfaces T CO gold foil aluminum steel aluminum truss radiator white Moyles The surface properties do not have any effect on the thermal or optical proper ties they are solely for display purposes The other way to define an object is with geometric primitives Available geo metric primitives are given in Table 7 3 on page 6 Table 7 3 Geometric primitives m type m info antenna x X width y y width d depth theta angular width of the antenna associated with d u boresight vector t X axis unit vector n number of divisions box x y z dimensions cylinder 5 aU Upper radius Sa Lower radius ZUpper Upper z limit ZLOwer Lower z limit 7 6 Building a Spacecraft Model CHAPTER 7 Using the CAD Functions Table 7 3 Geometric primitives m type m info ellipsoid
22. by other functions Will all be eliminated in a future version of the toolbox Math Math functions Orbit Orbit analysis and dynamics functions Prop Propulsion system models SCData Data used by the functions Scripts Example scripts Sensor Sensor models SimulinkIF Interface function for Simulink SNPC Functions used to implement a sun nadir pointing control system Thermal Thermal analysis functions t New in V3 0 CHAPTER 4 Basic Functions Function Features Functions have several features that are helpful to understand when using them Features that are available in the functions are listed in Table 4 2 Features in SCT functions 4 4 Built in demos Features Default parameters Built in plotting Error checking Variable inputs These are illustrated in the examples given below Built in demos Many functions have built in demos A function with a built in demo requires no inputs and produces a plot for a range of input parameters to give you a feel for the function An example of a function with a built in demo is Atml Dens2 which generates the following plot Function Features CHAPTER 4 Basic Functions Figure 4 1 Atmospheric density from AtmDens2 Atmospheric Density 10 T T T Density kg m 0 100 500 300 400 500 500 700 500 300 1000 Altitude km Default parameters Most functions have default parameters There are
23. data structure For example you could implement the above data structure with a cell array b 1 1 0 0 b 2 Sun Sensor Unlike data structures you can concatenate cell arrays The following C afa Bests would give you c 1 1 0 0 c 2 Sun Sensor e 3 1 0 0 c 44 Sun Sensor You can perform operations on cell contents For example af 1 diag 1 2 3 b 1 1 1 1 when multiplied together give 1 2 3 Cell arrays are a convenient way of storing strings For example you could write a First String 3 Second Long String being careful to make sure they were the same length or write CHAPTER 5 Data Structures Classes a l First String af2 Second String uicontrol functions will often take cell arrays of strings Classes are a form of data structure in which both the data and the operations that can be done on the data are defined together The Spacecraft Control Tool box includes several classes For example you might define a class called names You could then create the method which would overload the MAT LAB function so that if you let a names Emily b names Stuart would be the same as c names Emily Stuart names would be the class constructor and is a method that overloads An important aspect of a class is that you cannot get access to the internal data s
24. directories stay open in the hierarchical display The Example Pane This pane gives an example for the function displayed Not all functions have examples The edit display has scroll bars You can edit the example create new examples and save them using the buttons below the display To run an example hit the Run Example button You can include comments in the example by using the symbol Find All Button Find all returns to the list of all of the functions This is used after one of the search options has been used Find A11 will return to either an alphabetical or hierarchical list depending on which is selected above the file pane File Help 2 7 CHAPTER 2 Getting Help Figure 2 9 Find all 2 8 Devar walar ie a arkit plea t rhit swale i ie in aha DCI irem PrinceronSATELLITE abe He ce haj Sa L GC 5 alpha ba I Alpita ical Wi Hararchicel bears i Eei ley L Legible al she semiding mda WA ef rh tike Ample cd a mem wnb rompers wi paip bats wah of a er Sith a gt thi Hiit phe dwp a Light woreraiers im ba BCD deen cs bjim ier of cha GO coe rv de ABR Dect i bet lp kita SS CTS CTT Edit Button This opens the MATLAB edit window for the function selected in the list Search File Names Button Search file names for a string This function looks for exact but not case sensi tive matches The file display displays all matches File Help CHAPTE
25. following table You enter the needed 7 12 Table 7 6 Disturbance Disturbance Description Torque Force Albedo Reflected sunlight from a Yes Yes planet Radiation Infrared radiation from a Yes Yes planet RF Radiation from antennas Yes Yes Gravity Gradient Torque due to the mass dis Yes No tribution of a satellite Magnetic Magnetic dipoles on the Yes No spacecraft Aero Aerodynamic interaction Yes Yes Optical Sunlight Yes Yes Thermal Thermal radiation from Yes Yes radiators etc data either in your script or using the interactive property editor Disturbances can be used either in batch mode by inputting arrays of kinematic data in the spacecraft data structure or to calculate one disturbance vector at a time In batch mode it will perform Fourier analysis on the distur bances torques and forces In interactive mode you can run it concurrently with DrawSC to visualize the spacecraft SCDisturb shows you how to run it interactively The disturbance display shown below gives you a snapshot of the disturbance results When you enter vertex lists you must organize the vertices into triangles oth erwise Disturbance will not use them Computing Disturbances CHAPTER 7 Using the CAD Functions Figure 7 5 Disturbance display a Disturbances B lbt in lbf X Torque YTorque Z Torque X Force Y Force Z Force
26. in the elements plugin 24 Figure 9 5 GUIPlugIn at the end of the simulation 25 Figure 9 6 GUIPlugIn 3D Spacecraft Display 25 Listing 9 1 GUIPlugin 26 Listing 9 2 CreateGUI 28 Listing 9 3 Initializing the simulation 29 Listing 9 4 The simulation loop 30 Listing 9 5 Plotting 30 Listing 9 6 Update GUIPlugin 31 Listing 9 7 Get data from the plug ins 31 Listing 9 8 Utilities 32 A Worked Design Example 8 1 Figure 10 1 Listing 10 1 Listing 10 2 Listing 10 3 Listing 10 4 Listing 10 5 Listing 10 6 Listing 10 7 Listing 10 8 Listing 10 9 Listing 10 10 Listing 10 11 Listing 10 12 Listing 10 13 The Microwave Anisotropy Probe 8 2 TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim TMAPSim File header 8 4 Sampling intervals 8 4 Mass properties 8 5 Tachometer loop design 8 5 ACS design 8 6 Rate loop 8 6 Initialize the control system 8 7 Set up the simulation 8 8 Start of the simulation loop 8 9 Sensor models 8 9 Control system 8 10 Error computation 8 10 Attitude loop 8 11 iii Chapter 11 Chapter 12 Listing 10 14 Listing 10 15 Listing 10 16 Listing 10 17 Figure 10 2 Listing 10 18 Figure 10 3 TMAPSim Compute wheel speed demand 8 11 TMAPSim RWA tach loops 8 11 TMAPSim Simulation 8 12 TMAPSim Saving plot information 8 12 TMAPSim Motion of the unit vector 8 13 TMAPSim Plotting 8 13 TMAPSim Precession of the unit vector 8 14
27. is just qCToA QPose qATOC 6 2 Transformation Matrices CHAPTER 6 Coordinate Transformations You can extract Euler angles by eATOC Q2Eul qATOC or matrices by mAToC Q2Mat qAToC If we convert the three Euler angles to a quaternion QIToB Eul2Q e qIToB will transform vectors represented in I to vectors represented in B This quaternion will be the transpose of the quaternion that rotates frame B from its initial orientation to its final orientation or gqIToB QPose qBInitialToBFinal Given a vector of small angles eSma11 that rotate from vectors from frame A to B the transformation from A to B is uB eye 3 SkewSymm eSmall uA where SkewSymm 1 2 3 ans 0 3 2 3 0 1 2 1 0 Note that SkewSymm x y is the same as Cross x y Quaternions 6 3 CHAPTER 6 Coordinate Transformations 6 4 Quaternions CHAPTER 7 Using the CAD Functions CHAPTER 7 Using the CAD Functions This chapter shows you how to use the CAD functions These functions allow you to work with 3 dimensional representations of your spacecraft You can assemble spacecraft from components and use the resulting models for multi body simulations disturbance analysis and visualization Introduction The Spacecraft Control Toolbox provides several CAD functions to simplify your design and simulation tasks You can create a spacecraft model with Build3DSC or import it using the LoadCAD fu
28. x sim orbit r sim orbit v jD sim time jDEpoch nSim duration sim time dT y 1 zeros 6 nSim jo 0 DrawSCPlugIn bring to front h scWindowTag Writing Your Own GUI Function 9 29 CHAPTER 9 GUI Plug Ins The simulation is run with the following code Listing 9 4 The simulation loop for k 1 nSim Plotting a y 1 k x t c R ll Transformation matrices QLVLH QLVLH x 1 3 x 4 6 h g body 1 bHinge q QPose qLVLH h g rECI x 1 3 h g qLVLH qLVLH DrawSCPlugin update spacecraft h scWindowTag h g jD oe Propagate the orbits oe x RK4 FOrb x sim time dT t car sim orbit mu Update the time P 0 ct t sim time dT jD jD sim time dT 86400 end The plots are created with the following code Listing 9 5 Plotting if isempty y PlotPlugIn clear plots h plotPlugiIntTag k p xLabel Time sec p yLabel xECI yECI ZECI vXECI vYECI vZECI p title p yLabel PlotPlugIn update labels h plotPlugInTag p PlotPlugIn add points h plotPlugInTag struct x u y y 7 PlotPlugin plot h plotPlugInTag end OrbitDisplayPlugiIn draw h orbitDisplayTag y 1 1 3 sim time jDEpoch u 86400 sim orbit planet PutH h 9 30 Writing Your Own GUI Function CHAPTER 9 GUI Plug Ins
29. 0 90 100 Step Example Functions 4 17 CHAPTER 4 Basic Functions 4 18 Example Functions CHAPTER 5 Data Structures CHAPTER 5 Data Structures MATLAB 5 x have a number of useful new data types These are used exten sively in the newer functions in the toolbox All of the CAD and GUI functions use them This chapter discusses data structures and cell arrays and gives some tips on how to use them Data Structures Data structures allow you to collect disparate data elements into a single vari able For example suppose you needed to pass the name of a sensor and its unit boresight vector to a function You might write u 1 0 0 name Sun Sensor x Sensor name u With data structures you can write a struct uw 1 0 0 name Sun Sensor or a u 1 0 0 a name Sun Sensor instead Now your function call is x Sensor a You can imagine how much more convenient passing a data structure is than passing a long list of inputs If you say b a b will be b u 1 0 0 b name Sun Sensor You cannot add data structures or use arithmetic operations on them 5 2 Data Structures CHAPTER 5 Data Structures Cell Arrays Cell Arrays You can have an array of data structures For example u 1 a eye 3 u 1 b rand 3 4 u 2 a 6 eye 3 u 2 b rand 3 4 A cell array is an array in which any element can contain any other type of
30. 1 Data Structures 5 2 Cell Arrays 5 3 Classes 5 4 SCT Classes 5 5 Coordinate Transformations 6 1 Transformation Matrices 6 2 Quaternions 6 2 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Using the CAD Functions 7 1 Introduction 7 2 Building a Spacecraft Model 7 2 Introduction 7 2 Introduction 7 3 Adding a Component 7 3 Adding a Body 7 9 Linking Bodies 7 10 Displaying a Spacecraft Model 7 10 Interfacing to the Tree Model 7 11 Computing Disturbances 7 12 Importing CAD Models 7 13 UlElements 15 UlIElement 16 EditPM 17 EditScroll 17 CheckBoxList 17 DataStructureList 18 List 18 ListWithButton 19 Closing UIElements 19 GUI Plug Ins 21 GUIPlugIn 22 Writing Your Own GUI Function 26 A Worked Design Example 8 1 The MAP Mission 8 2 Control Modes 8 2 Sensing and Actuation 8 3 Control System Design 8 3 Simulation Results 8 3 Using the Spacecraft Control Toolbox 8 4 Summary 8 14 iii Chapter 11 Simulation 9 1 Dynamics Models 9 3 Wire Model 9 6 Tree Model 9 12 Orbit Simulation 9 16 Introduction 9 16 NORAD Elements 9 16 Chapter 12 Orbit Propagation 19 Orbit Propagation 20 Introduction 20 Limitations 20 Using the Graphical User Interface 21 Overview 22 Panes 22 Setting Up a Batch Script 29 Plugin Functions 30 Building a Plugin Function 34 Reference Frames 38 Coordinate Transformations 38 Finding ECI ECR coincidence 38 Sun 39 Interfacing to STK 39 Ground Coverage 40 Ch
31. 39 GPMargin 4 12 Index 1 INDEX Gravity Model GEM T1 20 JGM 2 20 JGM 3 20 WGS 84 20 GroundCoverage 40 GUIPlugIn 22 gyro 8 2 H help 2 10 help system 2 2 HFS 1 3 hydrazine thruster 8 2 inclination drift 10 8 ISO 1 3 J Jacobian 9 4 JD2000 39 JD2Date 4 14 Julian Date 39 K Kalman Filter 8 3 L LeadLag 4 9 List 16 ListWithButton 16 LoadCAD 7 2 Macintosh 1 3 MagTComp 4 7 Mat2Q 6 2 MathWorks 20 Index 2 Matlab 4 6 4 x 4 5 5 x 4 5 MATLAB 1 2 Matlab Command Window 2 10 MBModel 4 12 MergeConstantDB 3 4 mex 1 2 Microwave Anisotropy Probe 8 2 monitor resolution 1 2 N Netscape 1 2 Nichols 4 10 NORAD 9 16 north south stationkeeping 10 8 O ObjectAgent 1 2 online help 2 10 orbit 22 OrbitDisplayPlugin 22 P password 1 6 PBudget 10 2 PID 8 3 IDMIMO 8 6 ivotMch 4 15 lanckL 4 6 lot2D 4 14 otPlugIn 22 Plotv 8 13 progress bar 2 9 PropagateOrbitPlugIn 29 PSS website 1 3 U U u y td Q Q2Eul 6 3 Q2Mat 4 12 6 3 QForm 6 2 INDEX QIToBDot 9 4 QMult 5 6 6 2 QPose 6 2 6 3 OTForm 6 2 quat 5 5 quaternion 6 2 9 4 R RBModel 9 4 rigid body 9 4 RK45 8 12 RVO rbGen 4 16 S SC directory 1 8 SCDisturb m 7 12 SCMat 1 8 SCTConstants mat 3 4 ser 1 6 Series 4 10 Silicon Graphics 1 3 SkewS ymm 6 3 source code 1 2 Spacecraft Control Toolbox 2 5 spacecraft longitude 10 8 spherical coordinates 9 16
32. 50 cB h elementsPlugInTag ElementsPlugin initialize h fig 300 320 450 90 cB Initialize the 3D window 2 2 sim GetSimData h h g load TechSat 21 if isfield sim orbit r amp isfield sim orbit v h g body 1 bHinge q QLVLH sim orbit r sim orbit v else h g body 1 bHinge q 1 0 0 0 end h g name TechSat 21 if isfield sim orbit r h g rECI sim orbit r else h g rECI sim orbit el 1 0 0 end h g qLVLH h g body 1 bHinge q h scWindowTag DrawSCPlugiIn initialize h g h fig 400 40 350 270 earth sim time jDEpoch PutH h 9 28 Writing Your Own GUI Function CHAPTER 9 GUI Plug Ins It first creates a figure window then creates the Run HELP and QUIT buttons The rest of the code initializes the plug ins They all have the same format The spacecraft model is also read in from a mat file and used to initialize the DrawSCPlugin The following code is the orbit simulation It gets the data from the plug ins and updates the 3D display Listing 9 3 Initializing the simulation function Run Get the simulation data oe GetH sim GetSimData h a I Duration duration datenum sim time duration 86400 Check duration if duration msgbox The duration is zero Will not run the simulation return end Create the basic state vector from required plug ins oe
33. APTER 4 Basic Functions The torque transmission is found from the closed loop system FResp aT bT cT dT Figure 4 5 Torque transmission 4 10 Input 1 to Output 1 Magnitude db g i T Angle deg f L a 1 o 1 2 3 Frequency rad sec Create a frequency array for the following examples w logspace 1 1 You need the open loop plant for stability analyses aS bS cS dS Series a b c 0 aC bC cC dC Compare the Bode and Nichols plots FResp aS bS cS dS 1 1 w nichols Example Functions CHAPTER 4 Basic Functions Figure 4 6 Nichols plot a Input 1to Output 1 w 1 00e 01 40 30 3 2t A w 9 54e 10 A ob 2 95e 00 oi w 1 00e 01 20 L L 1 L L 180 170 160 150 140 130 120 Angle deg FResp aS bS cS dS 1 1 w Figure 4 7 Bode Plot Input 1 to Output 1 Magnitude db 120 Angle deg a amp B i oO oO a So 170 10 10 10 Frequency rad sec To compute the gain margins you first need to generate a frequency response array using FResp g FResp aS bS cS dS 1 1 w Pass the array and frequency vector to GPMargin Example Functions 4 11 CHAPTER 4 Basic Functions gM wG pM wP GPMargin g w gM wG pM 46 50814520467711 wP 2 94705170255181 Coord Euler angles are useful for initializing the attitude but are not suitabl
34. Convert torque demand to RWA angular acceleration demand wDRWA oe aRWA tC Integrate to get wheel speed demand oe WRWAC wRWAC tSamp wDRWA The wheels are commanded through the tach loops Listing 10 15 ae H oe TMAPSim RWA tach loops he RWA Tach Loops wError tRwA xTL Tach wRWAC L wError cl TL xTL L aTL xTL bTL w Error This is the simulation We are using the gyrostat model for this simulation The gyrostat model FGs is called by RK4 RK4 is a Fourth Order Runge Kutta method that works well for most spacecraft control simulation problems It does not do automatic error cor rection or computation This means that you cannot tell how accurately it is integrating the equations of motion from a single run To check on numerical errors you should run your simulation at half the time step and compare the results If they are significantly different Using the Spacecraft Control Toolbox 10 11 CHAPTER 10 A Worked Design Example you will need to go to a smaller step size The RK45 with somewhat greater overhead can Listing 10 16 TMAPSim Simulation oe oe Update the equations of motion oe RK4 FGs x dTSim t inr t dTSim t x ll be used in situations where you need to control the precision of your simulation In the following listing we are saving information for the pl
35. PSim e D O O O m o oxn TimeGUI nSim 0 tToGoMem 0 tSamp 10 8Using the Spacecraft Control Toolbox CHAPTER 10 A Worked Design Example This is the start of the simulation loop The first function displays the status message in the command window Listing 10 9 TMAPSim Start of the simulation loop Run the simulation oe for k 1 nSim oe Display the status message oe ratioRealTime tToGoMem TimeGUI nSim k tToGoMem ratioRealTime tSamp We are using very simple sensor models for this demonstration Just the true states without sensor dynamics scale factor errors noise or any other effects that are quite important in practice Listing 10 10 TMAPSim Sensor models oe oe Sensors oe RWA Tachometer oe oe oe Q K R O n oe wCore x 5 7 Using the Spacecraft Control Toolbox 10 9 CHAPTER 10 A Worked Design Example Finally we get to the control system implementation The first part is the momentum management system which is just a proportional controller Listing 10 11 TMAPSim Control system oe oe The Attitude Control oe System oe Momentum Management oe oe Neglect the rat rrors in the body component assume exact tracking hTotal QTForm gIToB inr wCore 1 wCore 2 wCore 3 inrRWA uW wTach wCore oe oe We could feedforward Proportional controller for
36. R 2 Getting Help Figure 2 10 Find orbit in the file names Re ek nat a hs ee Fa kakra kan i te BO Plea Prince ronSA7ELLITE aya Tare BE Thee Wea ret ieg sirada pii a aTa rere a are bea ee pia H ior od wth a opie cin pralki A l BCI s zi ib WAEL 11000 PHOrbH a D0 D D O D pirs E la a 11 PIED EADY al jD Spin TT TR TN ed OT ST Search Headers Button Search headers for a string This function looks for exact but not case sensi tive matches The file display displays all matches A progress bar gives you an indication of time remaining Figure 2 11 Progress bar Seac hing Headers E Search String Edit Box This is the search string Spaces will be matched so if you type attitude con trol it will not match attitude control with two spaces File Help 2 9 CHAPTER 2 Getting Help Run Example Button Run the example in the display Some of the examples are just the name of the function These are functions with built in demos Results will appear either in separate figure windows or in the MATLAB Com mand Window Save Example Button Save the example in the edit window Hitting this button only saves it in the temporary memory used by the GUI You can save the example permanently when you Quit Help Button Open this help system Quit Quit the GUI If you have edited an example it will ask you whether you want to save the example b
37. Total 5 1301 2 5201 3 1504 0 00e 00 1 83e 20 6 4402 Agro Planetary Radiation 8 3009 4 06009 S 13e 12 0 0000 3 4ie 28 1 04 e 09 Optical S i3e01 252e01 S lde04 O 00e H00 1 55e 20 4 44e 02 Thermal 0 00010 0 00e 00 0 0000 0 00010 0 000100 0 00 00 RF 1 120 06 1 1206 0 00e 00 0 00e 00 0 00e 00 4 5007 SG 0 00e 00 0 00010 0 00e 00 Magnetic 3 ite06 O 00e H0 3 1406 Importing CAD Models The toolbox has the ability to import CAD files from other packages Not all of the elements of supported packages are recognized only the subset needed to represent 3D models The following table lists the supported file formats and the elements that the importing functions will recognize The script Cassini Table 7 7 CAD File Importing Format Applications Supported Constructs 3DMF 3D World Mesh Infini D DXF AutoCAD 3DFACE but only triangles OBJ Wavefront v ii S gives an example in which DXF files for the Cassini orbiter and Huygens probe are loaded and displayed Once you import a CAD file you can use the interactive editor to add surface and material properties Alternately you can write a script to add the proper ties Importing CAD Models 7 13 CHAPTER 7 Using the CAD Functions 7 14 Importing CAD Models CHAPTER 8 UlIElements CHAPTER 8 UlElements This section shows you how to use UIElements UIElement UIElement mis am file that implements a number of user interface ele ments that
38. a X radius 10 Y radius e Z radius thetaUpper Upper angle 5 ial Number of divisions wan r radius u Spin axis unit vector surface of revolution 22 2S a Luimecilom Or polynomial z at ik Zin ar aA 2 me e ial 20 ial imi 18 6 Bx Number of divisions a ZUpper Upper z limit ZLOwer Lower z limit triangle x y z dimensions truss r end points for the truss members c connection matrix Component properties are given in Table 7 4 on page 7 Table 7 4 Component properties pani Component Size Description optical sigmaT 1 1 Transmission coefficient sigmaA 1 1 Absorption coefficient sigmaD 1 1 Diffuse reflection coefficient sigmas 1 1 Specular reflection coefficient thermal alpha 1 1 Absorptivity epsilon 1 1 Emissivity cP 1 1 Specific heat temp 1 1 Temperature deg K magnetic dipole 3 1 Dipole Building a Spacecraft Model CHAPTER 7 Using the CAD Functions 7 8 Table 7 4 Component properties Data ohh Component Size Description structure aero cD 1 1 Drag coefficient If entered the next two will be ignored sigmaN 1 1 Normal surface accommoda tion coefficient sigmaT 1 1 Tangential surface accommo dation coefficient mass mass 1 1 Mass inertia 3 3 Inertia matrix cM 3 1 Center of mass wrt origin rE flux 1 1 flux u 3 1 Un
39. ae Tra Ere t oH 4 Pri ngeton SATELLITE iHi ol Tmi mjr anie 4 il i Teaver There are four main panes in the window On the left hand side is a display of all files in the toolbox The list initially is alphabetical On the right hand side is the header of the first file Immediately below the header display is the edit able example To its left is a template for the function You can cut and past it into your script our function The List Pane Above the list pane are two buttons If you hit hierarchical the names of the SCT directories appears File Help 2 5 CHAPTER 2 Getting Help Figure 2 7 Hierarchical file display File Hele System PrincetonSATELLITE aha lp aba ical W Hirarchica F c hiapH diigd 0001 3 C cere Cer Come IL A sign is in front of each name Click the file with a plus sign to see which toolbox functions are in each directory To view a file s header example and template click on the file name 2 6 File Help CHAPTER 2 Getting Help Figure 2 8 Open directory PrinceronSA7TELLITE a vwaiTar F Adee died Ooi gt CN ST CTT TT This list is of the toolbox as you receive it on CD ROM or as downloaded from the web It will not show any of your functions A build script is included if you want to customize this help display If you toggle from hierarchical to alphabetical and back you will notice that the open
40. all of the constants in the database You can enter a search string and look for matches by hitting Find If you then click one of the selections the GUI looks like it does in the following figure This function always loads its constants from the mat file SCTConstants mat 3 2 The Constant Database CHAPTER 3 Using Databases Figure 3 2 Searching for mass Cenphent Detebece Sines ese Pd TEIA Ln OO Faa a apn i Ta ee Conatend rasa Iuin pupa or The string field shows the parameter name Directly below it is the value for the parameter The value may be any MATLAB construct Directly below that is a field for units then a field for reference information and finally a field that gives a template for the function You can cut and paste this into any function or script Searches are case and whitespace insensitive You can add new constants Just type a constant name in the String field a value in the value field and optionally units and reference information Hit Add You will get a warning if you try and replace an existing constant You always hit Add even if you are modifying the value of an existing con stant You can delete a constant by hitting the Delete button You can access the database through the command line Just type Constant mass sun mass jupiter ans 1 0474e 03 The database loads its constants from a database the first time it is launched Once it is launche
41. anges Optionally a safe hold mode could be added 10 2 The MAP Mission CHAPTER 10 A Worked Design Example Sensing and Actuation Nominally MAP uses gyros for attitude determination and a star tracker to cor rect for gyro drift and for absolute attitude information The gyro and star tracker data would be integrated using an extended iterated Kalman filter A backup mode using just the star tracker would also be available During most of the mission the reaction wheels are used for attitude control Secular momentum growth due to solar pressure would be controlled using the thrusters Momentum unloading could be autonomous or ground commanded During orbit adjust modes the thrusters would be used for attitude control since the disturbances due to the orbit adjust thrusters would quickly saturate the reaction wheels Control System Design The control system design is a modification of Princeton Satellite Systems standard three axis control system The control system employs tachometer inner loops for the three reaction wheels The outer loops are two Proportional Integral Differential PID loops for the transverse axes and a Proportional Integral PI loop for the spin axis The integral term in the PID controllers insures accurate tracking of the spin axis target The inner reaction wheel loops are PI controllers The outer loops output an acceleration demand that is con verted to a wheel speed demand and passed to the reaction w
42. apter 13 Budgets 10 1 Pointing Budget 10 2 Fuel Budgets 10 3 Figures Tables and Listings Chapter 1 Chapter 2 Chapter 3 Chapter 4 Installing The Spacecraft Control Toolbox 1 1 Figure 1 1 Home page for the PSS website 1 4 Figure 1 2 The upgrades page 1 5 Figure 1 3 Password and user id 1 6 Figure 1 4 Upgrades 1 7 Table 1 1 Archives 1 7 Table 1 2 Files included in the Spacecraft Control Toolbox 1 8 Figure 1 5 Webboard 1 10 Getting Help 2 1 Figure 2 1 DemoSC 2 2 Figure 2 2 Opening ACSDesigns 2 3 Figure 2 3 Edit Window 2 3 Figure 2 4 Time to Go Display 2 4 Figure 2 5 Results of TGimbal 2 4 Figure 2 6 The file help GUI 2 5 Figure 2 7 Hierarchical file display 2 6 Figure 2 8 Open directory 2 7 Figure 2 9 Find all 2 8 Figure 2 10 Find orbit in the file names 2 9 Figure 2 11 Progress bar 2 9 Figure 2 12 SCHelp GUI 2 10 Figure 2 13 An open directory in SCHelp 2 11 Figure 2 14 Help 2 11 Figure 2 15 Webboard 2 12 Using Databases 3 1 Figure 3 1 Constant database 3 2 Figure 3 2 Searching for mass 3 3 Figure 3 3 MergeConstantDB function 3 4 Basic Functions 4 1 Table 4 1 Toolbox Organization 4 2 Chapter 5 Chapter 6 Chapter 7 Table 4 2 Figure 4 1 Figure 4 2 Figure 4 3 Figure 4 4 Figure 4 5 Figure 4 6 Figure 4 7 Figure 4 8 Figure 4 9 Figure 4 10 Figure 4 11 Figure 4 12 Figure 4 13 Figure 4 14 Features in SCT functions 4 4 Atmospheric density from AtmDens2 4 5 Dual Spin
43. are not available in Matlab UILELementDemo shows the elements that will be discussed in this section Figure 8 1 UIElementDemo The UJElements shown are from left to right and top to bottom e EditPM e EditScroll e CheckBoxList e DataStructureList e List e ListWithButton All except EditScroll are implemented using UIElement 8 16 UlElement CHAPTER 8 UlElements EditPM Edit PM is implemented as shown in Listing 8 1 on page 17 This creates an edit box with Listing 8 1 EditPM v Parent h fig Units pixels fontunits pixels s Pts h editPM UIElement v Position 5 215 130 20 style editpm string 1 min 1 max 5 callback s plus and minus buttons Clicking on the buttons increments or decrements the number in the edit box min and max limit the values EditScroll EditScroll isimplemented as shown in Listing 8 1 on page 17 This creates a scrolla Listing 8 2 EditScroll EditScroll initialize h fig 140 215 355 801 ble edit window CheckBoxList CheckBoxList is implemented as shown in Listing 8 1 on page 17 This is a variant on Listing 8 3 CheckBoxList s One Two Three Four Five Six Seven Eight for k 1 length s c k 1 string s k end h checkBoxList UIElement parent h fig style Wwidth 130 position 5 110 130 100 tast checkboxlist
44. ationkeeping the corresponding function is dVNS dTNS DVIDrift box year where the second argument is the year for which the calculation is done The inclination drift is a function of the earth moon geometry which is included in DVIDrift 13 8 Fuel Budgets INDEX Symbols p 1 2 A Acker 4 8 Ackerman s formula 4 8 Acrobat Reader 3 x 1 8 ACSDesigns 2 2 archives 1 7 ASim 9 4 AtmDens1 4 13 AtmDens2 4 5 beam pointing error 10 2 bisection search 10 2 Build3DSC m7 2 7 10 BuildMAP m 7 2 BuildSC m7 2 C case sensitivity 1 8 CD ROM 1 3 2 7 cell array 5 3 CheckBoxList 16 circular error 10 2 class 5 4 class 5 4 constructor 5 4 instance 5 4 method 5 4 5 5 object 5 5 overloading 5 5 polymorphism 5 5 CLoopS 4 9 Constant 3 2 constant database 3 4 Coordinate Frame ECI 20 ECIR 20 ECR 20 CoordinateTransform 38 Cross 6 3 D data structure 4 6 5 2 database 3 2 DataStructureList 16 Date2JD 4 6 4 14 delta V 10 8 DemoSC 2 2 2 4 Disturbance m7 12 Disturbance m 7 2 DrawSC m 7 10 7 12 DrawSC m 7 2 DrawSCPlugin 22 29 DSpnStab 4 7 DVIDrift 10 8 DVLDrift 10 8 E EarthRot 4 5 FarthRotationZero 38 ECITOECIR 39 EditPM 16 EditScroll 16 ElementsPlugin 22 error checking 4 6 Ful2Q 4 12 6 2 6 3 Euler angle 6 3 F FBudget 10 3 FEngine 31 FileHelp 2 5 FPlantNoise 33 FResp 4 11 FSolar 32 fuel budget 10 3 G GASTime
45. aved using the GUI interactively In the second the time step is customized Any field in the data structure may be customized In the third step the GUI is initialized In the fourth the datastructure d is loaded The orbit is then propagated Plots are closed after the pause and the final step is to quit tag identifies the GUI Pos sible commands are listed in the following table Table 6 3 PropagateOrbitPlugin API Prototype Purpose tag PropagateOrbitPlugin initial Initialize the plugin LAS A PropagateOrbitPlugin set data Set the data in the GUI tag Cl fF PropagateOrbitPlugin propagate Propagate the orbit tag PropagateOrbitPlugin close plots Close the plots tag Jz PropagateCrbatPlugin save tag Save the GUI data fileName Using the Graphical User Interface 6 43 CHAPTER 6 Orbit Propagation Table 6 3 PropagateOrbitPlugin API Prototype Purpose PropagateOrbitPlugin save plot Save the plot data data tag fileName PropagateOrbitPlugin quit tag Close the Gul Plugin Functions The orbit propagator has four plugin in functions that allow you to customize the simulation When you first bring up the GUI four default functions are shown They are described in the following table Table 6 4 Plugin Functions Function Description FEngine Computes engine force and spacecraft mass The
46. bject which is an empty object 1 by 1 5 7 CHAPTER 5 Data Structures 5 8 SCT Classes CHAPTER 6 Coordinate Transformations CHAPTER 6 Coordinate Transformations This chapter shows you how to use SCT functions for coordinate transforma tions Transformation Matrices Transforming u from its representation in A to its representation in B is easily done with a transformation matrix m cos theta sin theta 0 sin theta cos theta 0 0 0 1 uB m uA This neatly ties together transformation matrices and Euler angles Quaternions A quaternion is a four parameter set that embodies the concept that any set of rotations can be represented by a single axis of rotation and an angle In this case the axis of rotation is 0 0 1 andthe angleis theta Of course the axis of rotation could also be 0 O 1 andthe angle theta Quaternion transformations are implemented by the functions QForm and QTForm QFormrotates a vector in the direction of the quaternion and OTForm rotates it in the opposite direction In this case q Mat2Q m uB QForm q UA uA TForm q uB We could also get q by typing q Eul2Q 0 0 theta Much as you can concatenate coordinate transformation matrices you can also multiply quaternions if qAToB transforms from A to B and qBToC transforms from B to C then gAToC QMult gATOB gBTOoC The transpose of a quaternion
47. creating an input file for STK err message STKOrbit fileName ver epoch nPoints time position velocity type Table 6 6 T O for STKOrbit Sun Variable Description fileName Filename for output Will be overwritten if it already exists ver STK version number string 6 53 CHAPTER 6 Orbit Propagation Table 6 6 T O for STKOrbit Variable Description epoch Beginning date and time Y MD HM S nPoints Number of orbit data points time Time in seconds for each data point position Position data in km if type ECF or ECD or in degrees degrees km if type LLR velocity Velocity data in km sec if type ECF or ECI or degrees degrees km sec if type LLR type ECT ECF or LLR err err 0 means an error occurred message Error message Ground Coverage Ground coverage is found using x GroundCoverage xECI jD d where xECI is the ECI state vector r v JD is the Julian date and d is the data structure in which d fOV x is the x axis field of view d OV y is the y axis field of view and d m transforms from the body frame to the sensor frame The sensor is assumed to have its boresight along z in the sensor frame If d m were the identity matrix the sensor would point along z in the body frame For this function the satellite body frame is assumed to be aligned with the LVLH frame d e is a 3 by 1 vector
48. d it will not load a new database so there is relatively little overhead using it in your scripts and functions The Constant Database 3 3 CHAPTER 3 Using Databases Merging Constant Databases Periodically PSS will release new constant databases If you have customized your own database you can merge it with the PSS database using the Merge ConstantDB function Just type MergeConstantDB initialize a b where a and b are the mat files to be merged The standard PSS database is called SCTConstants mat In this example we have modified the value of accel grav mks tobe 9 8068 We type MergeConstantDB initialize SCTConstants mat SCT ConstantsOld mat You will see the following display Figure 3 3 MergeConstantDB function Merge Debebeces isc regency fend Select the desired colon socal gra Fi Bie gr is zat REDS OOOO o o males Cocotte Just click the button for the column you wish to include in SCT Constants mat 3 4 Merging Constant Databases CHAPTER 4 Basic Functions CHAPTER 4 Basic Functions This chapter shows you how to use a sampling of the Spacecraft Control Tool box functions Introduction The Spacecraft Control Toolbox is composed of over five hundred Matlab m files The functions cover attitude control and dynamics orbit dynamics and kinematics ephemeris thermal and mathematics operations Most of the func tions can be used individually al
49. e for numerical integration or simulation Consequently we convert the Euler sequence into a quaternion q Bul2Q pi 4 0 0 q 0 92387953251129 0 38268343236509 0 0 Quaternions and matrices are interchangeable It takes fewer arithmetic opera tions to transform a vector using a matrix than it does for a quaternion m Q2Mat q m 1 000000 0 0 0 0 707107 0 707107 0 0 707107 0 707107 Dynamics This function can return either a state space system or the state derivative vec tor MBModel has analytical expressions for the state space system a b c d MBModel diag 10000 2000 10000 0 400 0 0 7 291e 5 0 eig a 4 12 Example Functions CHAPTER 4 Basic Functions The resulting plant has a double integrator for pitch Roll yaw has two pairs of complex eigenvalues one at orbit rate due to pointing at the earth and one at the nutation frequency Both modes are undamped ans O 0 000072910000001 O 0 000072910000001 O 0 039941672000001 O 0 039941672000001 0 0 Environs Simple atmospheric models are available to compute the atmospheric density as a function of height The first model is simpler and much faster than the sec ond It also has data on some other planets AtmDensl AtmDens2 Figure 4 8 AtmDens1 Atmospheric Density T T T Density kg m L fi fi fi 120 140 160 180 200 fi fi fi fi 0 20 40 60 80 100 Altitude km Exam
50. efore you quit Graphical User Interface Help Each graphical user interface GUI has a help button If you hit the help button anew GUI will appear Figure 2 12 SCHelp GUI Help for CHelp You can access on line help about any of the GUIs through this display It is separate from the file help GUI described above 2 10 Graphical User Interface Help CHAPTER 2 Getting Help The display is hierarchical Any list item with a or in front is a directory means the directory list is closed means it is open If you click on one of the list elements you get the display shown in Figure 2 13 on page 11 Figure 2 13 An open directory in SCHelp If you click on any other name in the list you will get a text display in the right hand pane Figure 2 14 Help Tht List Pane T decor epee A ees is Proto cere Oke sireh pa My eh tiny Mine ata re Pe Uh HPCE Ta wire a Tile bade azemphi nmi armagina click ondha fil mre Thi int b o Pe fee bee m pea rara fo RDH r ence ied iraa Tesa Feel hn Dihi E abai i i a aid IT yon worl amp cerie this babs dopey Fega Pon heracchead tiaia andbace peu ed iron thet Ae cage gina Agere Yir bet i pii er ania ia pbi You can either search the headings or the text by entering a text string into the Search For edit box and hitting the appropriate button Restore List restores the list window to its previous configuration Graphical User Inter
51. emarks or registered trademarks of their respective companies or organi zations Printing History June 1999First Printing Princeton Satellite Systems Inc 33 Witherspoon Street Princeton New Jersey 08542 Technical Support Sales Info http www psatellite com Contents Chapter 1 Installing The Spacecraft Control Toolbox 1 1 Requirements 1 2 About this Tutorial 1 2 Background 1 2 CD ROM 1 3 Web 1 3 Included Files 1 8 Installation 1 8 Case Sensitivity 1 8 Function Overloading 1 9 Updates 1 9 Technical Support 1 9 Webboard 1 9 Chapter 2 Getting Help 2 1 Demos 2 2 File Help 2 5 Introduction 2 5 The List Pane 2 5 The Example Pane 2 7 Find All Button 2 7 Edit Button 2 8 Search File Names Button 2 8 Search Headers Button 2 9 Search String Edit Box 2 9 Run Example Button 2 10 Save Example Button 2 10 Help Button 2 10 Quit 2 10 Graphical User Interface Help 2 10 MATLAB Help 2 12 Technical Support 2 12 Webboard 2 12 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Using Databases 3 1 The Constant Database 3 2 Merging Constant Databases 3 4 Basic Functions 4 1 Introduction 4 2 Function Features 4 4 Built in demos 4 4 Default parameters 4 5 Built in plotting 4 5 Error checking 4 6 Variable inputs 4 6 Example Functions 4 7 Attitude 4 7 Control 4 8 Coord 4 12 Dynamics 4 12 Environs 4 13 Ephem 4 14 Graphics 4 14 Hardware 4 15 Orbit 4 16 Prop 4 16 Thermal 4 17 Data Structures 5
52. endent of the entered times Elements Pane The elements plug in allows you to enter and convert between Keplerian ele ments equinoctial elements and RV elements The planet used for the orbit center is also shown Element Sets are given in the following table Table 6 1 Element sets Equi Ko Bu nocti RV erian RA al a Semi major R Perigee a Semi major r axis radius axis i Inclination i Inclination P Ty Using the Graphical User Interface 6 37 CHAPTER 6 Orbit Propagation Table 6 1 Element sets Equi Ep PE nocti RV erian RA al Q Right Q Right P T3 Ascension Ascension of the of the Ascending Ascending N ode N ode 0 Argument oO Argument Q Vi or Perigee or Perigee e Eccentricity R Apogee Q V gt radius M Mean M Mean l Mean longi v anomaly anomaly tude The RV elements are position and velocity vector Atmosphere Pane You can select any one of four models The first two are altitude dependent and are based on a spherical planet model The third will enable the default Atmo spheric density plugin function FAtmDensity which implements the Jac chia J70 model Other allows you to enter your own atmosphere model Propagate Pane This selects the frame in which to propagate The ECIR frame is an inertial frame which coincides with the EF frame at the start of the simulation Gravity Model Pane The Database model i
53. face Help 2 11 CHAPTER 2 Getting Help MATLAB Help You can see the header for any file by typing help fileName in the MATLAB command window Technical Support Contact support psatellite com for technical support Webboard You can talk with fellow SCT toolbox users and PSS engineers using our Web board Go to http www psatellite com and hit Discussion Board You will then see the webboard Figure 2 15 Webboard Mikitin i D Pioioi tare te Dey ee orm bat Drove bee matte greeter ks apl rrek el eed be dome ee sama ee den ede sma Beh rs r ncn a bh dhiii pis a maf eae as a HE i fia Reds aie de eee Sey i irae re oom wee Dam d pnta Pa Pii Hae Pie F ih m Ci a Tid ls ba EE i bee Dei rda lia diia i H j Ute ahi and talar Lake ee Pii aes Be SDs o gt kiki 2 12 MATLAB Help CHAPTER 3 Using Databases CHAPTER 3 Using Databases This chapter shows you how to use the database and constant functions in the toolboxes These functions allow you to manage the various constants and parameters used in your projects and insure that all of your engineers are using consistent numbers in all their analyses The Constant Database The constant database gives a substantial selection of constants that are useful for the aerospace engineer If you type Constant you will get the following GUI Figure 3 1 Constant database Cenchant Detsbere bord albedo siare The list on the left is a list of
54. he control system oe xTL zeros 3 1 xRoll 0 0 xPitch 0 0 xYaw 0 TE 0 0 0 spinRate 0 464 rPMTORPS precRate 2 pi 3600 precAngleDemand 22 5 precAngle 0 precAngleGain 0 995 Momentum Management gain A ol kMM 0 000 oe The control distribution matrix converts torque demand to angular acceleration demand aRWA WRWAC eye 3 inrW 3 0 0 0 Using the Spacecraft Control Toolbox 10 7 CHAPTER 10 A Worked Design Example The following code sets up the simulation We allocate memory for plotting arrays to save processing time We also set up the time statistics function which will display time statistics Listing 10 8 TMAPSim Set up the simulation Plotting arrays A ol cPlot zeros 3 nPlot hPlot zeros 3 nPlot tPlot zeros 1 nPlot xPlot zeros 10 nPlot zPlot zeros 3 nPlot rPlot zeros 3 nPlot pPlot zeros 2 nPlot ePlot zeros 2 nPlot wPlot zeros 3 nPlot yPlot zeros 3 nPlot Time statistics function oe tToGoMem ratioRealTime zeros 1 3 0 Initial conditions oe ol q w wRWA x 1 0 0 0 0 0 spinRate 0 0 0 dTSim tSamp 0 nP 0 kP 0 tw zeros 3 1 roll 0 pitch 0 yaw 0 Initialize the time display tToGoMem lastJD tToGoMem lastStepsDone tToGoMem kAve ratioRealTime ratioRealTime tToGoMem TMA
55. heel tachometer loops The inner loops insure proper reaction wheel response regardless of bearing friction magnitude and uncertainty A sampling rate of 4 Hz was cho sen for the digital implementation of this control system Simulation Results Normal mode acquisition was simulated using the TMAPSim script The mass properties and the actuator characteristics for the baseline MAP spacecraft were not available so generic parameters were used in the simulation The spacecraft model is for a gyrostat with three reaction wheels All nonlinear terms are included The simulation models do not include sensor noise or external disturbances The spacecraft is initially spinning at 0 464 rpm with the spin axis aligned with the inertial Z axis The desired precession angle command of 22 5 deg is fed into the control loops through a low pass filter to eliminate transients The gains of the filter are chosen so that acquisition is completed within ten min utes Sensing and Actuation 10 3 CHAPTER 10 A Worked Design Example Using the Spacecraft Control Toolbox In this section we will walk through the TMAPSim script Once you understand how is was written you will be able to easily design and build your own control systems and simulations Listing 10 1 on page 4 This is the header which Listing 10 1 TMAPSim File header oe oe Implements and simulates the MAP normal mode control oe Copyright 1996 Princeton Satellite System
56. hing Distance Stop when r value and is decreasing Receding Distance Stop when r value and is increasing Increasing Velocity Stop when v value and is decreasing Decreasing Velocity Stop when v value and is increasing Flight Path Angle Stop when the flight path angle the value Perigee Height Stop when perigee radius valuey Apogee Height Stop when apogee radius valuey Geodetic Latitude Stop when geodetic latitude value Geocentric latitude Stop when geocentric latitude value Geodetic Altitude Stop when geodetic altitude value Semi major Axis Only relevant to non Keplerian orbits Stop when a valueyt 6 40Using the Graphical User Interface CHAPTER 6 Orbit Propagation Table 6 2 Stopping Conditions Stopping Condition Explanation Mean Anomaly Stop when M value Orbital Period Stop when orbital period value Right Ascension of Ascending Node Stop when Q value and only at the descending node Right Ascension of Descending Node Stop when Q value and only at the ascending nodet Change in Inertial Velocity Magnitude Stop when lvl value Vehicle Longitude Stop with earth fixed longitude value Argument of Perigee Stop when argument of perigee valueyt Eccentric Anomaly Stop when E value Only relevant to non Keplerian orbits Keplerian orbits in which the orbital elements do not change
57. ion disp sprintf nSDP8 n rV NORAD t 0 360 720 1080 1440 Ly 257 disp Position for k end disp sprintf nVelocity disp sprintf 11 2f 11 2f 11 2f 11 2f t k for k 1 5 end SGP Position 0 00 2328 360 00 2456 720 00 2567 1080 00 2663 1440 00 2742 Velocity 0 00 2 360 00 2 720 00 2 1080 00 2 1440 00 1 SDP8 Position 0 00 7466 360 00 3324 720 00 14228 1080 00 10138 1440 00 9430 Velocity 0 00 5 360 00 1 720 00 0 1080 00 si 1440 00 1 are SGP SGP4 SGP8 145 disp sprintf 11 2f 11 2f 11 2f 11 2f t k sdp8 97 01 40 03 86 x91 68 44 20 95 26 53 24 27 25 old 30 34 00 lt 12 5995 6071 6112 6115 6079 419 32340 24233 22216 33839 sdp txt 222 94 50 37 14 98 45 10 65 ai 45 61 73 15 76 44 aes z269 33 J83 LILO 96 7134 195 328 1222 5833 24675 4858 23409 15399 98 97 74 86 lt 09 223 32 36 539 52 30 57 87 16 18 28 08 dA 50 rV r k rV v k SDP4 SDP8 The first three are suitable for low earth orbiting satellites the last two for high altitude satellites All functions read in from files in the NORAD format which are available on line 11 17 CHAPTER 11 Simulation 11 18 Orbit Simulation CHAPTER 6 Orbit Propagation CHAPTER 6 O
58. it vector ol 3 1 Vector from reference to rF centroid inside If included the component is considered to be inside the spacecraft and will not be used in aero or optical distur bance calculations Building a Spacecraft Model CHAPTER 7 Using the CAD Functions Adding a Body When all components have been entered you can collect them into bodies Listing 7 2 Example body data structure m name Core m rHinge 0 0 0 m bHinge 001 1 0 0 0 1 0 m components 7 14 m rThruster zeros 3 n m uThruster zeros 3 n m magThruster zeros l n m previousBody g Build3DSC add body m g Listing 7 2 on page 9 shows an example The data structure bHinge has sev eral options bHinge b 3 3 Transformation matrix Gy 4 1 Quaternion a 3 1 Unit Vector angle 1 1 Angle about the unit vector You enter either b q or a and angle components is a list of com ponents that are attached to the body The thruster fields define the locations of thrusters attached to the body Building a Spacecraft Model 7 9 CHAPTER 7 Using the CAD Functions Linking Bodies The last step is to link the various bodies into a tree An example tree is shown in Figure 7 3 on page 10 Each body is connected to the previous body by a Figure 7 3 Topological tree hinge No closed loops are allowed You create the paths by typing g Build3DSC compute paths g Displaying a S
59. ity gt HH The J70 inputs are given in the following table Table 6 5 Jacchia J70 Atm inputs aP Geomagnetic index 6 7 hours before the computation f Daily 10 7 cm solar flux e 22 watts m 2 cycle sec fHat 81 day mean of f e 22 watts m 2 cycle sec fHat400 fHat 400 days before computation date Building a Plugin Function All plugin in functions have the same structure In this section we will walk you through the structure of FAero the simplest function 6 48 Building a Plugin Function CHAPTER 6 Orbit Propagation Listing 6 2 on page 49 shows the function call list and the switch statement that makes up the main function action is the argument for the switch state ment and modifier is the GUI tag which identifies the GUI Listing 6 2 FAero Main Function function x FAero action modifier u t if nargin lt 1 action initialize end switch action case initialize x Initialize modifier case update x Update modifier u t case get data x GetData modifier case store data h GetH modifier h d GetData modifier PutH h case set data SetData modifier case help HelpSystem initialize SCHelp case quit h GetH modifier PropagateOrbitPlugin close function h propagateOrbitPluginTag FAero CloseFigure h fig end Building a Plugin Function 6 49 CHAPTER 6 Orbit Propagation The Initiali
60. lWt2R 0 004 9 5514e 02 1000 CHAPTER 13 Budgets The following listing shows the initialization of the arrays Fuel Budget Array initialization initial Initial State Listing 13 5 Event 1 Initialization k k 1 event k type event k description event k aCSThruster event k dVThruster event k dVTotal event k dHTotal event k disturbance event k pulsewidthACs event k pulsewidthDV event k nPulses event k duration event k regulated event k cM The next listing shows the entry for a continuous Delta V burn Fuel Budgets Fuel Budget Continuous delta v burn 2 A continuous delta V burn using different ACS and DV thrusters Listing 13 6 Event k k 1 event k type event k description event k aCSThruster event k dVThruster event k dVTotal event k dHTotal event k dTControl event k disturbance event k nPulses event k duration event k regulated event k cM delta v Delta V Continuous t 1 r 0 0 L234 56 78 8 10 A E 13 14 3 100 Total delta V in m sec If not regulated use blowdown curves 0 0 13 5 CHAPTER 13 The next listing shows the entry for a delta v burn with off pulsing Fuel Budget Delta v with off pulsing Event 3 Delta V off pulsing some thrusters delta v Delta V Off Pulse 123 491011 12 1 2 3 4 100
61. ler s equation is usually sufficient RVO rbGen uses Kepler s equation el 8000 2 0 0 6 0 RVOrbGen el Figure 4 12 Elliptical orbit 1000 Z ECI KM 5000 5000 2000 Y ECI KM X ECI KM r v EL2RV el r 3200 0 0 y 13 83596536017765 2 80468902945837 Prop Many propulsion systems are blowdown designs that do not use a pressure reg ulator Therefore to know the thrust you need to know the properties of the propulsion system The following function designs a blow down propulsion propellant system v mP BDDesign 200 1000 300 350 6895 100 6895 BloDown mP 1000 v 300 linspace 0 200 4 16 Example Functions CHAPTER 4 Basic Functions Figure 4 13 Blowdown curve x 10 Blow Down 2 6 T T T Pressure 0 6 L f fi fi 0 fi fi fi i L 20 40 60 80 100 120 140 160 180 200 Fuel Mass Thermal The albedo of the earth is a significant disturbance on a spacecraft In this model the albedo is uniform angle linspace 0 2 pi u cos angle sin angle zeros 1 100 r 7000 6378 ones 1 100 EarthAlb r u 1 0 0 Figure 4 14 Earth Albedo Al 400 T T bedo T 8 300 f J4 lt 200 2 3 100 Si T 0 fi L 3 T T 22 4 T a lig 5 G a 0 fi fi 54 T T 8 gt 3 4 2 22H i no it 4 2 ito L 1 L L L L L L L 0 10 20 30 40 50 60 70 8
62. ll arrays and are not compatible with versions of MATLAB prior to 5 0 Your monitor should have a resolution of at least 800 by 600 pixels Color is desirable The Spacecraft Control Toolbox does not use any functions that were added after V5 2 of MATLAB About this Tutorial This tutorial uses the following conventions www psatellite com URL s and email addresses The first let ter is always lower case Beginnings of words after the first are always upper case monoSpace MATLAB code button GUI button The examples in this tutorial were run on a Macintosh PowerPC computer All pictures of GUIs were created using Macintosh screen shots and reduced 50 for inclusion in this tutorial All web pages were captured using Netscape 4 5 Background The Spacecraft Control Toolbox is a set of MATLAB m files All of the func tions are in m file format No mex files or p parsed files are supplied As a consequence you have complete access to all of the source code 1 2 Requirements CHAPTER 1 Installing The Spacecraft Control Toolbox Background You can obtain the software in two ways One is on CD ROM The second way is by downloading the software from the Princeton Satellite Systems website at www psatellite com CD ROM The software is supplied on a CD ROM with two partitions One is a Macin tosh Hierarchical File System HFS partition and the other is an ISO standard partition The latter uses Macintosh file naming c
63. lly does p 0 54 pb p to insure that the covariance matrix is symmetric You have the option to select Spherical Cov This uses a spherical earth model just to propagate the covari ance This is much faster than using the full model Buttons e Save Plot Data saves the plot data in a mat file of type OPP The plot is saved as a matrix with rows x y z vX vY vZ mass pXX pVZVZ pXY pYZ p is saved in columns starting with the main diagonal and moving up For example a 3x3 matrix would be saved as al 1 a22 a33 a12 a23 a13 e Close Plots Close the plot windows e Open Open a gui dat file of type OPG e Save Data Save the gui data in a mat file of type OPG e Propagate Run the propagator 6 42Using the Graphical User Interface CHAPTER 6 Orbit Propagation e QUIT Quit It will ask you to save unsaved plot and GUI data e Help Get help Setting Up a Batch Script You can run PropagateOrbitPlugtIn from a script This allows you to set up large numbers of cases and run them automatically OPDemo shows how to set up a batch run d load OPDemo mat d epoch dT 3600 tag PropagateOrbitPlugin initialize PropagateOrbitPlugin set data tag d PropagateOrbitPlugin propagate tag pause PropagateOrbitPlugin close plots tag PropagateOrbitPlugin quit tag In the first line a saved data file is loaded This file was created and s
64. ment of the list or hit ting the pushbutton selects an element of the list This code snippet shows you how to access the internal data structure of UIElements In this case the code hS get h listWithButton userdata gives you a handle to the UJElement data structure To set the list you type set hS list string One Two Three which is setting the listbox uicontrol string Closing UIElements To close a UIElement type CloseUIElement handleToKlement ListWithButton 8 19 CHAPTER 8 UlElements 8 20 Closing UlElemenits CHAP I ER 9 GUI Plug Ins CHAPTER 9 GUI Plug Ins This section shows you how to use GUI Plug ins GUIPlugIn GUIPlugIn misam file function that implements an orbit simulation using several GUI Plugin elements This can be used as a template for your simula tions Figure 9 1 GUIPlugIn on starting Epa Duron oT hi E ELT 07 00 00 Orbit Dir ry A i bof Ee ie 1G Baar Lasgiiaie ji E 1 i i ne aa al The GUIPlugins shown are from top to bottom starting on the left e OrbitDisplayPlugin e PlotPlugIn e TimePlugin e ElementsPlugin DrawSCPlugin The Run QUIT and HELP buttons are part of the GUIPlugIn function 9 22 GUIPlugin CHAPTER 9 GUI Plug Ins Figure 9 2 GUIPlugIn after changing inputs GLUAug inteme Epa uric DT Law eae sem J aos Orb Dir ry You can change any of the displayed properties i
65. momentum this to the controller oe tM QForm qIToB kMM hTotal We next compute the errors These are what we will be controlling Notice that the commanded precession angle is filtered This makes the system a two degree of freedom control system and prevents the operator from putting in a command that would saturate the actuators Listing 10 12 TMAPSim Error computation oe Compute the errors oe precAngl precAngleGain precAngle 1 precAngleGain precAngleDemand cP CosD precAngle sP SinD precAngle xT sP cos precRate t sP sin precRate t xTB QForm qIToB xT rollError asin xTB 2 pitchError asin xTB 1 yawError wCore 3 spinRate 10 10Using the Spacecraft Control Toolbox cP CHAPTER 10 A Worked Design Example These loops control the attitude and spin rate The output is torque demand Listing 10 13 TMAPSim Attitude loop The attitude control loops oe tc 1 xRoll tc 2 xPitch tc 3 xYaw cRoll xRoll dRoll rollError xRoll aRoll xRoll bRoll rollError cPitch xPitch dPitch pitchError xPitch aPitch xPitch bPitch pitchError cYaw xYaw dYaw yaw Error xYaw aYaw xYaw bYaw yawError We convert torque into a demand on the wheels which we integrate to get wheel speed demand Listing 10 14 TMAPSim Compute wheel speed demand oe oe
66. mulation Initialization of the model Listing 11 11 Tree Simulation Initialization Copyright 1997 Princeton Satellite Systems Inc All rights reserved oP oP ol Vectors from previous body reference to the hinge of the body ae ol lambdal 0 0 0 lambda2 2 0 0 lambda3 1 0 0 Vector from body reference to body c m For all but the core the reference is always the hinge that leads to the core oP oP ol pal 0 0 0 r2 0 0 5 r3 0 0 0 70 a5 r r Mass and inertia ml 100 m2 2 m3 5 i1 diag 200 200 300 i2 diag 1 1 1 i3 diag 3 3 Hys TreeAdd adds bodies to the link You can give them a name Listing 11 12 Tree Simulation Adding bodies Add each body to the tree data structure body 1 TreeAdd il rl lambdal ml 0 0 Core body 2 TreeAdd i2 r2 lambda2 m2 1 2 Link body 3 TreeAdd i3 r3 lambda3 m3 2 3 O O Payload Cause the inner link to acceleration Listing 11 13 Tree Simulation A hinge acceleration Internal torque body 2 torque 0 1 Tree Model 11 13 CHAPTER 11 Simulation Define a low earth orbit Listing 11 14 Tree Simulation A low earth orbit Initial orbit r 7000 0 0 v 0 sqrt 3 98600436e5 7000 0 This initializes the tree data structures and the state vector TreePrnt prin
67. n PutH h oe A ol set h fig UserData h Get the data from the figure handl A A al function h GetH hFig findobj allchild 0 flat Tag GUI PlugIn Demo h get hFig userdata Create a callback string A A ol function c CreateCallback action c GUIPlugin action 9 32 Writing Your Own GUI Function CHAPTER 10 A Worked Design Example CHAPTER 10 A Worked Design Example This section walks you through a complete design example that of the Micro wave Anisotropy Satellite normal and acquisition modes The MAP Mission The Microwave Anisotropy Probe is a three axis controlled spacecraft It employs reaction wheels for nominal attitude control with Figure 10 1 The Microwave Anisotropy Probe y ROZO as ty ti ge rt f ART PA f I 7 N star trackers and gyros for sensing Ten hydrazine thrusters are available for backup attitude control orbit adjust maneuvers and momentum unloading Control Modes The MAP spacecraft requires three control modes e Mission control mode using reaction wheels with thrusters for momentum unloading This mode would also include the acquisition function e Backup mission control mode with thrusters for three axis attitude control e Orbit adjust mode using thrusters for three axis attitude control The reac tion wheels are kept in a tachometer mode during orbit ch
68. n the three frames on the right Whenever you change the properties the changes are passed to the rest of the GUI For example if you select the earth as the camera center and zoom out you get the following display Figure 9 3 GUIPlugIn with the earth as center 0 30 Spacecratt display FA You can change planets GUIPlugin 9 23 CHAPTER 9 GUI Plug Ins Figure 9 4 Selecting planets in the elements plugin If you hit Run the simulation will run The results at the end are shown in the following figure 9 24 GUIPlugin CHAPTER 9 GUI Plug Ins Figure 9 5 GUIPlugIn at the end of the simulation Orbi Dir ry The 3D window which is animated looks like the figure below Figure 9 6 GUIPlugIn 3D Spacecraft Display QS 3p Spacecraft disptay p GUIPlugin 9 25 CHAPTER 9 GUI Plug Ins Writing Your Own GUI Function GUIPlugin is implemented as shown in Listing 9 1 on page 26 This first Listing 9 1 GUIPlugin function GUIPlugIn action oe Process the input arguments oe if nargin lt 1 action create gui end oe Perform actions oe switch action case help HelpSystem initialize SCHelp case create gui h GetH if isempty h CreateGUI else figure h fig end case run Run case changed Update case quit h GetH CloseFigure h fig end part uses a switch statement to get the right action when GUI Plugin is
69. nce would be significant In that case if you pass it invalid inputs you will get a MATLAB error message Variable inputs Some functions can take different kinds of inputs An example is Date2JD You can pass it either an array year month day hour minute seconds or the data structure month day year hour minute second aaaaa a 4 6 Function Features CHAPTER 4 Basic Functions Example Functions Attitude Stability for a dual spin spacecraft in geosynchronous orbit Many commercial satellite are dual spin stabilized since such a design is very robust dass DSpnstab 1 100 1000 1000 0 7 291e 5 DSpnStab 1 100 1000 1000 The result is dss 0 which means the system is unstable A stability plot is shown below One means stable DSpnStab is a typical function in SCT If no outputs are specified it generates a plot Figure 4 2 Dual Spin Stability gt 2 D Dual Spin Stability Oo BR Platform Rate rad sec Rotor Rate rad sec Compare magnetic torquers with thrusters at geosynchronous altitude The specific impulse is 120 sec and the moment arm is 0 8 m MagTComp 120 0 8 75e 9 The following plot shows the trade off between thrusters and magnetic torqu ers for geosynchronous orbit where the magnetic field is 75 nano Tesla Example Functions 4 7 CHAPTER 4 Basic Functions Figure 4 3 MagTComp 10 T T gt BE Mass kg a T
70. nction You can interactively draw the spacecraft using DrawSC and visualize its attitude and orbit motion by passing the kinematic and position vectors to DrawSC You can generate disturbances using Disturbance and create topological tree models using Tree BIdCAD Building a Spacecraft Model Introduction Build3DSC is used to build a spacecraft model The scripts BuildSc and BuildMAP give examples Build3DSC has several actions which are described in the following table Input data is always entered in the data struc Table 7 1 Build3DSC actions Mode Function g Buildshsey Tinite Initialize the display g Build3DSC add m Add a component g Build3DSC add body m Add a body which is made up of components g Build3DSC compute paths Compute paths to the core body for use in DrawSC ture m You can enter components as vertex face lists or as objects such as an ellipsoid antenna rwa etc The interactive display is shown below 7 2 Introduction CHAPTER 7 Using the CAD Functions Figure 7 1 Build3DSC Lace Compacart Yew Properties big aed Coripe Wee iiaa T Dharat ohai aasa a i a a fet fai pik ipii Ea Trg mmaa Gt o a ie i O mid Hami dera Bevin apa einen apa Each component is shown in the list on the left If you click on the component the properties will appear on the right You can edit them and hit Set Pro
71. nctions 30 FEngine GUI 31 Chapter 13 Figure 12 3 Figure 12 4 Figure 12 5 Listing 12 1 Table 12 5 Listing 12 2 Listing 12 3 Listing 12 4 Listing 12 5 Listing 12 6 Table 12 6 FAero GUI 31 FSolar GUI 32 FPlantNoise GUI 33 FAtmDensi ty GUI 34 Jacchia J70 Atm inputs 34 FAero Main Function 35 FAero Initialize 36 FAero CreateCallback 37 FAero Getting and setting data 37 FAero The Update subfunction 37 VO for STKOrbit 39 Budgets 10 1 Listing 13 1 Listing 13 2 Listing 13 3 Listing 13 4 Listing 13 5 Listing 13 6 Listing 13 7 Listing 13 8 Listing 13 9 Listing 13 10 Listing 13 11 PBudget Example 10 2 Fuel Budget Fuel Budget Fuel Budget Fuel Budget Fuel Budget Fuel Budget Fuel Budget Fuel Budget Fuel Budget Moment Arms 10 3 Thruster performance data 10 4 General spacecraft data 10 4 Array initialization 10 5 Continuous delta v burn 10 5 Delta v with off pulsing 10 6 Unloading momentum 10 6 Using ACS thrusters 10 7 Firing a few pulses 10 7 Fuel Budget Example 10 7 Vi CHAPTER 1 Installing The Spacecraft Control Toolbox CHAPTER 1 Installing The Spacecraft Control Toolbox This chapter shows you how to install the The Spacecraft Control Toolbox SCT It also shows you how to control the path to the Spacecraft Control Toolbox functions Requirements MATLAB 5 2 is required to run all of the functions Most of the new functions use data structures and ce
72. ng a Plugin Function 6 51 CHAPTER 6 Orbit Propagation Reference Frames Coordinate Transformations CoordinateTransform transforms between e ECI e ECR e Geodetic latitude longitude and altitude For example r 6524 834 6862 875 6448 296 x CoordinateTransform eci ef r 2449773 x 1 0e 03 2 85101441662010 9 03243563995045 6 44514208556912 x CoordinateTransform eci t llr r 2449773 x 1 0e 03 0 00059923067422 0 00126505172630 5 08520910899186 Finding ECI ECR coincidence FarthRotationZero finds a Julian date for which the Greenwich Appar ent Sidereal Time GAST is zero For example x EarthRotationZero JD2000 2 5047e 06 6 52 Reference Frames CHAPTER 6 Orbit Propagation gives a Julian Date within a day of JD2000 For this date GASTime x ans 7 2978e 09 You can also find the transformation matrix from ECI to ECR at any time by typing m ECITOECIR jD m transforms from ECI to the frame aligned with EF at time jD This constant offset frame can be used to propagate equations in the ECIR frame Sun SunV1 provides a moderate precision 0 01 deg sun angle uSun SunV1 jD rA dec U2RADec uSun The second function gives the right ascension and declination for the sun Interfacing to STK You can interface to STK using the function STKOrbit STKOrbit allows you to exchange data with STK by
73. nstructor statespace State Space System series connection of two sys tems parallel connection of two sys tems amp append two systems statespace constructor 5 5 CHAPTER 5 Data Structures The operations in the table use underlying toolbox functions For example the in the quaternion methods uses QMu1t m Using the methods you can also multiply transmat objects times quat objects without converting their format yourself The statespace class is used in many of the new control functions An example is shown in the following code listing Listing 5 1 Example of using the statespace class a 0 1 1 2 b 0 1 c 1 0 d 0 g statespace a b c d Second Order x1 x2 x y FrespG g The resulting plot is shown in the following figure Figure 5 1 Second order response 5 6 Input x to Output y De is Magnitude db 5 k RW o z T T 1 L L D T 1 pA Angle deg E T L a oS T 1 L fi 10 1 2 to o Frequency rad sec Notice that the input and output names are in the title The statespace class allows you to keep track of all the matrices state input and output names and the type of state space system in one convenient variable If you type statespace SCT Classes CHAPTER 5 Data Structures SCT Classes without any arguments you get ans statespace o
74. onditions Pane select the stopping condition for the simulation e Customization Pane select simulation options and functions you wish to plug into the simulation e Buttons control the simulation The propagator can be run interactively or as part of a Matlab script Panes Time Pane The time plug in in the upper right corner of the Propagator window contains the values for the epoch maximum duration and time step of the next propaga tion run This plug in allows you to convert the epoch between Julian Date and UTC Calendar date The duration field allows you to enter a maximum dura tion for the run If the specified stopping condition is not met within the speci fied duration the run will stop The default duration is one hour The DT field allows you to specify the time step of the propagation The default DT is 100 seconds DT may be negative A set of times can be entered for the duration For example you could enter O25 Ar 6 36Using the Graphical User Interface CHAPTER 6 Orbit Propagation or linspace 0 60000 1000 sec or 0 1 7 9 11 22 43 900 min or 900 43 22 11 9 7 1 O hr or MyTimeSequence hr or 3 Orbs Any Matlab command or function can be entered into duration If anything except a time is entered DT is ignored The output will be computed at these specific times only The numerical integration routine will select the appropri ate time step to achieved the specified numerical accuracy indep
75. onventions so is not truly ISO compatible Macintosh files are mixed case and can have up to 32 characters It is important that the mixed case not be changed which sometimes happens with installers because the software is case sensitive Some systems such as Silicon Graphics UNIX machines by default will see the HFS partition Most will see the ISO partition Web First get to the PSS website at http www psatellite com The website uses frames The frame at the bottom of the webpage allows you to navigate throughout the site Click on the upgrades button CHAPTER 1 Installing The Spacecraft Control Toolbox Figure 1 1 Home page for the PSS website Bom SAS Forward Reibad Home Search Wetsvape mags Prit Seuurity Sto Te ohio B spet aR protien We can delve Gw Wist wchmolony becmure we are a inely eww Tato Tear ehnolopaes i much avar a actanced chem it pe i en 7 Whether you need review of your own work an algnothm in evtenri an existing design or a complete conn system we can supply the highest quality product at the lowest cost Control Sy6telG Princvton Satelite S ystra ran help you meet Gw chelienes of drierine a E SPETA SOR TOL Pyr berm or OVI VAPOTRTEU in SURTO DYSE TATTIS gian and evaluation Since wa bagan operations i 1002 aur wannie haa inchvied the GPS TIR attitude determination sutara the Calcawarta atitude contiol perian and the Taletar 4 ht onfa Softwar halal EE pee ior Lael weteets or celadl
76. ots The code under the com Listing 10 17 TMAPSim Saving pl Plotting inviInr tDist tMM inrW uW tRWA ot information if nP 0 kP kP 1 xPlot KP x tPlot 1 kP t cPlot kP tC hPlot kP hTotal zPlot kP tMM xI QTForm qIToB 0 0 1 rPlot kP xI pPlot kP acos xI 3 xT 3 ePlot kP rollError pitchError wPlot kKP xT yPlot kP xTB nP nPMax 1 else nP nP 1 end Time control switch simulationAction case pause pause simulationAction case stop return case plot break end end ment time control allows you to control the script from the time GUI 10 12Using the Spacecraft Control Toolbox CHAPTER 10 A Worked Design Example After the simulation is done we plot the results Listing 10 18 TMAPSim Plotting Plot2D tPlot xPlot 1 4 Time sec Qs Ox Oy Oz Quaternion Plot2D tPlot xPlot 5 7 Time sec Wx Wy Wz Body Rates Plot2D tPlot xPlot 8 10 Time sec W1 W2 W3 Reaction Wheels Plot2D tPlot cPlot Time sec X Y Z Control Torque Demand Plot2D tPlot hPlot Time sec X Y Z Body Momentum Plot2D tPlot zPlot Time sec X Y Z Momentum Management Torque Plot2D tPlot pPlot radToDeg Time sec Precession Angle deg Precession Angle Pl lot
77. pacecraft Model The function DrawSC is used to display spacecraft models It has two actions shown in the following table The data structure e contains planetary and Table 7 5 DrawSC Modes Mode Function h Drast rinit gp ll amp Initialize the display a Dranse rua Gy ilo p h Update the display spacecraft position data g is the spacecraft data structure generated in Build3DSC h is an internal data structure that you will not need to modify A typical display is shown below 7 10 Displaying a Spacecraft Model CHAPTER 7 Using the CAD Functions Figure 7 4 DrawSC Spacecraft CAMERA Rotate Plus Rotate Minus Y Rotate Plus Z Rotate Minus 2 C Ambient Light The camera commands allow you to manipulate the point of view The Ambi ent Light button adds artificial ambient light to the scene which is useful for deep space missions Planetary and moon images for all planets for which JPL has data are included Interfacing to the Tree Model TreeCAD is a version of TreeSim that shows you how to create a topological tree simulation using the CAD functions The function TreeB1dCAD replaces TreeAdd for creating topological trees Interfacing to the Tree Model 7 11 CHAPTER 7 Using the CAD Functions Computing Disturbances Disturbances can be compute automatically using Disturbance It will compute the disturbances listed in the
78. per ties to update the properties The valid ranges for all of the properties are shown in the properties display when All is selected When a component is selected the valid ranges are shown only for properties that have not been defined You do not have to define properties for components even if you have already defined properties for some of the components The display in the mid dle shows the spacecraft If you select Local Component View when you select a component only that component will appear in the display Otherwise the entire spacecraft will appear and that component will be highlighted The Azimuth and Elevation sliders allow you to rotate the view Introduction You create a spacecraft model by first entering in all of the components and then collecting them into bodies Adding a Component Each component has an image associated with it The image defines the surface geometry of the object You add a component with the function call Building a Spacecraft Model 7 3 CHAPTER 7 Using the CAD Functions g Build3DSC add m g g is the data structure that is used to store all of the data for the spacecraft m is the data structure that defines the data for the component There are two ways to define the surface geometry One is by defining arrays of vertices and faces The second is to specify a geometric primitive and its asso ciated data structure Listing 7 1 on page 4 shows how to enter a component Li
79. ple Functions 4 13 CHAPTER 4 Basic Functions Figure 4 9 AtmDens2 Atmospheric Density T T T Density kg m L L L L L i L 1 L 0 100 200 300 400 500 600 700 800 900 1000 Altitude km Ephem The ephemeris directory has functions that compute the time and the orienta tion of the earth and planets The most widely used function is to convert calen dar date to Julian Days D Date2JD JD2Date jD ki 2 451251504154273e 06 ans 1999 3 14 O 0 005 0 0589292138814 Graphics Plot2D is used to plot any data It simplifies you scripts by making most popu lar plotting options available through a single function Plot2D will print out a single answer if the inputs are scalar angle linspace 0 4 pi Plot2D angle sin angle Angle rad Sine Sine 4 14 Example Functions CHAPTER 4 Basic Functions Figure 4 10 Sine 0 2 0 4 0 6 0 8 Hardware Pivot mechanisms are nonlinear for large angles If you PivotMch you get a plot of a pivot mechanism angle versus pivot steps Figure 4 11 A sine wave using Plot2D Sine 0 8 0 6 0 4 0 2 Pivot Angle deg Example Functions 6 8 Angle rad Pivot Mechanism Pivot Mechanism type L L L L 400 300 200 100 0 100 200 300 400 Steps 500 4 15 CHAPTER 4 Basic Functions Orbit For attitude control purposes an orbit computed by Kep
80. rbit Propagation This chapter shows you how to propagate orbits and perform related tasks Orbit Propagation Introduction The function PropagateOrbitPlugin allows for 3 degree of freedom propagation of orbits It can be used interactively or in batch mode It has the following features e User selectable gravity models GEM T1 JGM 2 JGM 3 and WGS 84 are supported Other models can be downloaded e Ballistic propagation of covariance matrix for state vector A plug in func tion allows the user to control the plant noise covariance matrix e Propagate in ECI ECR earth fixed or ECIR The last is an inertial frame that is coincident with EF at time 0 e The user has complete control accuracy of numerical integration The prop agator uses the MathWorks state of the art odel 13 propagator e The user can select the time step The time step can be variable and nega tive It can be defined by any Matlab expression or function e The user can specify any one of over thirty stopping conditions e Flight path angle altitude geodetic latitude and longitude are automati cally computed e Outputs can be saved to a mat file for further analysis e Sun moon earth perturbations can be added if you are propagating in an earth centered or moon centered frame Limitations The following are some limitations that will be addressed in the next version e The propagator does not switch centers when the trajectory leaves one planet s
81. re no other perturbations on the orbit This is a good approximation for attitude control purposes but not very good for orbit determination simulations For more accurate orbit simulations use AEarth which generates the acceleration in spherical coordinates for a nonspherical earth gravitation model JSph2Cart is the Jacobian that transforms spherical to Cartesian coordinates The function RVOrbHF integrates the orbit equations using AEarth as the gravity model and can include the effects of the moon sun drag and other orbit perturbations NORAD Elements NORAD orbital elements also known as the NORAD two line elements are used to represent the orbits of all spacecraft tracked by NORAD The toolbox implements five different methods for propagating NORAD elements An example of using the NORAD function is shown below The five propagators Listing 11 18 NORAD m oe oe Demo two of the five NORAD element propagators oe Copyright 1997 Princeton Satellite Systems Inc All rights reserved A ol oe rV NORAD 0 1 5 sgp sgp txt t 0 360 720 1080 1440 disp sprintf nSGP n disp Position for k 1 5 disp sprintf 11 2f 11 2f 11 2f 411 2f t k rV r k end disp sprintf nVelocity for k 1 5 disp sprintf S11 2f 11 2f 11 2f 11 2f t k rV v k end 11 16 Orbit Simulation CHAPTER 1 Simulation 1 Listing 11 18 NORAD m Orbit Simulat
82. rimioiioniciion immira Cerirol lar yagla parici a r E i raria ib ijb ijD il Jha Erect rorraridar Select TGimbal and hit Run The Demo The following time display will appear It shows the ratio of simulation speed to real time gives the per Demos 2 3 CHAPTER 2 Getting Help centage completed and gives you an estimate of when the run will be done You can pause Figure 2 4 Time to Go Display T imbal Sim speed is 262 743 faster than real time 13 40 complete with 00 00 28 1 2 to go Should be complete by 04 06 99 22 50 21 16 the display stop the simulation or plot the current results using the buttons in the GUI If you let it run to completion several plots will appear The following is the last plot Figure 2 5 Results of TGimbal Figure Mo 3 Total Torque Tetal Torgus DemoSC has a wide range of demonstrations Not all use the Time GUI shown above These cannot be stopped using the GUI controls but all of these are short 2 4 Demos CHAPTER 2 Getting Help File Help Introduction The FileHelp function gives you access to the headers of all of the functions in the Spacecraft Control Toolbox You can browse the headers and try out exam ples associated with each function You can also edit the examples create new examples and save them into the help database When you type FileHelp the FileHelp GUI appears Figure 2 6 The file help GUI iep a
83. s If you have the SCT in front of the other MATLAB toolboxes this will not present a problem However some SCT functions will not work properly with the MATLAB Cross and Dot functions Updates You will receive email notification of updates The email will tell you which files need to be downloaded If you cannot download the files contact sup port psatellite com and we will send you a new CD Technical Support Contact support psatellite com for technical support Webboard You can talk with fellow SCT toolbox users and PSS engineers using our Web board Go to http www psatellite com and hit Discussion Board You will then see the webboard Function Overloading 1 9 CHAPTER 1 Installing The Spacecraft Control Toolbox Figure 1 5 Webboard o Netscape Princeton Satelite Systems HomePage 143 Aaeaaads f i Bai forward Reivad Home Search Netscape miages Prit Security Stoo tin Teen pep pei a n i r 1 r 7 Fost REFRCSW SEARCH pean PAGE el iniit Conferences Wacome w ihe Princeton Saiit Sy sma roum Guest amp information 3 l DINMIMO Quaction Amanymowel N10 W eoe Angie Question Anonymous O20 IEI U2 07 Ananya ua NAN To wlomtopiog mithin a sonfaronce aliak a pluc symbol CAN natta a oantornag nama forthe conference namg Heeh in tie hamre to the vent Tank pow for aang the Prmoeton Sakhik yems Fenm Rei Wieb Roan 3 50 00 CAA31997 Ouke Engineenng Ty Reih amp Assogla
84. s Inc All rights reserved oe oe oe Clean up the workspace oe close all Global for the time GUI oe global simulationAction simulationAction Constants degToRad Constant deg to rad radToDeg Constant rad to deg Constant rpm to rad sec K lgo z 5 vs AY wn ll defines a few useful constants The global variable is used to control the time GUI We routinely close all windows The sampling interval is both for the con Listing 10 2 TMAPSim Sampling intervals The control sampling period and the simulation integration time step g a pa s tSamp 0 25 Number of sim steps 2 ms ia nSim 4 3600 Plot every nPMax steps oe nPMax 40 nPlot nSim nPMax Print the time to go message every nITGo steps oe nTTGo 1000 10 4Using the Spacecraft Control Toolbox CHAPTER 10 A Worked Design Example troller and the simulation This is fine if your controller effectively sets the highest frequencies in the simulation If your model includes higher frequency terms which would cause jitter you would need to use a smaller integration steps The rest of the quantities are used to cause the simulation plot less fre quently than once per integration step Listing 10 3 TMAPSim Mass properties Spacecraft Inertias oe inr 2000 0 0 0 2000 0 0 0 4000 inrRWA 1 inrW inrRWA inrRWA inrRWA in
85. s a spherical planet model with the gravitational parame ter extracted from the Constant function Currently this the only model you can use for planets or moons other than the earth You can download GEMT JGM and WGS84 models from various web sites Any file with the suffix GEO will be displayed in the pull down menu You can enter the number of zonal and tesseral harmonics you wish to use If you just want the J2 or J4 zonal you can hit the button to set the appropriate model order 6 38Using the Graphical User Interface CHAPTER 6 Orbit Propagation Stopping Conditions Pane You can select any combination of stopping conditions listed in the pane For each you can enter a tolerance Some require data The stopping conditions are Using the Graphical User Interface 6 39 CHAPTER 6 Orbit Propagation described in the following table Some of the conditions aren t relevant to true Table 6 2 Stopping Conditions Stopping Condition Explanation Impact Stop when orbit crosses the central body ellipsoid This is the same as set ting the geodetic altitude to zero Ascending Node Stop at the ascending node Descending Node Stop at the descending node Apoapsis Stop at apoapsis Periapsis Stop at periapsis Argument of Latitude Stop when v value XZ Crossing Stop when ECI y 0 XY Crossing Stop when ECI z 0 YZ Crossing Stop when ECI x 0 True Anomaly Stop when v value Approac
86. s and wylot hudoet Wa ase well uamed in modam Buggen quch ae Ct aud Ada an wall an o Fuacksien we haw exten with he testing anal wikain of salis fishi yosma One of sw fiat job wen fe a entha far GF Atm Snare now nat att neeheed Marin We alen clevelnnerl a ommi enftuare atimia echmaine for Enreacat Other nminrie metre an Fan nome PrAguct mi omanan Contact if tii V3 Princeton SATELLITE STUTERS What s Hew Product Documentation Discussion Board ObiectAgent Sebbware Up dates fob Opportunitics F33 Aries amp Pagers apace vata Links This will take you to the upgrades page shown in Figure 1 2 on page 5 1 4 Background CHAPTER 1 Installing The Spacecraft Control Toolbox Figure 1 2 The upgrades page Itaj ddI Forward Relbad Home Search tetscape mages Print Securty Stoo roduct and File Updates k eri apiri Jare Le 559 he following link is for Toolbex subscribers and includes Version 9 0 a Software Uperaes Fao nome PrAdoct int imanin Contact if tigi 0s PrinceronSATELLITE SrITERS What s Hew Product Documentation Discussion Board Object Agent Software Updater Job Opportunities FJ Anies amp Pagers apace vata Links Click on Software Upgrades A dialog box will appear Background CHAPTER 1 Installing The Spacecraft Control Toolbox Figure 1 3 Password and user id Enter Your Name And Password 5 Enter username for Princeton Satellite Systems Upgrades Download at www psatellite com
87. s for 6 50 Building a Plugin Function CHAPTER 6 Orbit Propagation edit boxes seen in the GUI uicontrols require you to pass them parame ters in pairs To simplify the code we put a lot of the parameters in the cell atray v The CreateCallback subfunction generates a call back to the FAero function For example the last line creates the call FAero quit tag Listing 6 4 FAero CreateCallback function s CreateCallback action modifier s FAero action modifier See the Matlab documentation on how to build GUIs for more information gets data stored in the GUI and set data sets the data Set Data is used by Listing 6 5 FAero Getting and setting data function d GetData modifier h GetH modifier d cDA str2num get h gui cDA string function SetData modifier d h GetH modifier set h gui cDA string num2str d cDA the orbit propagation function when you pass it the saved propagator data structure Get Data is used internally as shown in the next listing The Update subfunction computes the aerodynamic drag It gets the figure handle gets the data from the figure handle and combines it with the velocity stored in data structure u to compute the force Listing 6 6 FAero The Update subfunction function x Update modifier u t h GetH modifier d GetData modifier x 0 5 d cDA u rho Mag u v u v 1e3 Buildi
88. sphere of influence and enters another 6 34 Orbit Propagation CHAPTER 6 Orbit Propagation e Only the moon and sun are added as perturbations when the earth is the center and the sun and earth are entered as perturbations when the moon is the center e Only centers for which the toolbox has pictures are included This leaves out many moons e Only Mean of Aries 2000 Earth Fixed and inertial coincident with earth fixed frames are available e The noise function is not computed automatically Using the Graphical User Interface The graphical user interface displays all options for using the propagator Figure 6 1 Orbit Propagation GUI oT fo ETE i fe O Pragi Coeur D iper kai tamie Ert Using the Graphical User Interface 6 35 CHAPTER 6 Orbit Propagation Overview The orbit propagator interface which is created by PropagateOrbitPlugin m allows you to propagate any type of orbit using ode113 the MathWork s state of the art propagator The GUI has several different panes These are summarized below The fol lowing sections discuss each in more detail Time Pane set the time e Elements Pane set the initial orbital elements These are always refer enced to the ECI frame e Atmosphere Pane select one of four atmosphere models e Propagation Pane select the coordinate frame in which to propagate e Gravity Model Pane select the gravity model and the order of the model e Stopping C
89. star tracker 8 2 statespace 5 5 stationkeeping box 10 8 STKOrbit 39 Stuffit 1 7 SunV1 39 T tachometer 8 3 Technical Support 1 9 2 12 tesseral gravitational harmonics 10 8 TGimbal 2 3 Time GUI 2 4 TimePlugIn 22 TMAPSim 8 3 TPBudget 10 2 transformation matrix 6 2 transmat 5 5 tree model 9 12 TreeAdd m7 11 TreeBLdCAD m 7 2 7 11 TreeCAD 7 11 TreeCAD m 7 11 TreeSim 7 11 two dimensional probability density function 10 2 U uicontrol 32 UIElement 16 17 19 UNIX 1 3 updates 1 9 upgrades page 1 4 user id 1 6 W Webboard 1 9 2 12 wire model 9 6 Index 3 INDEX Index 4
90. sting 7 1 Adding a component by defining faces and vertices Spacecraft dimensions xW 66 2 yW 62 2 ZW 74 2 m name Nadir Panel m f 1 4 3 2 1 2 3 4 m v xW yW zW xW yW zW xW yW zW xW yW zW m faceColor gold foil g Build3DSC add m g with vertices The origin of the vertex coordinates will depend on how it is later collected into bodies The origin is always defined as the hinge point for the body The hinge point is the point at which the body is connected to the previ ous body in the chain that leads to the core If the body is the core body then the origin is the origin of the spacecraft You can modify the position and orientation of the object using the following fields rB rA rCM b aeaea8a These fields modify both the picture and when an inertia and mass is defined effect the inertia and center of mass contribution of the component These rep resent physical rotations of the components 7 4 Building a Spacecraft Model CHAPTER 7 Using the CAD Functions Figure 7 2 Geometry of a component rCM rB b rA When adding a component it is sometimes desirable to show its location as it would be after it was attached to a body This is done by specifying a position vector m rOffset and a rotation vector m boOffset This position vector and rotation matrix do not effect the vertices once they are attached to a body The color of the faces can
91. t 12 1 xPlot 13 xPlot 13 1 magH abs hPlot 1 hPlot hPlot magH Plot2D tPlot xPlot 1 3 Time sec rECI km Plot2D tPlot xPlot 4 6 Time sec vECI km sec i Plot2D tPlot xPlot 7 10 Time sec q ye Plot2D tPlot dOmega Time sec dOmega rad sec Plot2D tPlot hPlot 1 Time sec H H 0 1 Js WirePlot xPlot tPlot wireDS disp sprintf Max momentum change 12 4e with dT 8 4f and tSim 8 4f max abs hPlot 1 dT tSim The results of this wire simulation are shown in the following plot Figure 11 3 Wire simulation Results 10 x10 Wire 1 Position x m o 0 05 0 04 E 0 03 J gt 0 02 4 0 01 z m L L 0 20 40 60 80 100 120 Time sec Wire Model 11 11 CHAPTER 11 Simulation Tree Model The tree model simulates multibody spacecraft arranged in a tree configuration Figure 11 4 Topological Tree There can be no closed loops which also means that for any component exactly one hinges leads to the core All of the subbodies are rigid and only rotational degrees of freedom are permitted at each hinge In addition the number of degrees of freedom at a hinge can be either 3 or 1 To simulate 2 dof hinge just interpose a massless and inertialess body The following script illustrates the use of the tree model 11 12 Tree Model CHAPTER 11 Si
92. talog of PSS products tutorial pdf This tutorial license pdf The software license Please read it The documentation is readable using Acrobat Reader 3 x or greater If you downloaded the files copy SCMat into the SC directory Installation Copy the directory into any convenient location on your system Start Matlab and find the function PSSInstaller Type in the command window PSSInstaller This will set the paths Case Sensitivity SCT files are case sensitive All SCT filenames use the convention that the first letter is capitalized and word breaks even if the word is represented by an ini tial are capitalized For example you should see RVOrbHF m not rvorbhf m If you see the latter either contact your system administrator or send email to support psatellite com If you see the latter and copied the files from a CD ROM you may have a problem with you copy utility or the CD has a problem If you downloaded from the web your decompression utility preferences may have to be changed 1 8 Installation CHAPTER 1 Installing The Spacecraft Control Toolbox Function Overloading The Spacecraft Control Toolbox overloads the MATLAB Cross and Dot func tions and the earth mat file The SCT functions have all the functionality of the MATLAB Cross and Dot functions but have additional features The SCT earth mat file is a special data structure used by the toolbox for dis playing planetary image
93. tes ine WebBoard ics tradamacl of O Paip Q Arosistar lr Fad rome Frodo ml oman Lonlacl i tigi Us PrinceronSATELLITE SPITERI What s Hew Droduct Doc umentati Discussion Board ObiectAgent Sobbware Up dates dob Oppertund Pa ANTES amp Pagers opaite ala tints Webboard CHAPTER 2 Getting Help CHAPTER 2 Getting Help This chapter shows you how to use the help systems built into the Spacecraft Control Toolbox There are three sources of help One is the demo functions the second is the file help function and the third is the graphical user interface help system Demos If you type DemoSC you will see the following GUI Figure 2 1 DemoSC The list on the left hand side is hierarchical The GUI checks to see which directories are in the same directory as DemoSC and lists all directories and files This allows you to add your own directories and demo files The first category is ACSDesigns Click on the name to open the directory The sign changes to and the list changes 2 2 Demos CHAPTER 2 Getting Help Figure 2 2 Opening ACSDesigns Pensare Demos Tea hn Seript If you would like to look at or edit the script hit Show the Script This opens the MATLAB edit window Figure 2 3 Edit Window vip o gisbeled thorter rintiongeeping conirel mias Thin ip the iypa of mai cad wiih ihe Gheriile OF kriyir Copyright Princeton Goialliie Gaiss ini AII rights ramara ictal
94. though some are rarely called except by other toolbox functions The SPACECRAFT CONTROL TOOLBOX is organized into a number of directo ries based on topic These directories organize the on line help feature in MAT LAB Currently the toolbox is broken into the directories listed in the following table Several of the directories are new in V3 0 4 2 Table 4 1 Toolbox Organization Directory Purpose Actuator Actuator models Attitude Attitude control analysis functions CAD Compute aided design Classes MATLAB classes for state space systems quaternions and rotation matrices Control Control system design functions Coord Coordinate transformation Database Database examples Dynamics Functions for numerically simulating spacecraft Environs Environmental models including magnetic field atmospheric density etc Ephem Ephemeris functions giving orbital elements of the planets earth orientation etc t New in V3 0 Introduction CHAPTER 4 Basic Functions Introduction Table 4 1 Toolbox Organization Directory Purpose General General purpose functions Graphics Drawing plots 3D pictures etc GSC Functions implementing a geosynchronous satellite control system GUIPlugin Graphical user element plug in elements Hardware Miscellaneous hardware models Help Help system functions LowLevel Functions used
95. ting errors the category totals and the totals The 3 sigma error is the angular error that there is a 0 98655 probability that the beam center is within If the last input is given PBudget will create a pointing budget file called MyBudget The circular error is computed by numerically integrating the two dimensional probability density function for azimuth and elevation The Matlab quad rou tine is used to perform the inner integration A bisection search is used to find the value of angular radius with that marks the 3 sigma boundary A complete pointing budget is given in the script TPBudget 13 2 Pointing Budget CHAPTER 13 Budgets Fuel Budgets Computation of fuel budgets is a straightforward bookkeeping exercise The most important point to remember is that the fuel consumption of the thrusters is a function of system pressure Consequently fuel budgets must be done chronologically FBudget generates fuel budgets There are four types of maneuvers supported They are spin precession maneuvers spin changes AKM firings and station keeping maneuvers You set up each maneuver using the FBudget data struc tures as shown in the following example Listing 13 2 Fuel Budget Moment Arms Fuel Budgets oe You need position vectors and moment arms 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 O a2 2 02 OZ 5 0 9 0 8 0 7 0 8 0 8 0 8 0 8 0 8 0 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 9 0 8 0 8 0 7 O 0 2
96. tructure from outside of a class method This allows the class designer control access to the data so that the user cannot use it in an incorrect manner Object oriented design terms are listed in the following table Table 5 1 Object oriented design terms 5 4 Term Definition class A data structure definition and functions that operate on that data structure constructor A method that creates an object of type class instance A variable of type class In MATLAB if you type x 2 you create an instance of class double method A function that is part of a class Classes CHAPTER 5 Data Structures Table 5 1 Object oriented design terms Term Definition object An instance of a class When you type x 2 you create an object of class double inputs overloading Giving a meaning to an operation that is specific to a class For example in the statespace class means paral lel connection of state space systems polymorphism When a function behaves differently for different types of SCT Classes The following table lists all of the classes used in the toolbox and some of their methods SCT Classes Table 5 2 Classes Class quat Use Quaternions Methods matrix converts to a transforma tion matrix quat constructor scalar vector transmat Transformation Matrices x quaternion converts to a quater nion transmat co
97. ts out all of the information in the data structure Initialize the multibody tree and preallocate arrays Listing 11 15 Tree Simulation Initialization Initialize the multibody tree oe treeDS x TreeInit body r v Print out the tree oe TreePrnt body treeDS Plotting and initialization tSim 20 dTSim 0 1 nSim floor tSim dTSim hPlot zeros 1 nSim tPlot zeros 1 nSim xPlot zeros length x nSim t 0 11 14 Tree Model CHAPTER 11 Simulation Run the simulation The angular momentum is computed for informational purposes only Listing 11 16 Tree Simulation The simulation loop Run the simulation oe for k 1 nSim oe Save for plotting oe hPlot k Mag TreeH x t treeDS body xPlot k x tPlot k t oe Update the equations of motion oe x RK4 Tree x dTSim t treeDS body t t dTSim end Plot the results Listing 11 17 Tree Simulation Plotting TreePlot tPlot xPlot treeDS body hPlot An example plot is shown below Figure 11 5 Tree Simulation One of several plots Tree Model nee Rate Link 0 15 0 17 0 05 1 0 2 4 6 8 10 12 14 16 18 Time sec 20 11 15 CHAPTER 11 Simulation Orbit Simulation Introduction The orbit models presented so far have assumed that the earth is a spherically symmetric body and that there a
98. two ways to get default parameters If you pass as a parameter the function will use a default parameter This is only necessary if you wish to use a default for one parameter and input the value for the next input For example g EarthRot 1 g gt 0 8091 0 5877 0 0 5877 0 8091 O 0 0 1 0000 Built in plotting Many of the functions in the toolbox will plot if there are no output arguments In many cases you do not need any input arguments to get useful plots due to built in defaults Most of the functions in the toolbox are compatible with MATLAB 4 x or ear lier However many of the newer functions make extensive use of data struc tures and are compatible with versions 5 x or newer We recommend that you Function Features 4 5 CHAPTER 4 Basic Functions get the latest version of MATLAB since in the future we will make even more extensive use of data structures and other object oriented features The following function will generate a plot PlanckL and so will 32 PlanckL because there is no equal sign If no inputs are given it automatically computes a range of values To prevent plotting and to get an output you must type PlanckL 5760 1 or x PlanckL Error checking Many functions perform error checking However functions that are designed to be called repeatedly for example the right hand side of a set of differential equations tend not have error checking since the impact on performa
99. vinr inv inr tDist 0 0 0 oe Wheel spin axis unit vectors oe uW eye 3 Listing 10 3 on page 5 defines the spacecraft mass properties This set is not based on the actual MAP properties but is for demonstration purposes only We are using a gyrostat rigid body wheels model that allows for any number of reaction wheels so we must include the spin axis inertias of the wheels We will use three orthogonal wheels Listing 10 4 TMAPSim Tachometer loop design Design the control loops ea asas za pe fo RWA Tach loops zeta 0 7071 Damping ratio wN 1 0 Closed loop undamped natural frequency aTL bTL cTL dTL PIDesign zeta wN inrW 3 tSamp Delta First design the inner tach loops for the reaction wheels Our attitude control loops will actually command rate changes to the wheels The inner loops will handle uncertainty in friction wheel motor scale factors etc PIDesign uses pole placement to design a PI loop In this example we will implement the con trollers in delta form so that state space equations produce delta s to the control commands not the actual value Using the Spacecraft Control Toolbox 10 5 CHAPTER 10 A Worked Design Example Next design the attitude loops We are only controlling the spin axis orienta tion so we only need two loops roll and pitch we are spinning about yaw PIDMIMO designs a PID controller with a rate filter
100. with the x dimension y dimension z dimension of the ellipsoid If the planet is spherical the three dimensions are the same 6 54 Ground Coverage CHAPTER 13 Budgets CHAPTER 13 Budgets This chapter discusses how to generate pointing and fuel budgets These bud gets are some of the most important elements of spacecraft system design Pointing Budget PBudget generates antenna beam pointing budgets Its inputs are a n by 3 matrix of error contributions an n by m matrix of categories an n by m matrix of descriptions and a 2 by 1 matrix of antenna offsets For the category and description matrices m signifies the length of the longest string PBudget Listing 13 1 PBudget Example errors 0 01 0 02 0 03 0 02 0 04 0 01 0 04 0 03 0 05 0 05 0 00 0 06 degrees categ Bias categ str2mat categ Bias categ str2mat categ Diurnal categ str2mat categ Diurnal desc Thermal desc str2mat desc Misalignments desc str2mat desc Thermal desc str2mat desc Misalignments aZ 0 0 eL 0 0 cep r s t PBudget errors categ desc aZ eL MyBudget always adds categories and combines errors within categories by taking the square root of the sum of the squares You can have as many categories as you wish The descriptions have no effect on the computations The outputs are the 3 sigma circular error the azimuth and elevation beam poin
101. y the other modes but also the attitude determination function the momentum unloading system and the telemetry and command functions Although the spacecraft is mostly single string a fault detection and isolation system might also be included to protect the spacecraft against tem porary problems Summary CHAPTER 11 Simulation CHAPTER 11 Simulation Several different functions are included in the toolbox for simulating space craft attitude and orbit dynamics They range from simple rigid body models to sophisticated multi body models CHAPTER 11 Simulation Dynamics Models The following table lists the dynamics models and their capabilities Some Table 11 1 Attitude Simulation Functions State Function eae Purpose Rana Output ASim Attitude simulation of a rigid body DIModel Double integrator model FAKM Solid rocket simulation FDC constrained equations in the form MxDot F FGs Gyrostat dynamics with quaternion kinematics GSMode1 Gyrostat dynamics FPivot Spacecraft with pivoted momentum wheel and quater nion kinematics SCwPivot Spacecraft with pivoted momentum wheel FRB Rigid body with quaternion kinematics RBMode 1 Rigid body FTB Two body with quaternion kinematics TBModel Two body FXModel Flexible spacecraft model MBMode1 Momentum bias spacecraft dynamics only Dynamics Models CHAPTER 11
102. ze subfunction draws the GUI and returns the tag for the fig Listing 6 3 FAero Initialize function tag Initialize propagateOrbitPluginTag nam Aero Model Initialization position 5 5 300 200 tag GetNewTag name h fig figure position position color 0 66 0 66 0 66 NumberTitle off name name resize off tag tag fontSize position 4 9 185 v parent h fig fontunits pixels fontsize fontSize horizontalalignment left space position 3 40 x0 space dX position 3 2 xW dX space dy position 4 2 space 3 yw dY space x x0 y position 4 d The orbit propagator tag h propagateOrbitPluginTag propagateOrbitPluginTag Inputs h gui cDAText uicontrol v position x y xW yW string cD A style text x x xW space h gui cDA uicontrol v position x y xW yW VS tring Su Oa style edit x x0 y y d GUI controls xW position 3 5 space 3 x position 3 xW space y y space h gui help uicontrol v position x y xW yW string Help callback CreateCallback help tag x x xW space h gui quit uicontrol v position x y xW yW string QUIT callback CreateCallback quit tag x x xW space PucHi ih ure The Inputs and GUI controls lines show you how to write uicontrol

Spacecraft Control Toolbox User's Guide V3.0

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