Douglas G. MacMynowski

Linear models for control of cavity flow oscillations

Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.

Factors Affecting ENSO’s Period

Accurately capturing the observed mean period of ENSO in general circulation models (GCMs) is often challenging, and it is therefore useful to understand which parameters and processes affect this period. A computationally efficient simulation-based approach is used to extract both the dominant eigenvalues and corresponding eigenvectors of the linearized model from the Zebiak–Cane intermediate-complexity model of ENSO without having to directly construct the linearization. The sensitivity of the period to a variety of parameters is examined, including atmosphere–ocean coupling, atmospheric heating parameterization, thermocline depth zonal profile, western boundary reflection coefficient, atmospheric and ocean wave speeds or Rossby radii of deformation, ocean decay time, and the strength of the annual cycle. In addition to the sensitivity information, the spatial structures of the main fields (SST, thermocline thickness, and more) that are involved in period changes are obtained to aid in the physical interpretation of the sensitivities. There are three main time lags that together compose one-half of a model ENSO period: the Rossby-plus-Kelvin wave propagation time for a wind-caused central Pacific disturbance to propagate to the western ocean and back, SST dynamics that determine the lag between eastern ocean thermocline anomalies and eastern ocean SST anomalies, and the “accumulation” lag of integrating a sufficient delayed wave signal arriving from the western ocean to cancel the eastern ocean anomalies. For any of the parameter changes considered, the eigenvector changes show that the largest contributor to the period change is from changes to the last of these three mechanisms. Physical mechanisms that affect this accumulation delay are discussed, and the case is made that any significant change to ENSO’s period is in turn likely to involve changes to this delay.

Can we test geoengineering

Solar radiation management (SRM), a form of geoengineering, might be used to offset some fraction of the anthropogenic radiative forcing of climate as a means to reduce climate change, but the risks and effectiveness of SRM are uncertain. We examine the possibility of testing SRM through sub-scale deployment as a means to test models of climate response to SRM and explore risks prior to full-scale implementation. Contrary to some claims, this could provide meaningful tests of the climates response to SRM within a decade. We use idealized simulations with the HadCM3L general circulation model (GCM) to estimate the response to SRM and signal-to-noise ratio for global-scale SRM forcing tests, and quantify the trade-offs between duration and intensity of the test and its ability to make quantitative measurements of the climates response to SRM forcing. The response at long time-scales would need to be extrapolated from results measured by a short-term test; this can help reduce the uncertainty associated with relatively rapid climate feedbacks, but uncertainties that only manifest at long time-scales can never be resolved by such a test. With this important caveat, the transient climate response may be bounded with 90% confidence to be no more than 1.5 °C higher than its estimated value, in a single decade test that used roughly 1/10th the radiative forcing perturbation of a CO2-doubling. However, tests could require several decades or longer to obtain accurate response estimates, particularly to understand the response of regional hydrological fields which are critical uncertainties. Some fields, like precipitation over land, have as large a response to short period forcing as to slowly-varying changes. This implies that the ratio of the hydrological to the temperature response that results from a sustained SRM deployment will differ from that of either a short-duration test or that which has been observed to result from large volcanic eruptions.

The frequency response of temperature and precipitation in a climate model

Dynamic aspects of the climates response to forcing are typically explored through transient simulations in the time domain. However, because of the large range of time-scales involved, some features are more easily observed in the frequency domain. We compute the frequency-response of the HadCM3L general circulation model (GCM) to sinusoidal perturbations in solar radiative forcing, with periods between 2^(−1/2) and 2^9 (512) years. The global mean temperature response decreases with increasing frequency, and the frequency scaling at time-scales longer than one year is consistent with the behavior of diffusion into a semi-infinite slab. The land-sea contrast and land-averaged precipitation, however, exhibit relatively little dependency on the frequency of the imposed perturbation, with significant response at both short and long periods. Understanding these relative characteristics of different climate variables in the frequency domain is important to understanding the transient response of the climate system to both anthropogenic and natural (e.g., volcanic) forcings; the frequency response is also relevant in understanding the spectrum of natural variability.

Warm-started wavefront reconstruction for adaptive optics.

Future extreme adaptive optics (ExAO) systems have been suggested with up to 10(5) sensors and actuators. We analyze the computational speed of iterative reconstruction algorithms for such large systems. We compare a total of 15 different scalable methods, including multigrid, preconditioned conjugate-gradient, and several new variants of these. Simulations on a 128x128 square sensor/actuator geometry using Taylor frozen-flow dynamics are carried out using both open-loop and closed-loop measurements, and algorithms are compared on a basis of the mean squared error and floating-point multiplications required. We also investigate the use of warm starting, where the most recent estimate is used to initialize the iterative scheme. In open-loop estimation or pseudo-open-loop control, warm starting provides a significant computational speedup; almost every algorithm tested converges in one iteration. In a standard closed-loop implementation, using a single iteration per time step, most algorithms give the minimum error even in cold start, and every algorithm gives the minimum error if warm started. The best algorithm is therefore the one with the smallest computational cost per iteration, not necessarily the one with the best quasi-static performance.

Wind loads on ground-based telescopes

One of the factors that can influence the performance of large optical telescopes is the vibration of the telescope structure due to unsteady wind inside the telescope enclosure. Estimating the resulting degradation in image quality has been difficult because of the relatively poor understanding of the flow characteristics. Significant progress has recently been made, informed by measurements in existing observatories, wind-tunnel tests, and computational fluid dynamic analyses. We combine the information from these sources to summarize the relevant wind characteristics and enable a model of the dynamic wind loads on a telescope structure within an enclosure. The amplitude, temporal spectrum, and spatial distribution of wind disturbances are defined as a function of relevant design parameters, providing a significant improvement in our understanding of an important design issue.

Analysis of TMT Primary Mirror Control-Structure Interaction

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.

Wind buffeting of large telescopes

Unsteady wind loads due to turbulence within the telescope enclosure are one of the largest dynamic disturbances for ground-based optical telescopes. The desire to minimize the response to the wind influences the design of the telescope enclosure, structure, and control systems. There is now significant experience in detailed integrated modeling to predict image jitter due to wind. Based on this experience, a relatively simple model is proposed that is verified (from a more detailed model) to capture the relevant physics. In addition to illustrating the important elements of the telescope design that influence wind response, this model is used to understand the sensitivity of telescope image jitter to a wide range of design parameters.

Parametric modeling and control of telescope wind-induced vibration

A parametric model of the dynamic performance of an optical telescope due to wind-buffeting is presented. The model is being developed to support the design of next generation segmented-mirror optical telescopes through enabling rapid design iterations and allowing a more thorough exploration of the design space. A realistic performance assessment requires parametric descriptions of the wind, the structural dynamics, active control of the structure, and the optical response. The current model and its assumptions are presented, with the primary emphasis being on the parameterization of the wind forces. Understanding the temporal spectrum and spatial distribution of wind disturbances inside the telescope enclosure is one of the most challenging aspects in developing the overall parametric model. This involves integrating information from wind tunnel tests, computational fluid dynamics, and measurements at existing observatories. The potential and limitations of control to mitigate the response are also discussed, with realistic constraints on the control bandwidth obtained from the detailed structural model of a particular point design. Finally, initial results are presented on performance trends with a few key parameter variations.

Dynamic analysis of TMT

Dynamic disturbance sources affecting the optical performance of the Thirty Meter Telescope (TMT) include unsteady wind forces inside the observatory enclosure acting directly on the telescope structure, unsteady wind forces acting on the enclosure itself and transmitted through the soil and pier to the telescope, equipment vibration either on the telescope itself (e.g. cooling of instruments) or transmitted through the soil and pier, and potentially acoustic forces. We estimate the characteristics of these disturbance sources using modeling anchored through data from existing observatories. Propagation of forces on the enclosure or in support buildings through the soil and pier to the telescope base are modeled separately, resulting in force estimates at the telescope pier. We analyze the resulting optical consequences using integrated modeling that includes the telescope structural dynamics, control systems, and a linear optical model. The dynamic performance is given as a probability distribution that includes the variation of the external wind speed and observing orientation with respect to the wind, which can then be combined with dome seeing and other time- or orientation-dependent components of the overall error budget. The modeling predicts acceptable dynamic performance of TMT.