LSST Telescope Modeling Overview
    J. Sebag
    a
    , J. Andrew
    a
    , G. Angeli
    a
    , C. Araujo
    a
    , J. Barr
    a
    , S. Callahan
    a
    , M. Cho
    a
    , C. Claver
    a
    , F. Daruich
    a
    ,
    W. Gressler
    a
    , E. Hileman
    a
    , M. Liang
    a
    , G. Muller
    a
    , D. Neill
    a
    , B. Schoening
    a
    , M. Warner
    a
    , O. Wiecha
    a
    ,
    B. Xin
    a
    , Alfredo Orden Martinez
    b
    , Manuel Perezagua Aguado
    b
    , Luis García Marchena
    b
    ,
    Ismael Ruiz de Argandoña
    c
    a
    Large Synoptic Survey Telescope, 950 N Cherry Ave, Tucson, AZ, 85719, USA
    b
    GHESA Ingeniería y Tecnología, S.A.
    c
    IK4 Tekniker Research Alliance
    ABSTRACT
    During this early stage of construction of the Large Synoptic Survey Telescope (LSST), modeling has
    become a crucial system engineering process to ensure that the final detailed design of all the sub-systems
    that compose the telescope meet requirements and interfaces. Modeling includes multiple tools and types
    of analyses that are performed to address specific technical issues. Three-dimensional (3D) Computer-aided
    Design (CAD) modeling has become central for controlling interfaces between subsystems and identifying
    potential interferences. The LSST Telescope dynamic requirements are challenging because of the nature
    of the LSST survey which requires a high cadence of rapid slews and short settling times. The combination
    of finite element methods (FEM), coupled with control system dynamic analysis, provides a method to
    validate these specifications. An overview of these modeling activities is reported in this paper including
    specific cases that illustrate its impact.
    Keywords:
    LSST, telescope, modeling, FEM
    1.
    INTRODUCTION
    The Large Synoptic Survey Telescope (LSST) Project is a public-private partnership to conduct a wide,
    fast and deep survey, and to process and serve the data
    1
    . It has been in the construction phase of the complete
    observatory system since August 2014. The summit construction site is located on Cerro Pachón in Chile.
    The LSST telescope baseline design that was developed during the design and development phase
    2
    preceding the construction phase, has been transforming into a final detailed telescope design as the
    different subsystems that compose the telescope are now being fabricated
    3,4,5
    . During this transition period,
    modeling plays a crucial role in the system engineering process to ensure that the final detailed design of
    all the sub-systems meet requirements and interfaces. Because of the increasing complexity of modern
    telescope systems, many key requirements must be analyzed combining different modeling activities. LSST
    is also developing an integrated simulation model
    6
    that incorporates subsystem modeling where the output
    of the structural FEM analysis is key to providing the matrices for the nodal or modal model of the
    subsystem response. The dynamic analyses are implemented in Matlab using the object-oriented Simulink
    environment.
    Specific examples relevant to LSST construction are described in this paper to demonstrate how important
    this activity is, even during construction. Telescope 3D CAD implementation is detailed to explain how the
    process is controlled, followed by an example of finite element analysis done during construction to
    complete fabrication of the primary/tertiary (M1M3) mirror cell
    7
    . Then, the LSST telescope slew and settle
    requirements and analysis are discussed. These have a direct impact on the LSST M1M3 mirror support
    system that must be able to prevent excessive loads on the six locating actuators to maintain the mirror in

    place in real time. The last example describes the modeling of the behavior of the pneumatic actuators that
    support the mirror to develop the control strategy to counteract for these dynamic forces during slewing.
    2. 3D CAD MODELING
    CAD modeling is a critical activity for the development of the LSST telescope design and construction.
    During the design and development phase of the project, LSST modeled the entire telescope and facility to
    create a baseline model. This baseline model allowed the project to establish requirements and interfaces
    between the different subsystems that compose the telescope and support facility. LSST installed
    SolidWorks 3D CAD design and analysis software in conjunction with its enterprise product data
    management (ePDM) software. The ePDM functionality proved to be a reliable method to organize and
    exchange the model with multiple users under version control by storing the information in a data vault
    repository based on an SQL database. Workflows within the ePDM allows the project to define and control
    the release and revision process.
    During the construction phase, all the subcontractors selected to build the telescope subsystems received a
    copy of the baseline 3D CAD model in addition to the specifications documents as a means of improving
    communication and increasing understanding of the entire system. Similarly, LSST received models from
    the subcontractors during their design periods in order to capture and to explain changes required from the
    baseline model. LSST is now in the process of creating the telescope and facility “as-designed” 3D CAD
    model by collecting the final design 3D CAD models from all subcontractors into this vault repository. This
    activity will continue until the end of the construction phase to conclude with the establishment of the LSST
    telescope and facility “as-build” 3D CAD model.
    Figure 1: Utilities Interface between the back of the science camera and the telescope
    CAD modeling is used not only for mechanical design but also for verifying interfaces, for defining
    integration sequences and handling operations and maintenance. The interface between the back of the
    LSST science camera
    8
    and the utilities provided by the telescope is shown in figure 1 as an example of a
    complex interface. 3D CAD modeling is critical to verifying that all the required utilities can be provided
    within the allocated volume and for the different camera rotator angle positions.
    Figure 2 shows an example of how the 3D CAD model of the whole facility permits sequencing of the
    integration tasks. The LSST telescope integration requires the handling of large subsystems such as the
    8.4m diameter M1M3 mirrors (surrogate mirror and real glass mirror) and their associated mirror cells. The
    space required for this operation is intrinsically large. The 3D model allows the project to verify that enough

    space is available in the facility building, optimizing the sequence to minimize the amount of space required
    for this operation.
    Figure 2: M1M3 Mirror integration with M1M3 Mirror Cell in the Summit Facility
    Figure 3 shows another example of how 3D modeling is used by LSST for maintenance and to ensure
    sufficient and safe access to tight areas. Access to the interface between the back of the science camera and
    the telescope utilities (shown in figure 1) is needed to disconnect all the utility lines when the science
    camera is removed from the camera rotator. Judging if enough space is available for this operation is
    improved by inserting a human shape into the model.
    Figure 3: Using 3D CAD modeling to assess access to the utility lines on the telescope located at the back of the science camera
    3. FINITE ELEMENT MODELING
    Finite element modeling is used extensively during telescope design but is also critical during the
    construction phase. It provides quantitative results to answer many of the mechanical detail questions that
    arise during fabrication. For this reason, LSST maintains finite element models that are updated with the
    as-built design in order to keep an accurate representation of the subsystems
    9
    . The example discussed below

    shows how the results from finite element analysis (FEA) were used to finalize the M1M3 cell design during
    fabrication.
    Figure 4: 3D CAD model of the M1M3 cell showing the deck plate and the stiffening structure
    One of the critical requirements for the M1M3 cell is to serve as the lower vessel of the coating chamber.
    This requirement is due to the fact that the M1M3 mirror is fragile and therefore after final integration of
    the M1M3 mirror with its cell, it remains in its cell to avoid any handling of the mirror. During coating,
    the cell is placed under vacuum loading. To avoid bending the mirror in this configuration, the deck plate
    deflection is limited to a maximum of 1mm. This avoids excessive bending stresses which could harm the
    mirror’s integrity. Minimizing deck plate deflection was accomplished primarily by structurally decoupling
    it from the cell floor, which deflects significantly during vacuum loading. Segregated deck versus floor
    structural systems are incorporated into the cell. FEA guided the design of both systems and verified their
    independent behaviors.
    During review in preparation for fabrication, the vendor realized that the secondary floor stiffening scheme
    in our design could not be economically fabricated and proposed another solution based on their experience
    in building barge hulls. FEA was key to engineering a final floor stiffening solution that satisfied both the
    vendor and LSST. Shown in figure 5 is a comparison between the original baseline floor design and the
    agreed-upon design.
    To maintain the completion schedule, cell fabrication started before all structural calculations had been
    completed. We communicated frequently with the vendor, releasing portions of the cell for fabrication
    based on the calculated risk that those portions would not need revision pending finalization of the structural
    analysis. In the end, no significant structural rework was needed. However, several locations on the vacuum
    trusses and openings in the outer shell structure required minor local stiffeners in order to boost the buckling
    load factors to acceptable values. FEA buckling analysis was used to locate these areas and re-evaluate
    them, resulting in added stiffening. No delay of any fabrication effort resulted, largely due to frequent
    communication with our vendor. Figure 6 show an example of added local stiffening around an opening in
    the cell outer structure.

    Figure 5: Comparison between the original baseline floor design and the agreed design.
    Figure 6: (Left) Buckling of the outer shell opening for Load Case Seismic Y while on the cart occurs at load factor 1.19. Need
    for stiffening indicated by the low Buckling Load factor. (Right) Stiffeners added around the opening. The buckling load factor
    has increased to an acceptable value of 4.59 for buckling around this opening, for any load case considered.
    Original floor stiffener arrangement, floor plate
    not shown. Both shell bottom and floor plates
    act compositelyfo r high structural efficiency, but
    difficult to build due to
    poor weldingaccess .
    Modified floor stiffener arrangement, floor plate not
    shown. In this case, the floor plate is a lightly bolted on
    series of aluminum panels which do not act compositely
    with the shell bottom and the bottom stiffeners. Primary
    stiffeners have bent flanges to improve stiffness and
    strength. Stiffener frequency based primarily by buckling
    limitation of bottom plate under vacuum loading.

    4. DYNAMIC PERFORMANCE MODELING
    4.1 TMA Slew and Settle Control Modeling
    The LSST survey requires a high cadence of rapid slews and short settling times. For a 3.5 degree field of
    view change and for any zenith angle 30 degrees or larger, the telescope mount assembly (TMA) is required
    to slew and settle in less than 4.0 seconds. The TMA vendor used a combination of FEM coupled with
    damping analysis in Matlab using the object-oriented Simulink environment to validate this specification.
    Figure 7: Finite Element Model of the LSST Telescope Elevation Structure
    The resulting TMA frequencies and damping with the conventional speed and position control loops closed
    are given in table 1 for the lower modes. A structural relative damping of 2% has been considered for all
    modes in open loop. Both the Altitude and Azimuth control loops have been tuned to have a speed control
    loop bandwidth around 9 Hz and a position control loop bandwidth around 2.3 Hz. Thus, operation of the
    main drives avoids excitation of the natural frequencies for both slewing and tracking.
    Table 1: TMA natural frequency and damping with speed and position control loops closed for the lower modes
    Mode
    Frequency (Hz)
    Damping (%)
    3
    6.06
    2.17
    4
    6.97
    2.01
    5
    11.16
    3.35
    6
    11.69
    4.76
    7
    12.72
    2.74
    8
    13.59
    2.03
    9
    13.70
    3.11
    10
    14.56
    2.1
    In addition, the TMA mount control system (MCS) performs an active damping control of the TMA as a
    secondary control loop. The active damper has been tuned to have a damping around 10% in the translation
    modes although many other tunings are possible. The impact on the damping is highlighted in grey in table
    2.

    Table 2: TMA natural frequency and damping with speed and position control loops closed with added active damping from
    MCS for the lower modes
    Mode
    Frequency (Hz)
    Damping (%)
    3
    6.07
    10
    4
    6.57
    9.57
    5
    11.27
    4.17
    6
    11.70
    4.88
    7
    12.72
    2.75
    8
    13.72
    3.04
    9
    13.86
    3.11
    10
    14.71
    2.92
    The results from the dynamic analysis show that the TMA is able to meet the 4 seconds slew and settle
    requirement and that the active damping could provide almost a gain of 1 second after implementation.
    Figure 8 shows an example of the line of sight (LOS) oscillation error along the X-axis versus time for an
    azimuth slew with and without the MCS active damping. The mount is considered settled when the LOS
    error is below 10 mArcseconds.
    Figure 8: Line of Sight oscillation along the X-direction versus time (second) for an azimuth slew with the MCS active damping
    enabled (green) and without the MCS active damping (blue). The red lines indicate the settling limits
    4.2 M1M3 Mirror Support System Control Modeling
    These challenging slewing requirements have a direct impact on the LSST M1M3 mirror support system
    that must be able to prevent excessive loads on the six locating actuators to maintain the mirror in place in
    real time. The mirror support system control loop was implemented in Matlab using the object-oriented
    Simulink environment. The purpose is to model the behavior of the pneumatic actuators that support the
    mirror to develop the control strategy to counteract for these dynamic forces during slewing.

    During operation, the mirror is suspended by an array of axial and lateral pneumatic actuators. These
    actuators carry all the gravity-induced weight of the mirror but do not define the mirror position in space.
    The mirror is located by a hexapod arrangement of axially stiff hard point linear actuators that connect
    between the mirror and its cell.
    Through the hard point load cell readings, the control system determines the net forces and moment
    produced by the hard points on the mirror. A smoothly distributed set of actuator force values is determined
    to counteract these forces and moments. In case uncorrected axial loads build up in the hard point actuators
    beyond the mirror safe limit, these will ‘breakaway’ by design. The
    air pressure will then be bled in a
    controlled fashion from the pneumatic actuators,
    allowing the mirror to settle several millimeters onto an
    array of static supports fastened to the cell deck plate.
    Since the LSST telescope undergoes relatively large slewing accelerations and velocities, excessive load
    will be produced on the hard points which could result in the possible activation of the breakaway
    mechanism. For efficiency purposes, the hard points shall not breakaway during a telescope slew.
    Consequently, the figure control actuators may have to be used during a slew to counteract the resulting
    dynamic loads to avoid the breakaway.
    For this reason we are considering using two types of valves, running in parallel, to drive the actuators. One
    type of valve is a pressure servo-transducer (PST), already installed in similar mirror support systems which
    is very precise in controlling the output force, but very slow. The other type of valve is a flow valve also
    called a turbo valve (TV) that provides a large air flow to the actuators at a high speed. With this
    configuration, we expect the PST will provide the precision needed when not slewing while the TV will act
    during slews to avoid the breakaway.
    Simulink models were developed to model the system applying a force profile corresponding to a slew of
    the telescope in the most stringent case which is a short slew in 2 seconds. This simulates how the demand
    would change during a slew. As shown on figure 10, the force demand is set to 1000 N, changed to 1500 N
    during the motion and returned to 1000 N once the motion is finished. During a slew, speed is needed more
    than precision to avoid the breakaway. As visible on the force plot, the actuator follows the demand fast
    enough to avoid the breakaway, with maximum force errors during the slew of 123.5 N and -192.5 N. Then,
    after the slew, the force comes back to 1000 N in less than an extra second.
    This configuration has been tested in the lab in open loop and it is running according to the model so we
    plan to use the model to develop the best controller for our system and then embed it into the controller.

    Figure 10: Force plot showing the behavior of an M1M3 mirror support actuator during a slew, with time (seconds) along the x-
    axis and Force (N) along the y-axis
    5. CONCLUSION
    An overview of telescope modeling activities during construction were presented in this paper to
    demonstrate how important this activity is even during the construction phase. This fact shouldn’t be
    minimized or ignored in future projects due to the increased complexity of telescope systems.
    ACKNOWLEDGEMENTS
    This material is based upon work supported in part by the National Science Foundation through Cooperative
    Agreement Award No. AST-1227061 under Governing Cooperative Agreement 1258333 managed by the
    Association of Universities for Research in Astronomy (AURA), and the Department of Energy under
    Contract No. DEAC02-76SF00515 with the SLAC National Accelerator Laboratory. Additional LSST
    funding comes from private donations, grants to universities, and in-kind support from LSSTC Institutional
    Members.
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