TECHNICAL NOTE NASA TJN D-5869 - Klabs

NOMENCLATURE (Conthued). . ([GS VG; 5 ) : .instantaneous and terminal gravitationalin the terminal referencesystem, respectively.*Ndescending nodal angle of target orbitmeasured counterclockwise from thelaunch meridian in the equatorial plane.null out the velocity deficiencies in theremaining estimated flight time, withoutregard to terminal radius measured in thet ,q , 5 coordinate system.(tGT,qGT, G Tcomponents)7. 7Tangle between perigee vector and targetvector in the nominal transfer ellipse.uangle used to estimate the location of theterminal radius vector in the desiredorbit plane, measured positive clockwisefrom the positive X , -axis.@TXYi-XZi%instantaneous and desired terminal flightpath angle, respectively, measured posi tive counterclockwise from the localhorizontal.IGM computed pitch and yaw angles asmeasured in the 5, n, 5 coordinate system. ’angle between theignition.First stagefrom initiation of IGM calculations afterS-II stage ignition until the propellantmixture ratio change occurs.Second stagefrom the time the mixture ratio changeoccurs until S-II cutoff.Third stageS-IVB stage burn into orbit.Fourth stagefrom after S-IVB reignition until the pro pellant mixture ratio change occurs.Fifth stagefrom the time the mixture ratio changeoccurs until S-IVB second cutoff.pitch and yaw attitude steering hngles.UXY, xzx.;‘ ,X i ’pitch and yaw steering angles required to.viis and Tp at S-IVB re

DESCRIPTION AND PERFORMANCE OF THE SATURN LAUNCHVEHICLE'S NAVIGATION, GUIDANCE , AND CONTROL SYSTEMSUMMARYA review of the navigation, guidance, and controlsystemof the Saturnlaunch vehicle includes the system analysisand design, signal flow diagrams, redundancy, and selfchecking features used to obtain extreme reliability forcrew safety.The iterative path adaptive guidance mode, featuringflight path optimization, is explained and presented inits computational form. Following the analytical con siderations, the main guidance and control componentsa r e described. The navigation and control informationis obtained inertially by a gyro-servo-stabilized, threegimbal platform system with three mutually orthogonalpendulous-integrating gyro accelerometers; the single degree-of-freedom gyros a s well a s the accelerometersuse externally-pressurized gas bearings. Rate gyro scopes provide attitude stabilization; some vehicle con figurations require additional accelerometer control toreduce wind loads. The digital computer system servesa s the computation, central data, and onboard program ing center. which ties in with the ground computer sys tem during the prelaunch checkout of the overall system.The control signals a r e combined. shaped, attenuated,and amplified by an analog type control computer forengine actuator control.Results from recent launchings of Saturn V vehicles a r epresented to confirm the adequacy of the navigation,guidance, and control system and its overall perform ance even under extreme flight perturbations.of the Saturn class launch vehicles is used as a typicalexample for the design requirements and the solutionsto obtain an optimal system that guides and controls themultistage launch vehicle.LAUNCH VEHICLE FLIGHT PHASESAerodynamic pressure (Q), acceleration (F/m), and ve locity (V,) for a typical three-stage Saturn V flight tra jectory into earth orbit a r e shown in Figure I.&ringthe first stage flight, the vehicle traverses the highaerodynamic pressure region. Structural load8 fromaerodynamic forces a r e kept a s small a s possible bycontrolling the vehicle with a minimum angle of attack;therefore, in this first stage flight, a standard tilt pro gram is used and guidance corrections are not intro duced before the early part of the second stage flight.For attitude stabilization, attitude control signals fromthe inertial platform stabilized by three orthogonallyarranged single-degree-of-freedom gyros and angularrate signals derived from rate gyroscopes are used; inspecific cases, control accelerometers can generateadditional attitude control commands. The actual shap ing of these signals and their application will be de scribed later.,An iterative guidance mode for flight path adaptive guid ance has been developed to guide the vehicle along ILminimum propellant trajectory to fulfill the desiredorbital or transearth conditions. The guidance systemdetermines the crossrange flight path corrections andthe proper cutoff commands to obtain the required ve locity vector for the flight vehicle.INTRODUCTIONITERATIVE PATH ADAPTIVE GUIDANCE MODEThe missions of large launch vehicles comprise mannedflights a s well as unmanned flights. For these flights,it is not economically feasible to use different guidanceand control systems; therefore, the same system mustfulfill the various operational requirements necessarytomeet the severe combinations of accuracy, reliability,and lifetime. For vehicles with nonrecoverable boosterstages, a single guidance and control system must ac complish all the requirements. The present technologysolves the control problems of the different flightphaseeby discrete, preprogramed operating modes rather thanby self-adapting or learning methods as foreseeable infuture systems.In the following review, the guidance and control systemThe optimizing techniques of the calculus of variationewere used to develop the iterative path adaptive guidancemode. Experience with hundreds of minimum propellanttrajectories for various orbital injection missione hasdemonstrated that the optimum thrust direction relative.to the local vertical is very nearly a linear function oftime duringvacuum flight. Moreover, the s h e of theangle between the optimumthrust direction and the localhorizon is never very large for an orbital mission (Fig.2). These observations show a remarkable agreementwith the mathematicalresults obtained fromthe calculusof variations when a flat earth model having a constantgravitational field is used and position and velocity con straints a r e imposed at cutoff. A closed solution, which

IIIIII.--. I.1.-.--.I.1,.-.1.48 36 24 12 0-F I G U R E 1.A C C E L E R A T I O N , V E L O C I T Y , AND A E R C D Y N A M I C P R E S S U R E FOR A T Y P I C A L SATURN V TRAJECTORY,.OPTIMUM THRUST DIRECTIONRELATIVE TO LOCAL HORIZONTAL AT CUTOFFX p a r c tan ( A t E t )zA BtOPTIMUM THRUST DIRECTIONRELATIVE TO WCAL HORIZONTALI.--.FLIGHT TIME ( 5 )F I G U R E 2.2L.600550O P T ! M U M THRUST A N G L E P R O F ! L E .II650700

can be obtained with this mathematical model, yields anexplicit equation for the optimum thrust direction. (1)This equation has the formIX.11: SPACE-FIXEDIXv. .'NAVIGATION:S P A C E - F I X E S:(11XP arc tan (A Et)I: INSTANTANEOUSVALUESc TERMINAL VALUESwhere x is the optimum thrust direction for minimumPpropellant consumption. Constants A and B a r e deter mined by the specified cutoff velocity and position, theinitial values of the state variables, the vehicle thrustacceleration, and the engine specific impulse. The com parison of this equation with the results of trajectorystudies suggests the use of the approximationI :G U I D A N C ECOORDINATEL."*C"POI",VALUES7XP A Bt.A guidance coordinate system (Xv, Yv, 2,) (Figs. 3 and4 ) is established with the origin at the center of the earthand with the XV axis lying along the vertical which inter sects the calculated cutoff position of the vehicle. Sim plified equations of motion a r e derived to approximatethe motion over an oblate earth with a realistic gravita tional field. These equations of motion a r e solved dur ing flight to determine the instantaneous range angle tocutoff, the time-to-go to cutoff, and the gravitationaleffects occurring over the remaining flight time. Thisinformation is used to compute values for A and B con tinuously during flight except near cutoff.F I G U R E 4.NORTHPLATFORMAND CENTERr%(x.Y,Z)VGeodetic latitude of launch s i t e .Space-fixed coordinate system for guidance computations with itsdefine the nightorigin at the earth's center. The x and z( . I I , & ) Inertial coordinate system established by the orientation of theaccelerometers on the stabilized platform and parallel to the X,Y,zsystem at launch.(U,V , W )Space-fixed coordinate system with its origin at the earth's center.The U-V plane contains the launch point.F I G U R E 3. G U I D A N C E C O O R D I N A T E S Y S T E M S .C O O R D I N A T E S Y S T E M OF T H E I T E R A T I V EGU ID AE!C E SC H E ME.Special procedures a r e required during the last severalseconds before cutoff because the equations give an in determinate command angle a t the cutoff point. Thisprocedure is established a s follows: the quantity A maybe expressed a s the sum of a function of velocity, A (V),and a function of altitude, A @). Near cutoff, the alti tude term will require very large command angles evenfor small altitude errors. Since the vehicle attains thedesired altitude before the desired cutoff velocity isreached, the altitude term may be dropped from the cal culations several seconds before cutoff without degrad ing the injection accuracy. Moreover, the rate term, B.is not needed because the vehicle turning rate is smalland nearly cons Aat; this term may also be droppedk o m the calculations without penalty. The altitude con straint and the rate term a r e preseatly dropped in theSaturn V flight program a t approximately 46 seconds be fore cutoff. The resulting steeringlaw is termed thechi tilde mode. A further improvement is accomplishedin the cutoff region by freezing the command angles atapproximately 8 Se"before cutoff. A represent tive s e t of equation8 la shown in Tables 1 and 2. (2) Asimp1epresetting isto Mtiate en@e cut off going into earth orbit, and an energy equation irused to effect engine cutoff for injection into lunar trr jectory.3

Table ia. IGM Navigation and Guidance into Earth OrbitI'FOR ORBITALINJECTION ONLYIII1IIIIIIII,IIIIIUPDATE STAGEINTEGRAL VALUESUSING NEW TIMETO- GO ESTIMATE4I4COMPUTEICOMPUTE VELOCITYPITCHVELO C I TY 0NLYSTEERING ANGLESIIL ,STEERINGONLYIIINTEGRAL VALUES&EYA- - - ---1GUIDANCEYESUPDATEOUT-OF-ORBITRANGE ANGLERANGE ANGLEIICOMPUTE NEWTERMINAL VALUESOUT- 0F- 0R B ITONLYESTIMATE OFTIME TO- GO-IIIIITERMINALsNTO ;F REEZECOMMANDS)COMPUTEIIROTATE TERMINALVALUES OUT-OFORBIT ONLYI, T RATE OF THEISTEERINGCOMMANDS TERMINAL VELOCITY

Table ib. Iterative Guidance Mode EquationsSTAGE INTEGRAL CALCULATIONS[GI[r&[l.[G]uz OZrZ-vEX2 ;/61YAW STEERING PARAMETERS1TiPARAMETERS UPDATEDUP I,T3 T3Ti:T iL3: I) A L JyJIz t Ja LaTlcSySi2OyO l z t 0 3 S 3 T i t T t T 3 1 J l zKy L y /JyDy Sy-KyOyA7:7K; A 7 / D y corxz-Ja LyT3,Ly L y * A L a Tl ?cT:1 2 t S y sinXZ1REMOVEALTITUDECONSTRAINTKI :K 2 0K3 K 4 0K 3 : K; [l-lK:lz/TRY]K4iKyK3'ITCH STEERING PARAMETERSLp:LycosZzcp cq IJpsp OP Kp Dp A t KI KIRT, VT ,yTRTCOMPUTATIONS T a f tKZ r - - -.'Ip/(l ecortGUIDANCETIMEUPDATEIGM STEERING ANGLESX:'x z - K 3 K,ICUTOFFWHEN VTACHIEVE0II

Table 2a.FORGuidance Inputs and Out-of-Orbit GuidanceRESTARTCONTINUEORBITALOPPORTUNITYVA R IA 8L UESVALUESl lLYESYESCOMPUTESTEERINGCOMMANDSbI No40CUTOFFWHENDESIRED ENERGY1 YESCOMPUTE OUT-OFORBIT VALUESTCOMPUTE STEERINGANGLESFORRESTART ATTITUDEISACHIEVED

Table 2b.Guidance Inputs and Out-of-Orbit GuidanceDEF IN ITlONSpPI i SEMI-LATUS RECTUM OF THETERMINAL ELLIPSE.PRODUCT OF UNIVERSALGRAVITATIONAL CONSTANTAND EARTH MASS.TARGETVECTOR I NEPHEMERAL COORDINATES.See,,NODAL VECTOR.ECCENTRICITY OF THETRANSFER ELLIPSE.' ECCENTRICITY OF THENOMINAL TRANSFER ELLIPSEVARl ABLESOUT-OF-ORBIT [GI MATRIX CALCULATIONSINPUTS. .FOR BOOST-TO-ORBITTI' TIME REMAINING I N THE FIRST T iSTAGE OF I G M G U I DANCE.T2 ' TIME REMAINING I N THE SECOND TcSTAGE OF I G M GUI DANCE.Vexl EXHAUST VELOCITIES FORT4NFIRST STAGE OF IGM.Vexes EXHAUST VELOCITIES FOR SECOND R,'STAGE OF IGM.VT Vex3' EXHAUSTVELOCITIES FOR THIRD YTSTAGE OF IGM.7, ESTIMATED TIME TO DEPLETE'VEHICLE MASS BEFORE SECOND As MRS.72 ESTIMATED TIME TO DEPLETE VEHICLE MASS FROM MRS TO n STAGE CUTOFF.73ESTIMATED TIME TO DEPLETES-IVB MASS.TIME REMAINING I N THIRD ORFIFTH STAGE BURN.COAST TIME BETWEEN 8-1 IBURNOUT AND S-IVB IGNITION.NOMINAL TIME I N 3RD IGMSTAGE.DESIRED TERMINAL RADIUS.DESIRED TERMINALVELOCITY.DESIRED TERMINAL FLIGHTPATH ANGLE.N 4Z Ln lTt - T gl".N OLIFTOFF TIME.OPENING OF LAUNCH WINDOW.GEODETIC LATITUDEOF THELAUNCH S ITE. ";1lNPUTS FOR OUT-OF-ORBIT '2R 'IR'3R Ken M2R '3,ROVR* TRPRJRYRMNR CONSTANT TIME FOR SELECTION OFGUIDANCE OPTION 'XHICH ENFORCESONLY TERMINAL VELOCITY END CONDI TIONS DURING S-IVB SECOND BURN.CONSTANT TIME FOR SELECTION OFGUIDANCE OPTION WHICH ALLOjVSAN ALTERNATE COMPUTATION OFTHE TERMINAL RANGE ANGLE DUR ING S-IVB SECOND BURN.CONSTANT TIME FOR SELECTION OFGUIDANCE WHICH FREEZES THETERMINAL CONDITIONS DURING THESECOND S-IVB BURN.CONSTANTTO UPDATE ECCENTRICITYFOR SECOND OPPORTUNITY INJECTION.MASS FLOW RATE OF 5-IVB PRIORTO MRS DURING SECOND BURN.MASS FLOW RATEOF S-IVB AFTERMRS DURING SECOND BURN.CONSTANTFOR BIASING THE TERMINALRANGE ANGLE PREDICTION DURINGS - I V 9 SECOND BURN.CONSTANTS USED TO BIAS THEPITCH & Y A I STEERING PARAMETERSDURING S-IVB SECOND BURN.STAGES OF IGM.MASS OF VEHICLE AT THE NOMINALS-IVB REIGNITION POINT.0.8'.CONSTANT ANGLE DEFINING THE LOCATIONOF THE PSEUDO NODAL & VECTOR 'VITHRESPECT TO THE RADIUS VECTOR I N THEIGNITION PLANE AT 8 - I V B RESTARTPREPARATION TIME FOR 1st & 2ndOPPORTUNITIES, RESPECTIVELY.p,,p; CONSTANT ANGLE DEFINING THE LOCATIONOF THE NODAL ISIVECTOR WITH RESPECTTO THE RADIUS VECTOR I N THE IGNITIONPLANE AT S-IVB REIGNITION OF 1st &2nd OPPO2TUNITIES. RESPECTIVELY.THEN OMIijAL PLANE ANGLE BETWEENa&THE IS1 & T VCCTORS AT REIGNITION.,T,NOMINAL dlh STAGE BURN TIME.ESTIMATE 5th STAGE BURN TIME.T'xa INITIAL ESTIMATE AT THE LOCATION OFTHE TERMINAL RADIUS VECTOR FORS-IVB SECOND BURN.ESTIMATED TIME TO DEPLETE VEHICLE7. x 0MASS I N THE SECOND BURN OF 8-IVB.NOMINALTHRUST AT 8 - I V B REIGNITION.FNRKal COEFFICIENTS OF POLYNOMIAL DEFININGK D THE ANGLE UTS. RADIUS AT NOMINAL 8 - I V B REIGNITIONRNRIGHT ASCENSION OF THE LAUNCH SITE.RA:DE DECLINATION OF LAUNCH SITE.ENERGYOFTHE DESIRED TRANSFER ELLIPSE.C3COSa . COSINE OF THE ANGLE BETWEEN THEPERIGEE &TARGET VECTORS I N THENOMINAL TRANSFER ELLIPSE., i Ti"8.'1,aREIGNITIONYES

F / z .INERTIAL,-qAVELOCITY - - INCREMENTAL INERTIAL VELOCITY VECTORXI- T O T A L I N E R T I A L V E L O C I T Y VECTORAXIXIXg--TOTALI N E R T I A L ACCELERATION VECTOR-TOTALGRAVITATIONAL V E L O C I T Y VECTORXg-TOTALGRAVITATIONAL ACCELERATION VECTORN O T E : SUBSCRIPT i D E N O T E SINITIAL VALUE.-GRAVITYCOMPUTATIONx, (X,,Y,,Z,)XsiF I G U R E 5.M E A S U R E D V A L U E S AND N A V I G A T I O N C O M P U T A T I O N S .The guidance system requires inputs *om the naviga tion system to compute the thrust direction command.Figure 5 shows the process by which the inputs to theguidance equations are determined.Inertial velocitycaused by thrust and aerodynamic forces acting on thevehicle is measured by accelerometers mounted on theinertial platform. The readings a r e processed in theaccelerometer processing routine where they undergoreasonableness testa to determine the accelerometeroutputs to be used, After the inertial velocity is ob tained, these values a r e used in the navigation calcula tions to compute the inputs required in the guidanceequations. These inputs a r e the vehicle state vector(position and velocity vector), the vehicle inertial ac celeration magnitude, and a measure of the time, T,necessary to burn the complete vehicle (assuming aconstant mass flow rate and thrust).8LAUNCH VEHICLE CONTROLIntroduction to LauEch Vehicle Control. ProblemDuring propulsion, the attitude control system must ap propriately orient the thrust vector relative to thevehi cle such that the required attitude commands a r e per formed in a satisfactorily damped mode of rotation.Problems in vehicle control arise because Saturn vehi cles cannot be considered rigid but must be treated aadistributed masses connected by an elastic structure.Forces acting on these masses resulting from atmos pheric perturbations or active control of the vehicle ex cite the complex spring-mass system and cause bodybending. Since the structure possesses low damping,oscillatory bending modes of considerable amplitudecan be produced; the control sensors may be subjected

to these large amplitude oscillations a t their particularlocation. Thus incorrect information about the total ve hicle behavior may cause self-excitation and instabilityof the vehicle control system.Another problem is that the vehicles a r e aerodynaml cally unstable during most of the propelled flight in theatmosphere. As an example, Figure 6 is a plot of thecenter of pressure and the center of mass for the firstphase of the Saturn V and shows that the vehicle ie un stable except for a short period of time around the 60thflight second.The conk01 system designer must consider that pro pellant sloshing exerts low frequency forces on the ve hicle, and excitation through the control loop must beprevented. Also many vehicle characteristic data varywidely with time and the individual propulsion stages;w40F2[[CENTER OF PRESSURE- *0-m0CENTER OF MASS20 -F I G U R E 6.V A R I A T I O N S O F C E N T E R O F P R E S S U R E AND C E N T E R O F M A S S D U R I N G F L I G H T .9

11111I 111 1111111111 II IIIIII111 I.Isome can be predetermined only to a certaindegree andtolerances must be Impose

TECHNICAL NOTE \ NASA- TJN D-5869 DESCRIPTION AND PERFORMANCE OF THE SATURN LAUNCH VEHICLE'S NAVIGATION, GUIDANCE, AND CONTROL SYSTEM by WuZter Huenssermunn George C. MurshuZZ Space FZight Center MurshuZZ Spuce Flight Center, AZu, 35 812 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. JULY 1970