HST - 1990 Sample Requirements Flowdown Process µ .
FIRST INTERNATIONAL WORKSHOP ON INTEGRATED MODELING OF TELESCOPES, LUND, SWEDEN, 5-7 FEBRUARY 20021Framework for Multidisciplinary IntegratedModeling and Analysis of Space TelescopesDavid W. Miller, Olivier L. de Weck and Gary E. MosierAbstract This paper presents a comprehensive framework for integrated modeling, simulation and analysis of optical telescopes.This framework is calledDOCS (Dynamics-Optics-Controls-Structures) and supports model development, model integration, analysis andmultidisciplinary design optimization of this class of precision opto-mechanical systems. First the research background and literature in this young eld is discussed. Nextthe structure and nominal process of an integrated modeling, simulation and analysis study for a generic opticaltelescope using the DOCS framework is discussed in detail. The major steps include subsystems modeling, modelassembly, model reduction and conditioning, initial performance assessment, sensitivity analysis, uncertainty analysis, redesign, design optimization and isoperformance analysis. Such a comprehensive analysis is demonstrated forthe NEXUS Space Telescope precursor mission. This mission was designed as a technology testbed for the NextGeneration Space Telescope. The challenge is to achieve avery tight pointing accuracy with a sub-pixel line-of-sight(LOS) jitter budget and a root-mean-square (RMS) wavefront error smaller than 50 despite the presence of electronic and mechanical disturbance sources. The frameworksuggested in this paper has the potential for becoming ageneral prescription for analyzing future, innovative telescope projects. Signi cant challenges remain in enablingfast simulations for large models, analytical sensitivity analysis for all sub-models, incorporation of slow-varying thermal or impulsive transient e ects and the e ective use ofexperimental results.Keywords Integrated Modeling, Telescopes, Nexus,Isoperformance, Multidisciplinary Design Optimization(MDO), Dynamics and Controls, Spacecraft Design, Optics, Sensitivity AnalysisI. IntroductionThe next generation of space and ground based astronomical observatories such as the Next GenerationSpace Telescope (NGST), the Space Interferometry Mission (SIM) or the Terrestrial Planet Finder (TPF) willsigni cantly surpass the present generation, for examplethe Hubble Space Telescope (HST), in terms of their sensitivity, angular resolution, spectral resolution and imaging stability [59], [35], [17]. The present work is motivated by the need to predict the dynamic behavior ofthese telescopes during the conceptual and preliminarydesign phases before substantial resources are committedtowards a particular system architecture. Figure 1 showsthe HST in the upper left corner and a number of proDavid Miller, Associate Professor, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A, millerd@mit.eduOlivier de Weck, Assistant Professor, Massachusetts Institute ofTechnology, Cambridge, MA 02139, U.S.A, deweck@mit.eduGary Mosier, Integrated Modeling Lead for NGST, NASA Goddard Space Flight Center, gary.e.mosier.1@gsfc.nasa.govposed successor spacecraft below. The science objectivesfor these missions are translated into functional requirements. These are further owed down to engineering system requirements. It is the ful llment of these engineeringrequirements, speci cally relating to dynamics and controls, which constitute the notion of \performance" in thepresent paper.HST - 1990Sample Requirements Flowdown ProcessScienceRequirementsFunctionalRequirements5 year wide-angle astroFringe Visibilitymetric accuracy of 4 µ asec 0.8 for astrometryto limit 20th Magnitude starsSpace-Based ObservatoryEngineeringRequirementsScience InterferometerOPD 10 nm RMSMultipurpose UV/Visual/IRImaging and 06TPF-2011Deployable Cold OpticsNGST Precursor MissionLightweight 8m-Optics Faint Star InterferometerIR Deep Field Observations Precision AstrometryNulling InterferometerPlanet DetectionFig. 1. Hubble Space Telescope and proposed successor missionsas part of NASA's space science program. Sample requirementsowdown for SIM.While the HST has performed admirably well over thelast decade [17], it is essentially a multi-purpose instrument providing imaging and spectroscopy capabilities inthe wavelength range 0.110-2.6 [ m], i.e. from ultraviolet (UV) to near-infrared (NIR). In order to achieve thislarge scope of science capabilities, a number of engineering compromises had to be made. The astronomical science community has realized that specialization is necessary such that the ambitiousastrophysical research goalsof the rst half of the 21st century (e.g. observation ofproto-galaxies at high redshifts, z, direct IR detection ofextra-solar earth-sized planets out to 15 parsecs) can beachieved [59]. Consequently a number of successor spacecraft have been proposed (Figure 1).At rst sight it appears impossible to attempt a unied engineering treatment of these various missions dueto the large di erences in their respective science objectives. Once these objectives have been broken down intotangible engineering requirements, however, the missionscan be analyzed with a common set of tools. All missionsrequire that electromagnetic radiation emanating from ascience or guide source (e.g. star, proto-galaxy, extra-solarplanet.) is collected by an aperture, compressed and
FIRST INTERNATIONAL WORKSHOP ON INTEGRATED MODELING OF TELESCOPES, LUND, SWEDEN, 5-7 FEBRUARY 2002redirected to an electronic detector (e.g. sprectrograph,CCD camera, fringe tracker). During this process it isparamount that the distortion of the wavefront (surface ofcommon phase of light) inside the optical train be kept toa minimum, while the boresight axis of the observatory beheld nearly xed in inertial space.For interferometers, additional requirements for the angular propagation of the wavefront (wavefront tilt-WFT),the pathlength the light travels in the di erent arms of theinterferometer (optical pathlength di erence-OPD) andthe amount of overlap the interfering light beams experience at the detector (beamshear-BS) must be formulated. In order to ascertain that these telescopes willmeet their stringent phasing and pointing requirements,the path from disturbance sources to the performance metrics of interest must be modeled in detail before construction, integration and testing. Additionally, for a numberof light-weight deployable structures, pre-launch tests in a1-g gravity eld are not feasible. Hence, it is paramountthat a preliminary design of the system is available, whichcan be used as a basis for a simulation model.The science target observation mode is in quasi steadystate and is of particular importance. Other modes of interest can be transient such as the slewing and acquisitionmode. Figure 2 shows a simpli ed block diagram of themain elements involved in a steady-state dynamics simulation. This is the reference problem setting considered inthis paper. The premise is that a number of disturbancesources (reaction wheel assembly, cryocooler, guide starnoise, etc.) are present during the science target observation mode as zero-mean random stochastic processes [6].Their e ect is captured with the help of state space shaping lters , such that the input to the appended systemdynamics is assumed to be a vector of unit-intensity whitenoises d, which are generally uncorrelated between disturbance sources. Reference input commands are designatedas r. The simplest assumption is that the reference commands are zero, i.e. r 0, this, however, is not alwaysthe case.The shaped disturbances w are then propagatedthrough the opto-structural plant dynamics, which includethe structural dynamics of the spacecraft and the linearsensitivity optics matrices [63]. A compensator is oftenpresent in order to stabilize the observable rigid bodymodes (attitude control) and to improve the disturbancerejection or tracking capability (optical control). The sensor outputs y and actuator inputs u might also be subjectto colored noise n. The goal of a disturbance analysis isto accurately predict the expected values of the performances Jz;i, where i 1; 2; :::; nz and nz is the numberof performance metrics. This has been previously developed and demonstrated by Gutierrez [25]. A summary ofthe disturbance, sensitivity and isoperformance analysisframework is contained in Appendix A. Outputs of theappended dynamics model are opto-scienti c metrics of11 Sometimesthese are referred to as pre-whitening lters.2Science Target Observation ModeWhite Noise InputPhasing (WFE)Reference commandsAppended LTI System Dynamics[Azd,Bzd,Bzr,Czd,Dzd,Dzr]Opto-Structural PlantrJ z E éên zT zDisturbanceDynamics,1z wz WFE[zCen]ë rayWFEùúû1/ 21dWFE RMS WFEPerformancesPointing �ActuatorNoise[Ac,Bc,Cc,Dc]SensorNoiseJ z E éë z T z,2CenCen RSS LOSùû1/ 2Fig. 2. Reference problem: Science target observation mode ofa space telescope with pointing (RSS LOS) and phasing (RMMSWFE) performances.interest, z. The performances are typically expressed interms of the root-mean-square (RMS) of the outputs. Alternatively we can combine channels in a RSS or RMMSmetric, see Appendix A for details. Note that nray is thenumber of light rays traced to compute the wavefront error(WFE). Other performance metrics could be the in nitynorm Jz;i kzi k1 or settling time Jz;i T sz;i of a particular transient signal.Another objective is to identify the \key" modal and/orphysical parameters of the system that strongly drive thesystem performance. Sensitivity analysis has been previously identi ed [25] as a useful tool for examining thedependency of the predicted performance values Jz;i onthese \key" system parameters pj , where j 1; 2; :::; npand np is the number of parameters . Some or all of theparameters might be subject to uncertainty. Oftentimesthe number of parameters, np, for which a designer hasto determine speci c values exceeds the number of performance metrics, nz , i.e. np nz 1. The traditionalapproach is to rst choose reasonable numbers for thesystem parameters pj and to predict the resulting performances Jz;i (initial performance assessment). If all orsome of the predicted performances do not initially meetthe speci ed requirements Jz;req;i for i 1; 2; :::; nz , including margins, a sensitivity analysis can provide partial derivatives @Jz;i @pj which can be used to identifyin which direction important parameters pj should bechanged. This is intended to drive the system to a design point that satis es all requirements, i.e. a conditionwhere Jz;i Jz;req;i for all i 1; 2; ::; nz is true. Thisprocess is called performance enhancement [25]. A %uncertainty on the predicted performances, 4Jz;i, canbe computed based on known or assumed % uncertainties of the parameters pj . This is useful in establishingperformance error bounds.22 It is assumed that these parameters are continuous over theirinterval pj 2 [pLB;j pU B;j ]
FIRST INTERNATIONAL WORKSHOP ON INTEGRATED MODELING OF TELESCOPES, LUND, SWEDEN, 5-7 FEBRUARY 2002II. Literature ReviewThis section gives a short overview of the scienti c literature which is relevant to the development and validationof integrated models for space and ground telescopes. Theliterature discussion begins with papers on the processesand tools used by systems engineers and designers during conceptual and preliminary design. The current stateof-the-art in performance assessment and enhancement oflinear time-invariant systems is discussed along with initial work in the area of isoperformance methodology. Thebuilding blocks of integrated modeling of such systems arestructural dynamics, classical and modern control theory,optical ray tracing as well as empirical and analytical modeling of various disturbance sources. In order to leverage these models and simulations in a multidisciplinarydesign optimization (MDO) context, issues of numericalconditioning, sensitivity analysis and uncertainty analysis cannot be ignored. Finally, past and presents e ortsin laboratory testing and implementation on space ightmissions are brie y discussed.The conceptual and preliminary design phases areimportant times during a program in which various system architectures are analyzed and estimates are madeof the top level and subsystem functional requirements.Additionally, initial budget allocations are made and enabling technologies are identi ed. The allocation of designrequirements and resources (costs) and an assessment ofrisk during these early stages of a program is based onpreliminary analyses using simpli ed models that try tocapture the behavior of interest [12]. This was a majordriver for the development of tools that allow quantitativeanalysis and design of these preliminary dynamics modelsearly in a program. The kernel of the performance assessment (disturbance analysis), sensitivity and uncertaintyanalysis framework was established by Gutierrez [25]. TheH -type performances used here are de ned in accordancewith Zhou, Doyle and Glover [73].The theory behind the performance assessment oflinear dynamical systems is well-developed. A specialcase of the general performance assessment of a dynamical system is given when stochastic random noise processes are present. In this instance we speak of disturbance analysis and governing equations and methodologies are presented in random vibration textbooks such asthose by Crandall [11] and Wirsching [71]. They characterize the response of systems driven by stochastic inputsin the time-domain (using autocorrelation functions) andequivalently in the frequency-domain (using power spectral density functions). The concept of a linear shapingor \pre-whitening" lter whose input is white noise andwhose output is \colored" noise, presumably containingmore disturbance energy in some frequency bands than inothers, is covered by Brown and Hwang [6]. For the caseof state-space systems driven by white noise, the outputsteady-state covariance matrix is known to be the solutionof a Lyapunov equation [25].23The idea of holding a performance metric or value of anobjective function constant and nding the corresponding contours has been previously explored by researchersin other areas. Gilheany [22] for example presented amethodology for optimally selecting dampers for multidegree of freedom systems [22]. In that particular work(Fig.5) the contours of equal values of the objective function are found as a function of the damping coeÆcientsd and d . In the eld of isoperformance methodology, work has been done by Kennedy, Jones and coworkers[41], [42], [40] on the need within the U.S. Department ofDefense to improve systems performance through betterintegration of men and women into military systems (human factors engineering). They present the application ofisoperformance analysis in military and aerospace systemsdesign, by trading o equipment, training variables, anduser characteristics. Once the level of operational performance is settled upon (e.g. \pilot will check out all aircraft ight systems within 30 seconds"), tradeo s amongequipment variables, adaptation, training, and individualpredisposing factors can be made. A systematic approachto isoperformance in complex, dynamic opto-mechanicalsystems was developed by de Weck [14].A eld that has received a lot of attention in the lastfew years is integrated modeling. This encompassesresearch and e orts to simulate complex systems in a unied and multidisciplinary environment. Several important initiatives in this eld, like NASA's Intelligent Synthesis Environment (ISE) described by Venneri, Maloneand coworkers [70] were undertaken. Important contributions to integrated modeling were made by the Jet Propulsion Laboratory (JPL) with the creation of abased nite element package and optical modeling software called IMOS (Integrated Modeling of Optical Systems) [37]. This code was developed to assist in the synthesis of initial models of optical instruments and to reduce the model creation, analysis and redesign cycle asdescribed by Laskin and San Martin [44].Structural dynamics fundamentals, in particular thesingle degree-of-freedom oscillator are treated by Craig[10]. More advanced concepts on the nite-elementmethod are presented by Bathe [2] and Cook [9]. Thestructural dynamics and controls of large exible spacecraft have been extensively studied by Junkins and Kim[38] as well as Crawley [12]. As will be seen laterthe stringent pointing and phasing requirements of optomechanical systems often require closed-loop attitude andoptical control. Thus, actuators, sensors, and compensators must be included in the integrated model. Controltextbooks by Van de Vegte [69] and Ogata [61] provide anoverview of classical control design techniques, while thoseof Zhou et.al, [73] and B elanger [3] emphasize moderncontrol theory (state space based). Typically control sys31122MATLAB3 The objective function in reference [22] is called ITSE integral of time multiplied by the sum of squares of displacements andvelocities of the masses.
FIRST INTERNATIONAL WORKSHOP ON INTEGRATED MODELING OF TELESCOPES, LUND, SWEDEN, 5-7 FEBRUARY 2002tems are implemented on digital computers as describedby Astr om [1] and Franklin and Powell [20]. It is interesting to note that there still is a large discrepancy betweentheoretical modern control theory based on LQR, LQGand sensitivity weighted LQG, H-in nity and -synthesistechniques and controllers that are actually implementedin space ight vehicles up to this day. Aerospace contractors, NASA and other space agencies still rely mainly onanalog or digital implementations of classical control techniques such as PID and loop-shaping for attitude, thermal, optical and, among others, end e ector control. Thisis likely due to an aversion towards risk and to the easewith which classical controllers are designed, understood,implemented and tested. Additionally the advantage ofextensive ight heritage frequently o sets the potentialperformance bene ts of modern controllers. This fundamental disparity was recognized by Mallory and Miller[49]. They proposed, developed and validated a MIMOcontroller tuning technique which begins with a simplelocal (often classical) baseline controller, which is thenanalyzed and iteratively tuned by opening up promisingcross-channels and adjusting controller parameter settingsbased on a gradient search technique.The fundamental work that allows the computation ofoptical linear sensitivity matrices and their incorporation into dynamics models is attributed to Redding andBreckenridge [63]. The linear sensitivity matrices allowcomputing optical metrics such as centroid position onthe focal plane, wavefront error, wavefront tilt or beamshear as a function of linear and rotational displacementsof the points where elements in the optical train (mirrors, beamsplitters, lter wheels etc.) are attached to thestructure. The software program called MACOS (Modeling and Analysis for Controlled Optical Systems) [36]creates the sensitivity matrix based on a prescription ofoptical elements in the system and unit perturbations ofthe structural degrees-of-freedom. General recommendedreferences for optics are by Born and Wolf [5] as well asHecht [30]. Telescope optics in particular are described byRutten and van Venrooij [64].When considering a disturbance analysis it is important to enumerate and characterize all potential energysources that might interfere with the opto-mechanical performance of the system. Eyerman and Shea [18] providea very complete overview of spacecraft disturbances.Reaction wheel disturbances are often expected to be thedominant source and Bialke [4], Davis, Wilson, Jewell andRoden [13], Melody [52] as well as Masterson [51] have contributed to this eld. Reaction wheel disturbance modelsare also included in this paper and an attempt is madeto derive performance deriva
Fig. 1. Hubble Space T elescop e and prop osed successor missions as part of NASA's space science program. Sample requiremen ts o wdo wn for SIM. While the HST has p erformed admirably w ell o v er the last decade [17], it is essen tially a m ulti-purp ose instru-men t pro viding imaging and sp ectroscop y capabilities in the w a v elength .
P9HST1 9mm Luger 124 HST 1150 P9HST2 9mm Luger 147 HST 1000 P9HST3 9mm Luger P 124 HST 1200 P9HST4 9mm Luger P 147 HST 1050 P357SHST1 357 Sig 125 HST 1360 P40HST3 40 S&W 165 HST 1130 P40HST1 40 S&W 180 HST 1010 P45GHST1 45 G.A.P. 230 HST 890 P
Sept. 13 HST 146 resumes HST 162 resumes Sept. 20 Sept. 27 Oct. 4 Oct. 11 Indigenous Peoples Day; Columbus Day (Federal) – no classes Oct. 18 HST 162 ends Oct. 25 HST
- HST-3000 — Handheld Services Tester 3000. In this user's guide, "HST-3000" is used to refer to the HST-3000 family of products or to the combination of a base unit and attached SIM. "HST" is also sometimes used to refer to the base unit/SIM combination. - SIM — Service Interface Module. Sometimes referred to
HST Curare Zusatz zum HST Zeitschrift f ur Medizinethnologie Erschverlauf 1.1978 - ISSN 0344-8622 Sigel Signatur Standort Bestand 305 - - 2.1979 - 13.1990 303 - - 12.1989 - 20.1997,2 431 Z 182 - 1.1978 - ZDB-Id 352835-2 HST Erziehungswissenschaft, Erziehungspraxis Zusatz zum HST Vierteljahresschr. d. Deutschsprachigen Sektion d. Weltbun-
HST Curare Zusatz zum HST Zeitschrift f ur Medizinethnologie Erschverlauf 1.1978 - ISSN 0344-8622 Sigel Signatur Standort Bestand 305 - - 2.1979 - 13.1990 303 - - 12.1989 - 20.1997,2 431 Z 182 - 1.1978 - ZDB-Id 352835-2 HST Erziehungswissenschaft, Erziehungspraxis Zusatz zum HST Vierteljahresschr. d. Deutschsprachigen Sektion d. Weltbun-
HST stands for Hydrostatic Transmission and is used in a travel system to connect the hydraulic pump with the motor in a closed circuit enabling continuous speed change from Forward to Stop/Neutral and Reverse or vice versa. HST is smoother in operation and smaller in siz
TRACTOR ATTACHMENTS TRACTOR 3540 PST 3540 HST 3550 PST 3550 HST 3540 PST Cab 3540 HST Cab 3550 PST Cab 3550 HST Cab LOADER 3550L 3550CL Maximum Lift Height 111.5” 111.5” Clearance with Attachment Dumped 92” 92” Reach at Maximum Height 24.75” 24.75” Maximum Dump Angle 40 40 Attachment Rollback Angle 20 20 File Size: 680KBPage Count: 6
2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of 30.00 to spend. Sandwiches cost 4.50 each and soft drinks cost 1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy? Problem 2 Three identical rectangles are put together to .
