Extremely large telescopes are characterized by high degree of freedom control systems used to coordinate multiple segments and mirrors. The dynamics can interact so that single loop requirements do not provide sufficient stability and performance robustness. This paper reviews the relevant multivariable robustness and performance methods, and presents examples from Giant Magellan Telescope (GMT) motion control systems.
Singular value bounds of multivariable frequency responses are well developed computational tools that provide a methodology that can be used for telescope analysis. The singular value bounds are relevant because they give the maximum sensitivity for coupled, multivariable systems. Singular values are recommended for analysis, and can be considered for requirements. With sufficient numbers of sensors, these multivariable bounds are measurable and hence can be validated. There is a practical reason for using multivariable tools, to combine many, perhaps thousands of transfer functions and/or measurements that can be compared against singular value bounds.
The first example is the AZ/EL mount control. Coupling tends to be small, hence single-input analysis tools suffice, nevertheless the mount control system provides a good introduction to multivariable methodology. The maximum singular value of both the sensitivity and complementary sensitivity functions provide a good bound for crossover robustness near the position control bandwidth, typically +6 dB near 1 Hz. The high frequency region of the complementary sensitivity function provides a good bound on robustness with respect to unmodeled structural dynamics, typically–40dB above the maximum frequency of the finite element modes.
Similar multivariable stability robustness bounds can be applied to position control of the M2 assembly, for both the macrocell relative to the top end assembly, and each mirror subassembly relative to the macrocell. The latter includes control of the Fast Steering Mirror, where 21 PZT actuators control the tip and tilt of seven secondary mirrors. The risk is the 21 PZT control loops meet good classical phase and gain margin robustness metrics when measured as individual, single-input-single-output systems, but the multivariable bound exceeds either the +6 dB or – 40 dB bound. This can occur due to interaction in the macrocell, the structure used to support the individual segments. Whether or not this interaction occurs depends on the bandwidth of the control system relative to the structural modes of the macrocell. This tradeoff is important, and the maximum singular value is a good tool to test for this sensitivity.
Launched in 2009, Keck Observatory’s Telescope Control System Upgrade (TCSU) project set out to improve Keck’s telescope pointing, tracking, and offsetting performance as well as increase maintainability and reliability. The project went online full time on the Keck 2 telescope in October 2017 and on the Keck 1 telescope in March 2018 after a notable delay due to a re-design of the azimuth and elevation encoder mounting systems. This paper discusses the details and challenges of implementing this large and complicated system while never requiring a shutdown of either telescope. The TCSU project replaced all of the major elements of the telescope controls, rotator and secondary mirror controls, and safety system. National Instrument’s reconfigurable I/O technology (i.e. NI RIO), with their embedded field programmable gate arrays (FPGAs), are used as the core of the telescope’s digital velocity control loop, structural filter, and tachometer filter. They were also used to create a monitoring and safety system for the rotator velocity controller as well as reading the newly installed tilt meters used to greatly improve pointing performance. Delta Tau’s family of “Brick” programmable multi-axis controllers, i.e. PMAC or BRICK, are used to control the rotator and secondary mirror. They enable better tuning and faster slew speeds for these subsystems. An Allen Bradley’s ControlLogix® controller and the family of FLEX™ Input/Output (IO) modules were used to create a distributed safety system able to handle a wide variety of signal types. This technology refresh based on commercial off the shelf equipment replaced much of our obsolete and custom equipment. A significant part of the project was the installation of new telescope azimuth and elevation position encoders based on Heidenhain’s 40 micron grading tape scales. Interpolated to a 10 nanometer resolution, the new encoders provide true 4 mas resolution in azimuth and 1 mas resolution in elevation. This is a big improvement to Keck’s position sensing when compared to the old rotary incremental encoders. The installation required a significant amount of mechanical infrastructure to house them. Additionally, two tilt meters were installed to sense the telescope’s varying vertical angle as a function of azimuth, mainly due to the azimuth bearing’s axial runout. The encoders and tilt meters are the primary reason for achieving the greatly improved pointing and tracking performance . Finally, a switching solution using solid state relays and dual network switches was installed to provide seamless and rapid switching between the old and new control systems during commissioning. Although this component is a simple design and does not boast of any new technology, it is one of the key components that enabled the successful testing of the new equipment while keeping the old system operational as a backup for night time observing as well as for baseline performance comparisons. It allowed us to switch a variety of signal types and was very cost effective when compared to available products.
CCAT will be a 25-meter telescope for submillimeter wavelength astronomy located at an altitude of 5600 meters on
Cerro Chajnantor in northern Chile. This paper presents an overview of the preliminary mount control design. A finite
element model of the structure has been developed and is used to determine the dynamics relevant for mount control.
Controller strategies are presented that are designed to meet challenging wind rejection and fast scan requirements.
Conventional inner loops are used for encoder-based control. Offset requirements are satisfied using innovative
command shaping with feedforward and a two-command path structure. The fast scan requirement is satisfied using a
new approach based on a de-convolution filter. The de-convolution filter uses an estimate of the closed loop response
obtained from test signals. Wind jitter requirements remain a challenge and additional sensors such as accelerometers
and wind pressure sensors may be needed.
The Keck I and II telescopes have been operational respectively since 1990 and 1996. Operational improvements are
sought to decrease the settling time in response to short moves. The structural response of the open loop system has been
re-identified and the mount control design has been re-examined. Changes to the mount control compensators and
command shaping architecture have been proposed in order to achieve improved response. Results from these studies are
presented, both theoretical and experimental.
The Thirty Meter Telescope primary mirror is composed of 492 segments that are controlled to high precision in the presence of wind and vibration disturbances, despite the interaction with structural dynamics. The higher bandwidth and larger number of segments compared with the Keck telescopes requires greater attention to modeling to ensure success. We focus here on the development and validation of a suite of quasi-static and dynamic modeling tools required to support the design process, including robustness verification, performance estimation, and requirements flowdown. Models are used to predict the dynamic response due to wind and vibration disturbances, estimate achievable bandwidth in the presence of control-structure-interaction (CSI) and uncertainty in the interaction matrix, and simulate and analyze control algorithms and strategies, e.g. for control of focus-mode, and sensor calibration. Representative results illustrate TMT performance scaling with parameters, but the emphasis is on the modeling framework itself.
The primary mirror control system for the Thirty Meter Telescope (TMT) maintains the alignment of the 492
segments in the presence of both quasi-static (gravity and thermal) and dynamic disturbances due to unsteady
wind loads. The latter results in a desired control bandwidth of 1Hz at high spatial frequencies. The achievable
bandwidth is limited by robustness to (i) uncertain telescope structural dynamics (control-structure interaction)
and (ii) small perturbations in the ill-conditioned influence matrix that relates segment edge sensor response
to actuator commands. Both of these effects are considered herein using models of TMT. The former is explored
through multivariable sensitivity analysis on a reduced-order Zernike-basis representation of the structural
dynamics. The interaction matrix ("A-matrix") uncertainty has been analyzed theoretically elsewhere, and is
examined here for realistic amplitude perturbations due to segment and sensor installation errors, and gravity
and thermal induced segment motion. The primary influence of A-matrix uncertainty is on the control of "focusmode";
this is the least observable mode, measurable only through the edge-sensor (gap-dependent) sensitivity
to the dihedral angle between segments. Accurately estimating focus-mode will require updating the A-matrix
as a function of the measured gap. A-matrix uncertainty also results in a higher gain-margin requirement for
focus-mode, and hence the A-matrix and CSI robustness need to be understood simultaneously. Based on the
robustness analysis, the desired 1 Hz bandwidth is achievable in the presence of uncertainty for all except the
lowest spatial-frequency response patterns of the primary mirror.
Finite element models (FEMs) are being used extensively in the design of the Thirty Meter Telescope (TMT). One such
use is in the design and analysis of the Primary Segment Assembly (PSA). Each PSA supports one primary mirror
segment on the mirror cell, as well as three actuators, which are used to control three degrees of freedom - tip, tilt, and
piston - of the mirror segment. The dynamic response of the PSA is important for two reasons: it affects the response
of the mirror to fluctuating wind forces, and high-Q modes limit the bandwidth of the control loops which drive the
actuators, and impact vibration transmissivity, thereby degrading image quality. We have completed a series of tests on
a prototype PSA, in which the dynamic response was tested. We report on the test methods used to measure the dynamic
response of the PSA alone and with candidate actuators installed, and we present comparisons between the measured
response and FEM predictions. There is good agreement between FEM predictions and measured response over the
frequency range within which the dynamic response is critical to control system design.
The Thirty Meter Telescope has 492 primary mirror segments, each incorporated into a Primary Segment Assembly
(PSA), each of which in turn has three actuators that control piston, tip, and tilt, for a total of 1476 actuators. Each
actuator has a servo loop that controls small motions (nanometers) and large motions (millimeters). Candidate actuators
were designed and tested that fall into the categories of "hard" and "soft," depending on the offload spring stiffness
relative to the PSA structural stiffness. Dynamics models for each type of actuator are presented, which respectively use
piezo-electric transducers and voice coils. Servo design and analysis are presented that include assessments of stability,
performance, robustness, and control structure interaction. The analysis is presented for a single PSA on a rigid base, and
then using Zernike approximations the analysis is repeated for 492 mirror segments on a flexible mirror cell. Servo
requirements include low-frequency stiffness, needed for wind rejection; reduced control structure interaction, specified
by a bound on the sensitivity function; and mid-frequency damping, needed to reduce vibration transmission. The last of
these requirements, vibration reduction, was found to be an important distinguishing characteristic for actuator selection.
Hard actuators have little inherent damping, which is improved using PZT shunt circuits and force feedback, but still
these improvements were found to result in less damping than is provided by the soft actuator. Results of the servo
analysis were used for an actuator down-select study.
The TMT mount control system provides telescope pointing and tracking. Requirements include wind disturbance
rejection, offsetting time and accuracy, control system robustness, and the magnitude of response at structural
resonances. A finite element model of the complete telescope has been developed and the transfer functions used for the
control designs are presented. Wind disturbance, encoder, and
wave-front-sensor models are presented that are used for
the control design. A performance analysis translates the requirements to a required bandwidth. Achieving this
bandwidth is important for reducing telescope image motion due to wind-buffeting. A mount control design is presented
that meets the demanding requirements by maximizing low frequency gain and using structural filters to roll-off
structural modes. The control system analysis includes an outer guide loop using a wave front sensor. Offsetting time
and accuracy requirements are satisfied using feed-forward control architecture.
The primary mirror control system (M1CS) stabilizes the 492 segments of the Thirty Meter Telescope primary mirror in
the presence of disturbances. Each Primary Segment Assembly (PSA) has three actuators and position sensors that
control the piston, tip, and tilt of the mirror segment. Requirements for the PSA position controller are presented, with
the main requirements being 10 Newton per micron stiffness below one Hertz, where wind is the primary disturbance.
Bandwidths of the PSA position controller of about twenty Hertz, assuming a soft actuator, are needed to meet this
requirement. A finite element model of the PSA was developed and used for a preliminary control design. PSA structural
modes at 40, 90, and 120 impact the control design. We have studied control designs with different actuators, sensors,
and structural filters in order to assess disturbance rejection properties and interactions with the PSA structural modes.
The performance requirements are achieved using voice coil actuators with modal control architecture for piston, tip, and
tilt. Force interactions with the underlying mirror cell are important, and we present the status of our studies of the
control structure interaction effect (CSIE). A related paper presents further analysis of the CSIE and MICS global
position control loop.
The Thirty Meter Telescope (TMT) project has revised the reference optical configuration from an Aplanatic Gregorian
to a Ritchey-Chrétien design. This paper describes the revised telescope structural design and outlines the design
methodology for achieving the dynamic performance requirements derived from the image jitter error budget. The usage
of transfer function tools which incorporate the telescope structure system dynamic characteristics and the control
system properties is described along with the optimization process for the integrated system. Progress on the structural
design for seismic considerations is presented. Moreover, mechanical design progress on the mount control system
hardware such as the hydrostatic bearings and drive motors, cable wraps and safety system hardware such as brakes and
absorbers are also presented.
The primary mirror control system (M1CS) keeps the 492 segments of the Thirty Meter Telescope primary
mirror aligned in the presence of disturbances. A global position control loop uses feedback from inter-segment
edge sensors to three actuators behind each segment that control segment piston, tip and tilt. If soft force
actuators are used (e.g. voice-coil), then in addition to the global position loop there will be a local servo loop to
provide stiffness. While the M1 control system at Keck compensates only for slow disturbances such as gravity
and thermal variations, the M1CS for TMT will need to provide some compensation for higher frequency wind
disturbances in order to meet stringent error budget targets. An analysis of expected high-wavenumber wind
forces on M1 suggests that a 1Hz control bandwidth is required for the global feedback of segment edge-sensorbased
position information in order to minimize high spatial frequency segment response for both seeing-limited
and adaptive optics performance. A much higher bandwidth is required from the local servo loop to provide
adequate stiffness to wind or acoustic disturbances. A related paper presents the control designs for the local
actuator servo loops. The disturbance rejection requirements would not be difficult to achieve for a single
segment, but the structural coupling between segments mounted on a flexible mirror cell results in controlstructure
interaction (CSI) that limits the achievable bandwidth. Using a combination of simplified modeling
to build intuition and the full telescope finite element model for verification, we present designs and analysis
for both the local servo loop and global loop demonstrating sufficient bandwidth and resulting wind-disturbance
rejection despite the presence of CSI.
Vibration and noise are two long-standing problems that have limited the expansion of military and commercial applications of rotorcraft. The source of these interrelated phenomena is the main rotor, which operates in an unsteady and complex aerodynamic environment. The trailing edge flap concept for smart blade control has been investigated by several researchers for possible use in noise and vibration reduction, and shows promise. The flaps are actuated using piezo-stack, bimorph or magnetostrictive actuators. It is however still unclear if there is a single actuation mechanism that addresses both noise and vibration reduction, while still having enough control authority available to act as an extra control effector in its own right. The uncertainty about the actuation mechanism, about the precise amount of flap deflection available, and about the accuracy of current constitutive models of the actuators lead to significant difficulties in analyzing the potential of the concept for helicopter applications. In this study we propose and execute an innovative approach to the above problem that consists of modeling the smart actuation mechanism using a simple low order linear model that matches test data (with an associated variation or uncertainty). We use this model in association with a helicopter flight dynamic model for carrying out an optimization of flap sizing and placement for minimum fixed frame vibration. Finally, we use the model to carry out an analysis of the effectiveness of the flap in reducing inter-axis coupling, and as a redundant control effector in case of primary actuator failure.
The servo design and model of the W. M. Keck telescopes autoguider is presented. Telescope servo models often do not include the guider loop and therefore do not take advantage of traditional control analysis and test techniques to improve performance. Guide camera dynamics, computational and transport lags, and compensation networks are discussed. A means of measuring the actual frequency response characteristics of the guide loop is presented and the results are compared to those predicted by the model. Guide performance as a function of integration time is illustrated. An improved compensation network is developed and its performance examined.
The azimuth and elevation sources of the W.M. Keck Telescope have been designed to meet stringent tracking, offsetting, and slewing requirements. The requirements and the achieved performance are presented. The feedback architecture of the position and rate loops is described. The analysis includes an identification of the telescope structure via frequency sweep test signals. The identified model is compared with the single resonance model used in the preliminary design. As expected there are numerous additional resonances, and the effects of these on performance and stability are discussed. The autoguider loop is also discussed. Shortcomings are noted and ideas for improved performance are examined.