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An explicit solution to the optimal LQG problem for flexible structures with collocated rate sensors

We present a class of compensators in explicit form (not requiring numerical computer calculations) for stabilizing flexible structures with collocated rate sensors. They are based on the explicit solution, valid for both Continuum and FEM Models, of the LQG problem for minimizing mean square rate. They are robust with respect to system stability (will not destabilize modes even with mismatch of parameters), can be instrumented in state space form suitable for digital controllers, and can be specified directly from the structure modes and mode 'signature' (displacement vectors at sensor locations). Some simulation results are presented for the NASA LaRC Phase-Zero Evolutionary Model - a modal Trust model with 86 modes - showing damping ratios attainable as a function of compensator design parameters and complexity.

Balakrishnan, A. V.

Robustness properties of LQG optimized compensators for collocated rate sensors

In this paper we study the robustness with respect to stability of the closed-loop system with collocated rate sensor using LQG (mean square rate) optimized compensators. Our main result is that the transmission zeros of the compensator are precisely the structure modes when the actuator/sensor locations are 'pinned' and/or 'clamped': i.e., motion in the direction sensed is not allowed. We have stability even under parameter mismatch, except in the unlikely situation where such a mode frequency of the assumed system coincides with an undamped mode frequency of the real system and the corresponding mode shape is an eigenvector of the compensator transfer function matrix at that frequency. For a truncated modal model - such as that of the NASA LaRC Phase Zero Evolutionary model - the transmission zeros of the corresponding compensator transfer function can be interpreted as the structure modes when motion in the directions sensed is prohibited.

Balakrishnan, A. V.

Design and Application of a Collocated Capacitance Sensor for Magnetic Bearing Spindle

This paper presents a collocated capacitance sensor for magnetic bearings. The main feature of the sensor is that it is made of a specific compact printed circuit board (PCB). The signal processing unit has been also developed. The results of the experimental performance evaluation on the sensitivity, resolution and frequency response of the sensor are presented. Finally, an application example of the sensor to the active control of a magnetic bearing is described.

Shin, Dongwon

A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Zhang, Yiqiang

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Balakrishnan, A. V.

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Balakrishnan, A. V.

Absorption of Solar Radiation by the Cloudy Atmosphere Interpretations of Collocated Aircraft Measurements

As part of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), we have obtained and analyzed measurements made from collocated aircraft of the absorption of solar radiation within the atmospheric column between the two aircraft. The measurements were taken during October 1995 at the ARM site in Oklahoma. Relative to a theoretical radiative transfer model, we find no evidence for excess solar absorption in the clear atmosphere and significant evidence for its existence in the cloudy atmosphere. This excess cloud solar absorption appears to occur in both visible (0.224-0.68 microns) and near-infrared (0.68-3.30 microns) spectral regions, although not at 0.5 microns for the visible contribution, and it is shown to be true absorption rather than an artifact of sampling errors caused by measuring three-dimensional clouds.

Valero, Francisco P. J.

Robust Stabilizing Compensators for Flexible Structures with Collocated Controls

For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.

Balakrishman, A. V.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Kouatchou, Jules

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Kouatchou, Jules

Glass-Cockpit Pilot Subjective Ratings of Predictive Information, Collocation, and Mission Status Graphics: An Analysis and Summary of the Future Focus of Flight Deck Research Survey

NASA Langley Research Center has been researching ways to improve flight crew decision aiding for systems management. Our current investigation is how to display a wide variety of aircraft parameters in ways that will improve the flight crew's situation awareness. To accomplish this, new means are being explored that will monitor the overall health of a flight and report the current status of the aircraft and forecast impending problems to the pilots. The initial step in this research was to conduct a survey addressing how current glass-cockpit commercial pilots would value a prediction of the status of critical aircraft systems. We also addressed how this new type of data ought to be conveyed and utilized. Therefore, two other items associated with predictive information were also included in the survey. The first addressed the need for system status, alerts and procedures, and system controls to be more logically grouped together, or collocated, on the flight deck. The second idea called for the survey respondents opinions on the functionality of mission status graphics; a display methodology that groups a variety of parameters onto a single display that can instantaneously convey a complete overview of both an aircraft's system and mission health.

Bartolone, Anthony

Response Times in Correcting Non-Normal System Events When Collocating Status, Alerts and Procedures, and Controls

Currently, most of the displays in control rooms can be categorized as status, alerts/procedures, or control screens. With the advent and use of CRTs and the associated computing power available to compute and display information, it is now possible to combine these different elements of information and control onto a single display. An experiment was conducted to determine which, if any, of these functions should be collocated in order to better handle simple anticipated non-normal system events. The results indicated that there are performance benefits and subject preferences to combining all the information onto one screen or combining the status and alert/procedure information onto one screen and placing the controls in another area.

Anna C. Trujillo

Spectrally Resolved Flux Derived from Collocated AIRS and CERES Observations and its Application in Model Validation: Clear-Sky Over the Tropic Oceans - Part I

Spectrally resolved outgoing IR flux, the integrand of the outgoing longwave radiation (OLR), has its unique value in evaluating model simulations. Here we describe an algorithm of deriving such clear-sky outgoing spectral flux through the whole IR region from the collocated Atmospheric Infrared Sounder (AIRS) and the Clouds & the Earth's Radiant Energy System (CERES) measurements over the tropical oceans. Based on the scene types and corresponding angular distribution models (ADMs) used in the CERES Single Satellite Footprint (SSF) dataset, spectrally-dependent ADMs are developed and used to estimate the spectral flux at each AIRS channel. A multivariate linear prediction scheme is then used to estimate spectral fluxes at frequencies not covered by the AIRS instrument. The whole algorithm is validated using synthetic spectra as well as the CERES OLR measurements. Using the GFDL AM2 model simulation as a case study, the application of the derived clear-sky outgoing spectral flux in model evaluation is illustrated. By comparing the observed and simulated spectral flux in 2004, compensating errors in the simulated OLR from different absorption bands can be revealed, so does the errors from frequencies within a given absorption band. Discrepancies between the simulated and observed spatial distributions and seasonal evolutions of the spectral fluxes at different spectral ranges are further discussed. The methodology described in this study can be applied to other surface types as well as cloudy-sky observations and corresponding model evaluations.

Huang, Xianglei

Evaluations of Thin Cirrus Contamination and Screening in Ground Aerosol Observations Using Collocated Lidar Systems

Cirrus clouds, particularly sub visual high thin cirrus with low optical thickness, are difficult to be screened in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to examine the susceptibility of operational aerosol products to thin cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the CALIPSO vertical feature mask (VFM) and the MODIS-derived thin cirrus screening parameters for the purpose of evaluating thin cirrus contamination. Key results of this study include: (1) Quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted. Although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons, (2) Challenges in matching up different data for analysis are highlighted and corresponding solutions proposed, and (3) Estimation of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.

Huang, Jingfeng

Optimization of Low-Thrust Spiral Trajectories by Collocation

As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.

Falck, Robert D.

Linkage among Ice Crystal Microphysics, Mesoscale Dynamics and Cloud and Precipitation Structures Revealed By Collocated Microwave Radiometer and Multi-Frequency Radar Observations

Ice clouds and falling snow are ubiquitous globally and play important roles in the Earth’s radiation budget and precipitation processes. Ice particle microphysical properties (e.g., size, habit and orientation) are not only influenced by ambient environment’s dynamic and thermodynamic conditions, but also intimately connect to the cloud radiative effects and particle fall speeds, which therefore impact up to the future climate projection and down to the details of the surface precipitation (e.g., onset-time, location, type and strength). Our previous work revealed that high-frequency Polarimetric radiance Difference (PD) from passive microwave sensors is a good indicator of the bulk aspect ratio of horizontally oriented ice particles that are often occur inside anvil clouds and/or stratiform precipitations. In this current work, we further investigate the dynamic/thermodynamic mechanisms and cloud/precipitation structures associated with ice-phase microphysics corresponding to different PD signals. In order to do so, collocated CloudSat radar (W-band) and Global Precipitation Measurement Dual-frequency Precipitation Radar (GPM-DPR, Ku/Ka bands) observations as well as European Centre for Medium-Range Weather Forecasts (ECMWF) atmosphere background profiles are grouped according to the magnitude of PD for only stratiform precipitation and/or anvil cloud scenes. We found that horizontally-oriented snow aggregates or large snow particles are likely the major contributor to the high-PD signals at 166 GHz, while low-PD magnitudes can be attributed to small cloud ice, randomly oriented snow aggregates, riming snow or super-cooled water. Further, high (low) PD scenes are found to be associated with stronger (weaker) wind shear and higher (lower) ambient humidity, both of which help promote (prohibit) the growth of frozen particles and the organization of convective systems. An ensemble of squall line cases is studied at the end to demonstrate that the PD asymmetry in the leading and trailing edges of the deep convection line is closely tied to the anvil cloud and stratiform precipitation layers respectively, suggesting the potential usefulness of PD as a proxy of stratiform/convective precipitation flag, as well as a proxy of convection life stage.

Ice crystal microphysics