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AIAA Guidance, Navigation, andControl Conference and Exhibit14-17 August 2000 Denver, CO AOO-37151 AIAA-2000-4452

INTERNATIONAL SPACE STATION CMG MOMENTUM DESATURATION DESIGN

Nazareth S. Bedrossian1,The Charles Stark Draper Laboratory, Inc.

2200 Space Park Dr, Suite 210,Houston, TX 77058

Abstract

The CMG momentum desaturationmethod developed by Draper Laboratory forthe International Space Station for useduring robotic payload operations ispresented. A frequency optimal feed-forward thruster pulsing strategy that isindependent of plant description isdeveloped to minimize structural excitation.The flight software implementation detailsare presented. Simulation results are used toillustrate the design.

Introduction

The assembly and operation of the InternationalSpace Station poses unique control challenges due toits complex, variable flexible structure and massproperties during assembly stage as well as variety ofoperational modes which include robotic payloadoperations using either the Space Station RemoteManipulator System (SSRMS) and/or the ShuttleRemote Manipulator System (SRMS). Robotic largepayload operations required for Space Stationassembly can saturate the momentum capability ofthe Control Moment Gyroscopes (CMGs) whichprovide attitude control. Consequently, the use ofthrusters will be required to desaturate the CMGssince free drift is not allowed due to thermalconstraints.

Thruster activity during robotic payloadoperations poses certain sub-system specific designissues. The primary issue is excessive roboticstructural loads either due to large or periodic thruster

1 Principal Member Technical Staff, The CharlesStark Draper Laboratory, Inc.; naz@draper.comCopyright © 2000 by C. S. Draper Laboratory, Inc.Published by the American Institute of Aeronauticsand Astronautics with Permission.

firing. The design should avoid exciting the roboticarm to its load limits, and must also be robust tovariable arm dynamics. Also, to reduce program costsboth in design and verification phases, a single designis to be used for all Station assembly stages androbotic operations. The design should also becompact with respect to on-board computer memoryutilization. Further, frequent desaturations areundesirable as they increase operational complexitiesand time required to complete the robotic operation.

In this paper, the CMG momentum desaturationmethod developed by Draper Laboratory for theInternational Space Station for use during roboticpayload operations is presented. The theoreticalfoundation for a frequency optimal thruster firingpattern with non-periodic delay times is reviewed,with the objective of robustly minimizing the inducedstructural loads. The flight software implementationdetails are then presented. Simulation results forSpace Station robotic assembly Stages 4A and 5Awere presented to illustrate the design and compare itto alternatives.

Momentum Desaturation Methods

Thruster momentum desaturation can beaccomplished in a variety of ways. At the highestlevel it can be classified as either closed loop(feedback) or open loop (feedforward). For closedloop methods, individual firings are commandedbased on current CMG momentum states untilmomentum reaches the desired levels. The pulsepattern can range from a single large pulse tomultiple high frequency small pulses. An issue withsuch an approach is pulse phasing which couldcoincide and excite a robotic structural mode andviolate load limits. An alternative approach is to usenon-periodic, i.e. variable delay times. However, theCMG control system's slow response time (attitudehold bandwidth -10-20 times orbital rate frequency)may cause excessive momentum desaturation errorsand may take an excessive long time to complete.Further, load limit verification for closed loopmethods are usually more computationally intensive

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than for open loop methods. For these reasons afeedback strategy was not considered.

For open loop momentum desaturation, a pre-defined number of individual thruster firings arecommanded at pre-determined start times while theCMGs are commanded in a feedforward manner tocounter the thruster induced momentum. The pulsepattern can range from a single large pulse tomultiple pulses with either periodic or non-periodicdelay times. A single large pulse is quick, efficientand simple to implement. However, this methodresults in large induced loads [1]. An alternative is toconsider using a form of "command preshaping" [2],[3], [4], which effectively notch out the dominantresonant frequencies. However, since preshaping is amodel-based approach it requires knowledge of thestructural modal frequencies. For flexible structureslike the Station, the uncertainty and variability inmode frequencies makes it difficult to use such anapproach.

Using multiple fixed pulse-width firings atperiodic delay times between firings doessubstantially reduce loads [1], however, the phasingof the multiple firings remains an issue as detailed inthe previous section. This is the preferred strategywhen structural characteristics are known. This typeof pulsing strategy is currently used by the SpaceShuttle Alternate Primary Reaction Control Systemmode [5]. Using multiple fixed pulse- width firings atnon-periodic delay times between firings can resolvethe phasing issue with periodic firings while at thesame time reducing loads. Hence, the designobjective is to choose delay times to robustlyminimize loads. The advantages of such an approachare that the pulse pattern can be chosen early in theSpace Station design phase and easily verified for allvehicles and operations. It also requires minimalground support during flight as well as meets all thedesired design characteristics. A concern is thatthruster pulses must be computed and appliedaccurately in order to achieve the desired momentumdesaturation. Due to the desirable features of anopen-loop approach to momentum dumping, multiplefixed pulse-width firings at non-periodic delay timeswas chosen as the design architecture to meet thedesign goals.

Theoretical Foundation

removed and the magnitude of thruster torques. Therate at which the CMGs desaturate, i.e. thefeedforward CMG momentum command, and thetotal momentum to be removed determines the totaldesaturation time. These two parameters determinethe maximum allowable delay time that can beutilized by a thruster pulsing policy.

To simplify the analysis, we assume that thethruster firing sequence is identical in each axis andtherefore can be modeled as a single input. Inaddition, the pulse width and amplitude are assumedconstant. The pulse width is assumed fixed in orderto reduce the dimension of the problem. In general,since longer pulses are more detrimental with respectto structural excitation than shorter pulse, one canassume a worst case long pulse. Of course if theactual thruster on-times are much longer than whatwas assumed, frequency optimality is lost. Hence, theindependent parameters are the number of delaytimes and their duration.

The design objective for the firing strategy givenconstraints on delay time is to minimize structuralloads in the presence of plant uncertainty, such that anew pulsing pattern is not required for every possibleSpace Station configuration. The delay timeconstraints are specified in terms of maximum totaldelay time and bounds on each delay between firings.An approach is to implement a non-periodic delaypulsing pattern in order to avoid interaction withshifting and unknown resonances. We consider thefrequency content or Power Spectral Density (PSD)of the pulsing pattern and to choose the delay timesuch that the flexible body mode excitation isminimized over a certain frequency range [6]. Thisresults in a pulsing strategy, which is robust withrespect to frequency. A brief review of the results in[6] follows.

Let u(t) denote the pulsing sequence of n pulsesseparated by n-1 delay times 7. To show therelationship between the PSD of the input signal andthe induced loads, we assume that a linear map canbe constructed from the thruster firing input, to astructural load variable y(s) = G(s)u(s). The meansquared value or average power can be computedfrom its PSD function O T(f t>) via [7]:

The CMG momentum desaturation process isparameterized by the total thruster on-time and totaldesaturation time. A generic desaturation timeline isshown in Figure 1. The total thruster on-time isdetermined by the amount of momentum to be

pow(y)2 =• (1)

Since the input is a scalar by assumption, the PSD ofthe output signal is given by [8]:

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(2)

This establishes the relationship between the PSD ofthe input pulse pattern and the average value of theload variables.

Power Optimal Pulse PatternFrom the previous development, the objective is

to choose the delay time such that the flexible bodymode excitation is minimized over a certainfrequency range. Since one of the requirements is tohave a single pulse pattern for all Station assemblystages and robotic operations this requires that thedesaturation pulse pattern be plant independent. Sincethe plant dynamics cannot be included in the costfunction and the optimization must be formulated asa function of the input signal only. Equation (2) canbe upper-bounded as a function of <l>ul((<w) in twodifferent ways by either minimizing the area under3>m((o) or its maximum value. The maximum valueupper bound is chosen since it translates directly intominimizing the excitation or concentration of powerat a particular frequency:

1 +"p0w(y)2<max <bm(o>) — \GG*da)co J

Hence, to minimize the average power of the outputsignal for any arbitrary (stable) plant dynamicsrequires minimizing the maximum PSD amplitude ofthe input signal. Hence, the optimization problem fora specified frequency range [a^,^ can be stated as:

min max $„„(»

subject to

(4)

a) Fixed thruster on-time/pulseb) Fixed total delay timec) Fixed delay time range

The solution (4) is termed the power optimal pulsepattern. Note that since the PSD of the input signal isa function of the number and magnitude of delay timeparameters, 1t, it can be shaped by a judiciousselection of the Tf. Such a selection has the effect ofmaximizing the uniformity of the power in thechosen band and reducing the concentration of powerat any particular frequency. Thus, if one has a systemwhose frequency can vary according toconfigurational parameters, then the pulsing patternthat is least likely to excite the system for arbitrary

settings of the parameters is the pattern thatminimizes the peak power spectral density over therange of frequencies of interest.

Solving For Optimal Delay Pattern

One approach to solving (4) is the direct testapproach outlined in [6]. The solution to theoptimization problem relies on an iterative techniqueto generate candidate pulsing patterns subject to theconstraints on delay time. The cost function isevaluated over the set of all possible delay timecombinations that satisfy the given constraints inorder to determine which one yields the lowest PSDpeak value. Since all possibilities are checked, thesequence with the lowest PSD can be said to beglobally optimal. To illustrate the procedure considera simple example with 3 delays, with a minimumdelay time of Isec and maximum of 5sec, with totaldelay time of 8sec, and using a delay time incrementof Isec. The resulting set of all possible delay timesis shown in Table 1.

1112

222

2 53 44 31 52 43 34 2

3 13 23 33 44 14 24 3

432

1321 (3)

Table 1 Set of all possible delay times for simpleexample

Optimal Desaturation Pulse PatternA candidate optimal desaturation pulsetrain was

developed using a momentum desaturation thresholdof 10,000ft-lb-sec [10], and an average CMGfeedforward torque of approximately 170ft-lb. Basedon these requirements the total desaturation time wasapproximately 60sec. Further, the thruster pulsewidths were assumed to be l.Ssec based on a 5pulse/4 delay pattern to reflect a worst case scenarioof a minimum of 1333ft-Ib thruster torque in a worstaxis during assembly of the Station. This results in aconstraint of 50sec on the total allowable delay time.With regard to frequency, a range of O.OlHz-lHz wasspecified by NASA Loads & Dynamics as arepresentative sample of expected Station/Roboticsstructural modes. The optimization was carried outwith a delay time increment (the search parameter) of0.1 sec, and a time range of 1.0sec-19.0sec for eachdelay. Solving for the optimal delay pattern results inthe delay and start times listed in Table 2.

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Delay Number

Delay (sec)

Start Time

1

17.3

0

2

10.9

18.8

3

8.4

31.2

4

13.4

41.1 56

Table 2 Optimal delays and pulse start times

To gain a perspective on the optimal pulsetrain,it is compared against two other pulse patterns; asingle 7.5sec duration pulse and a 5 pulse patternusing l.Ssec firings and a 12.5sec fixed delayresulting in a periodic (14sec or 0.07Hz) firingpattern. The time domain and PSD plots for thesefiring patterns are shown in Figures 2-7. A singlepulse excites low frequency (<0. IHz) modes whilethe 0.07Hz fixed delay excites harmonics of itsfundamental frequency. Comparing these plots it isseen that a substantial reduction in peak PSDamplitude is achieved in the frequency range ofinterest (0.01 Hz - 1.0 Hz) by using the optimal delaypulsetrain. However, this reduction is achieved at theexpense of exciting a larger frequency spectrum, i.e.the excitation is lower in peak power but broadbandin frequency.

Flight Software Implementation Details

The CMG momentum desaturation algorithmshave been implemented in the Russian ServiceModule vehicle flight code [9]. The general operationof the design is as follows. As the International SpaceStation CMGs reside in the US segment, once amomentum saturation condition is detected during anSSRMS payload operation, the crew commands thearm in a position hold/brakes-on mode. Once theSSRMS is immobilized, the US side generates acommand for the required change in momentum.This command is passed on to the Russian segmentfor thruster firings and also to the US segment inorder to command the CMGs open-loop fordesaturation. Once the command is received by theService Module, a jet selection is performed tocompute the thruster on-times on a per axis basisaccording to,

where t is a 3x1 vector of jet on-times (roll, pitch,yaw axes), T is a 3x3 torque matrix with its columnscorresponding to thruster torque in each axis, and AHis the requested change in momentum. Since eachcolumn of the torque matrix, T, can accommodateeither a positive or negative command in that axis,there are 2 = 8 possible torque matrices. Thus, foreach desaturation command, the software computeson-times for each of the 8 inverse torque matrices.Solutions with negative on-times are eliminated.

Finally, the solution with the lowest fuelconsumption is selected.

Once the total thruster on-time for eachcommanded axis has been calculated, it can bepartitioned into a string of pulses separated by delays.The pulse pattern is described by a template, which isreceived from the US segment. The template is anarray containing the start times for each burn. Theon-time/axis is then divided by the number of pulsesin the template. If the result is less than 0.2sec (onecontrol cycle), the number of pulses is reduced untilthe result is greater than 0.2sec. If only a single pulseremains, and the on-tme is greater than 0.1 sec, a0.2sec pulse is commanded. Otherwise, no commandis executed in that axis. All thruster firings for eachpulse start at the same time according to the starttimes in the template, and all three axes aredesaturated simultaneously.

Since CMG momentum desaturation isperformed open-loop, it is necessary to produceaccurate torque impulses. Hence, it requires estimatesof thruster torques be stored in on-board computers.This also requires that accurate estimates of systemcenter or mass be available. To address theuncertainty issue an accuracy requirement of ±20%on the magnitude and +15° in direction of thecommanded desaturation was levied [10]. Thisrequirement is levied on the sub-system level andmust be verified during robust performance flightreadiness analysis.

Examples

The variable delay pulsing strategy wasevaluated by simulating a CMG desaturation for ISSrobotic assembly stages 4A and 5A. For Stage 4A,the Shuttle Orbiter is docked to the Space Station,and the P6 integrated truss segment is moved fromthe Orbiter payload bay into place using the ShuttleRemote Manipulator System (SRMS) as shown inFigure 8. Similarly, in Stage 5A, the US Lab payloadis attached as shown in Figure 8.

The Space Station system was modeled as arigid/flexible/rigid body system. The Station, withattached Orbiter, and payload were assumed to berigid elements linked by a flexible SRMS. Therobotic arm was modeled as a linear equivalent 6x6stiffness matrix representing relative translation androtation between the two rigid bodies. An equivalentlinear stiffness was used to model the brakes-onservo mode. The complete system is described by aset of linear state space models with 12 modes (6rigid body), 10 thruster inputs and 13 outputs. The 13

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outputs are the 3 translational and 3 rotationaldisplacements of the ISS center of mass in SS frameand the 7 joint torques. Six intermediate SSRMS jointangle configurations along its prescribed trajectorywere used [11]. The structural modes for eachconfiguration are listed in Table 3.

Joint AngleSet

Point 1Point 2Point 3Point 4Point 5Point 6

Frequency (Hz)Model0.0400.0470.0420.0330.0320.035

Mode 20.0460.0550.0480.0380.0380.041

Mode 30.0960.1220.1290.1460.1150.113

Mode 40.1040.1340.1430.1720.2050.190

Modes0.3970.3140.4080.3480.2910.304

Mode 60.5090.8581.0360.6210.5810.583

Table 3 Stage 4A & 5A SRMS configurations

Of course the objective of the optimal pattern isnot to result in the lowest loading but rather toprovide acceptable performance over a wide range ofplants by trading performance in order to gainrobustness.

operations was presented. The theoretical foundationfor a frequency optimal thruster firing pattern withnon-periodic delay times was reviewed, with theobjective of robustly minimizing the inducedstructural loads. It was shown that the minimizationof the peak PSD amplitude of the pulsing sequenceminimizes the average induced load. The flightsoftware implementation details were also presented.Simulation results for Flight 12A with payload P34were presented for joint loads due to CMGdesaturation thruster firings while the Space StationRemote Manipulator System is in a fixedconfiguration to illustrate the design.

Acknowledgments

The author would like to Larry McGovern,Robert Beal of Draper Laboratory, and Alien Leungfor their assistance and contributions.

The analysis results for the scenarios underconsideration are shown in Figure 9. The figureshows the four largest joint torques corresponding tofour configurations of the arm as a function of therotational jet command index which is listed in Table4. It is seen that Point 5 results in the worst case jointload of 109 ft-lb in the Shoulder Pitch joint with theworst case command of +/- Roll (a positive ornegative pure Roll axis momentum desaturation). It isconcluded that for the ISS/SSRMS/P34 analysis,worst case joint loads are less than 10% of themaximum structural load limit of 1800 ft-lb [12].Hence, the fixed configuration analysis shows thatSSRMS desaturation joint loads are acceptable.

Index123456789

10111213

Rotational Jet CommandRoll

0000

Pitch111000

-1-1-1

1110

Yaw10

-110

-110

-110

-11

Index14151617181920212223242526

Rotational Jet CommandRoll

0000.-.-.-..-

Pitch0

-1-1-1

111000

-1-1-1

Yaw.)

10

-110

-110

-110

-1

Table 4 Listing of rotational jet commands

References

[1] N. S. Bedrossian, "SSRMS Loads During CMGDesaturation", Draper Memo SSDI-94-011, July1994.

[2] P. H. Meckl and W. P. Seering, "MinimizingResidual Vibration for Point-to-Point Motion",Journal of Vibration, Acoustics, Stress andReliability in Design, Vol. 107, Oct. 1985, pp.378-382.

[3] N. C. Singer and W. P. Seering, "Using AcausalShaping Techniques to Reduce RobotVibration", Proc. 1988 IEEE InternationalConference on Robotics and Automation, Apr.1988. pp. 1434-1437.

[4] B. Wie, Space Vehicle Dynamics and Control,AIAA Education Series, 1998.

[5] E. T. Kubiak and D. Sargent, "CR 89921C:Alternate Primary Jet Mode", Presentation to theShuttle Avionics Software Control Board,Johnson Space Center, Houston TX, June 29,1989.

Conclusions

In this paper, the CMG momentum desaturationmethod developed by Draper Laboratory for theInternational Space Station during robotic payload

[6] N. Bedrossian, J. Lepanto, N. Adams, J. Sunkel,and T. Hua, "Jet Firing Strategy To MinimizeStructural Loads ", Proc. 1995 American ControlConference, pp. 3622-3626.

[7] J. Doyle, B. Francis and A. Tannenbaum,"Feedback Control Theory ", Macmillan Pub.Co., 1992.

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[8] N. Adams, and C. Gettman, "MultivariableSignal Transmission: A Stability and LoadsAnalysis tool for the Space Shuttle withAttached Payloads", CSDL-ESC-93-128, May1993.

[9] RSC-Energia, "ISS Item 17Km N128 TerminalComputer Software Guidance, Navigation andControl System Information Memorandum",Software Version 4.0 Document, March, 1999.

[10] NASA/Boeing, "International Space StationGN&C Design Guidelines and Assumptions",Revision B, 1997.

[ll]Bedrossian, N., "DAC 2 TDS 3.2.4-1 le:SRMS/SSRMS Desaturation Loads", CSDLReport E41-95-128, August 95.

[12]Trudel, C. P., "RCS Activity During SSRMSOperation", Canadian Space Agency, CSA-SS-JR-0002, August 1994.

—————— Total Desaturation TimeFiring Pulse Delay

Dl D2 Dn

Desaturation Time

Figure 1 Generic desaturation pulsetrain

4» 80 180

0.09

0.08

0.07

8.8*

|0.«S

IL8.84

8,03

«"

Figure 3 Single Pulse - Frequency domain

i

0.9

I*'8

J? ;̂

1°-*0

J?*1**d* —30 4S 60 80 10

: 71m»j»t)

Figure 4 Fixed Delay Pulsetrain - Time domain

Figure 5 Fixed Delay Pulsetrain - Frequency domain

Figure 2 Single Pulse - Time domain

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"

40 60Tims (sec)

80 100

Figure 6 Optimal Delay Pulsetrain - Time domain

6,0»

e.os

0.68

Figure 7 Optimal Delay Pulsetrain - Frequencydomain

Figure 8 ISS Stage 12A robotic assembly

12012A w/ Orbiter / SSRMS / P34: Maximum Joint Loads

<r100-

E 80

S~ 60

20

SHP

ILP

10 15 20 25Rotational Jet Command Index (RJC)

30

Figure 9 ISS Stage 12A maximum joint torques

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