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Lunar Outpost Life Support Architecture Study Based on a High Mobility Exploration Scenario

As scenarios for lunar surface exploration and habitation continue to evolve within NASA s Constellation program, so must studies of optimal life support system architectures and technologies. This paper presents results of a life support architecture study based on a 2009 NASA scenario known as Scenario 12. Scenario 12 represents a consolidation of ideas from earlier NASA scenarios and includes an outpost near the Lunar South Pole comprised of three larger fixed surface elements and four attached pressurized rovers. The scenario places a high emphasis on surface mobility, with planning assuming that all four crewmembers spend roughly 50% of the time away from the outpost on 3-14 day excursions in two of the pressurized rovers. Some of the larger elements can also be mobilized for longer duration excursions. This emphasis on mobility poses a significant challenge for a regenerative life support system in terms of cost-effective waste collection and resource recovery across multiple elements, including rovers with very constrained infrastructure resources. The current study considers pressurized rovers as part of a distributed outpost life support architecture in both stand-alone and integrated configurations. A range of architectures are examined reflecting different levels of closure and distributed functionality. Different lander propellant scavenging options are also considered involving either initial conversion of residual oxygen and hydrogen propellants to water or initial direct oxygen scavenging. Monte Carlo simulations are used to assess the sensitivity of results to volatile high-impact mission variables, including the quantity of residual lander propellants available for scavenging, the fraction of crew time away from the outpost on excursions, total extravehicular activity hours, and habitat leakage. Architectures are evaluated by estimating surpluses or deficits of water and oxygen per 180-day mission and differences in fixed and 10-year-total equivalent system mass (ESM) relative to a reference case. Results are presented based on current assumptions for Scenario 12 and based on Monte Carlo simulations with assumed probability distributions for the high-impact mission variables. The calculated probability of no water or oxygen resupply from Monte Carlo simulations provides a quantitative measure of system robustness that can be used for cost/benefit analyses to identify leading architecture candidates. Areas of technology improvement that are likely to have a significant impact are also suggested.

Lange, Kevin E.↗

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗

Taking Stock of Circumboreal Forest Carbon With Ground Measurements, Airborne and Spaceborne LiDAR

The boreal forest accounts for one-third of global forests, but remains largely inaccessible to ground-based measurements and monitoring. It contains large quantities of carbon in its vegetation and soils, and research suggests that it will be subject to increasingly severe climate-driven disturbance. We employ a suite of ground-, airborne- and space-based measurement techniques to derive the first satellite LiDAR-based estimates of aboveground carbon for the entire circumboreal forest biome. Incorporating these inventory techniques with uncertainty analysis, we estimate total aboveground carbon of 38 +/- 3.1 Pg. This boreal forest carbon is mostly concentrated from 50 to 55degN in eastern Canada and from 55 to 60degN in eastern Eurasia. Both of these regions are expected to warm >3 C by 2100, and monitoring the effects of warming on these stocks is important to understanding its future carbon balance. Our maps establish a baseline for future quantification of circumboreal carbon and the described technique should provide a robust method for future monitoring of the spatial and temporal changes of the aboveground carbon content.

Biomass↗

Space Mission Options for Reconnaissance and Mitigation of Asteroid 2024 YR4

Near-Earth asteroid 2024 YR 4 was discovered on 2024-12-27 and its probability of Earth impact in December 2032 peaked at about 3% on 2025-02-18. Additional observations ruled out Earth impact by 2025-02-23. However, the probability of lunar impact in December 2032 then rose, reaching about 4% by the end of the apparition in May 2025. James Webb Space Telescope (JWST) observations on 2025-03-26 estimated the asteroid's diameter at 60 +/- 7 m. Studies of 2024 YR 4 's potential lunar impact effects suggest lunar ejecta could increase micrometeoroid debris flux in low Earth orbit up to 1000 times above background levels over just a few days, possibly threatening astronauts and spacecraft. In this work, we present options for space missions to 2024 YR 4 that could be utilized if lunar impact is confirmed. We cover flyby & rendezvous reconnaissance, deflection, and robust disruption of the asteroid. We examine both rapid-response and delayed launch options through 2032. We evaluate chemical and solar electric propulsion, various launch vehicles, optimized deep space maneuvers, and gravity assists. Re-tasking extant spacecraft and using built spacecraft not yet launched are also considered. The best reconnaissance mission options launch in late 2028, leaving only approximately three years for development at the time of this writing in August 2025. Deflection missions were assessed and appear impractical. However, kinetic robust disruption missions are available with launches between April 2030 and April 2032. Nuclear robust disruption missions are also available with launches between late 2029 and late 2031. Finally, even if lunar impact is ruled out there is significant potential utility in deploying a reconnaissance mission to characterize the asteroid.

Asteroid Disruption↗

Density fluctuations induced by nonlinear Alfven waves

The generation of plasma density fluctuations by nonlinear Alfven waves is considered. Of particular interest is the modification to the 'static approximation', describing the relationship between wave intensity and plasma density, when the Alfven wave packet is rapidly steepening. The study concentrates on a forced wave equation for the plasma density, which yields the static approximation in a select approximnation. An analytic solution to this equation is obtained for a reasonable model of a steeping wave packet. The principal results are: (1) the static approximation should give a surprisingly robust description of the coupling between Alfven wave intensity and plasma density; (2) departures of the plasma density perturbation from the static approximation result are determined by a parameter that is a simple function of the wave amplitude and plasma beta; (3) for rapidly evolving wave packets, the position of maximum density change is displaced from that of maximum wave intensity, and (4) the magnitude of the density fluctuation will not be much different than the static approximation estimate.

Spangler, Steven R.↗

Adaptive Strategies for Controls of Flexible Arms

An adaptive controller for a modern manipulator has been designed based on asymptotical stability via the Lyapunov criterion with the output error between the system and a reference model used as the actuating control signal. Computer simulations were carried out to test the design. The combination of the adaptive controller and a system vibration and mode shape estimator show that the flexible arm should move along a pre-defined trajectory with high-speed motion and fast vibration setting time. An existing computer-controlled prototype two link manipulator, RALF (Robotic Arm, Large Flexible), with a parallel mechanism driven by hydraulic actuators was used to verify the mathematical analysis. The experimental results illustrate that assumed modes found from finite element techniques can be used to derive the equations of motion with acceptable accuracy. The robust adaptive (modal) control is implemented to compensate for unmodelled modes and nonlinearities and is compared with the joint feedback control in additional experiments. Preliminary results show promise for the experimental control algorithm.

Yuan, Bau-San↗

Weighted slit extraction of low-dispersion IUE spectral data

The weighted slit extraction has been chosen by the IUE project as the standard extraction for low-dispersion spectra in the final IUE archives. In order to properly weight the data within the extraction slit and obtain the optimal evaluation of the true spectrum, a noise model is derived for IUE data. The exclusion of cosmic rays is demonstrated and the improvement in signal-to-noise ratio is quantified for spectra taken with a wide range of flux level. Problematic spectra, such as trailed spectra, multiple spectra, discontinuous spectra, and emission-line spectra, are extracted to demonstrate the robust nature of the method. Comparisons are made between the standard IUE Standard Image Processing System (IUESIPS) extraction, nonstandard narrow slit extraction, trailed IUESIPS extraction, and weighted extraction for these data. Other weighted slit extractions are briefly discussed. The advantages of the weighted slit extraction are: (1) the extraction improves the signal-to-noise ratio of the spectrum while conserving total flux; (2) most of the cosmic rays are automatically removed; (3) the output includes an error estimate for each point in the flux spectrum; and (4) the algorithm can be run in a batch mode that requires no special input parameters.

Kinney, A. L.↗

Development of a machine vision system for automated structural assembly

Research is being conducted at the LaRC to develop a telerobotic assembly system designed to construct large space truss structures. This research program was initiated within the past several years, and a ground-based test-bed was developed to evaluate and expand the state of the art. Test-bed operations currently use predetermined ('taught') points for truss structural assembly. Total dependence on the use of taught points for joint receptacle capture and strut installation is neither robust nor reliable enough for space operations. Therefore, a machine vision sensor guidance system is being developed to locate and guide the robot to a passive target mounted on the truss joint receptacle. The vision system hardware includes a miniature video camera, passive targets mounted on the joint receptacles, target illumination hardware, and an image processing system. Discrimination of the target from background clutter is accomplished through standard digital processing techniques. Once the target is identified, a pose estimation algorithm is invoked to determine the location, in three-dimensional space, of the target relative to the robots end-effector. Preliminary test results of the vision system in the Automated Structural Assembly Laboratory with a range of lighting and background conditions indicate that it is fully capable of successfully identifying joint receptacle targets throughout the required operational range. Controlled optical bench test results indicate that the system can also provide the pose estimation accuracy to define the target position.

Sydow, P. Daniel↗

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

Tessler, Alexander↗

Use of Modal Acoustic Emission to Monitor Damage Progression in Carbon Fiber/Epoxy Tows and Implications for Composite Structures

ASTM-based ILH methods were found to give a reproducible, quantitative estimate of the stress threshold at which significant accumulated damage began to occur. a) FR events are low energy (<2 V(exp 20 microsec) b) FR events occur close to the observed failure locus. c) FR events consist of more than 30% fiber breakage (>300 kHz) d) FR events show a consistent hierarchy of cooperative damage for composite tow, and for the COPV tested, regardless of applied load. Application of ILH or related stress profiles could lead to robust pass/fail acceptance criteria based on the FR. Initial application of FR and FFT analysis of AE data acquired on COPVs is promising.

Waller, Jess M.↗

Correlations Between the Contributions of Individual IVS Analysis Centers

Within almost all space-geodetic techniques, contributions of different analysis centers (ACs) are combined in order to improve the robustness of the final product. So far, the contributing series are assumed to be independent as each AC processes the observations in different ways. However, the series cannot be completely independent as each analyst uses the same set of original observations and many applied models are subject to conventions used by each AC. In this paper, it is shown that neglecting correlations between the contributing series yields too optimistic formal errors and small, but insignificant, errors in the estimated parameters derived from the adjustment of the combined solution.

Bockmann, Sarah↗

How Well Satellite Remote Sensing Can Inform Surface Level Ozone Production Sensitivity to Precursor Trace Gas Emissions?

Surface-level ozone (O3) pollution mitigation strategies rely on a clear understanding of the atmospheric chemical processes involving O3, NOx (nitric oxide (NO) + nitrogen dioxide (NO2)) and volatile organic compounds (VOCs). A robust spatiotemporal classification of O3 photochemical regimes with relative chemical sensitivity of local O3 formation to emission reductions of NOx (NOx-limited regime) versus VOCs (radical-limited regime) is required to design anthropogenic emission reduction policies in order to improve surface air quality. Numerous studies found that the ratio of satellite-retrieved Vertical Column Densities (VCDs) of formaldehyde (HCHO) to NO2 can diagnose O3 production sensitivity. However, uncertainty still remains about the accuracy of such estimates using satellite-based retrievals. This study conducts an investigation to identify how well satellite data can inform surface-level O3 sensitivity by validating satellite-based estimates against aircraft-based retrievals taken during the Long Island Sound Tropospheric Ozone Study (LISTOS-2018) and Ozone Water-Land Environmental Transition Study (OWLETS-2) field campaigns. For this study, we use HCHO and NO2 retrievals from the Ozone Monitoring Instrument (OMI) onboard the Aura satellite, and high spatiotemporal resolution TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor (S5P) satellite. The Community Multiscale Air Quality (CMAQ) modelling system is used to provide trace gas vertical profiles to recalculate air mass factor for deriving consistent satellite-based VCDs. To demonstrate the ability of satellites to diagnose O3 production regimes, we validate satellite-derived O3 sensitivity regimes, along with the OMI and TROPOMI products applied, using HCHO and NO2 retrievals from the aircraft-based instruments: Geostationary Trace gas and Aerosol Sensor Optimization (GeoTASO) spectrometer and Geostationary Coastal and Air Pollution Events Airborne Simulator (GCAS) instruments deployed during the LISTOS-2018 and OWLETS-2 campaigns. The results of this work will advance our fundamental knowledge of the spatiotemporal evolution of the complex O3-NOx-VOC chemistry, and will advance our understanding about the quality of remote-sensing, suborbital, and satellite data for accurately observing surface-level O3 production sensitivity.

Satellite↗

NASA's Carbon Monitoring System Flux-Pilot Project: A Multi-Component Analysis System for Carbon-Cycle Research and Monitoring

The importance of greenhouse gas increases for climate motivates NASA s observing strategy for CO2 from space, including the forthcoming Orbiting Carbon Observatory (OCO-2) mission. Carbon cycle monitoring, including attribution of atmospheric concentrations to regional emissions and uptake, requires a robust modeling and analysis infrastructure to optimally extract information from the observations. NASA's Carbon-Monitoring System Flux-Pilot Project (FPP) is a prototype for such analysis, combining a set of unique tools to facilitate analysis of atmospheric CO2 along with fluxes between the atmosphere and the terrestrial biosphere or ocean. NASA's analysis system is unique, in that it combines information and expertise from the land, oceanic, and atmospheric branches of the carbon cycle and includes some estimates of uncertainty. Numerous existing space-based missions provide information of relevance to the carbon cycle. This study describes the components of the FPP framework, assessing the realism of computed fluxes, thus providing the basis for research and monitoring applications. Fluxes are computed using data-constrained terrestrial biosphere models and physical ocean models, driven by atmospheric observations and assimilating ocean-color information. Use of two estimates provides a measure of uncertainty in the fluxes. Along with inventories of other emissions, these data-derived fluxes are used in transport models to assess their consistency with atmospheric CO2 observations. Closure is achieved by using a four-dimensional data assimilation (inverse) approach that adjusts the terrestrial biosphere fluxes to make them consistent with the atmospheric CO2 observations. Results will be shown, illustrating the year-to-year variations in land biospheric and oceanic fluxes computed in the FPP. The signals of these surface-flux variations on atmospheric CO2 will be isolated using forward modeling tools, which also incorporate estimates of transport error. The results will be discussed in the context of interannual variability of observed atmospheric CO2 distributions.

Pawson, S.↗

Tracing the Mass-Dependent Star Formation History of Late-Type Galaxies using X-ray Emission: Results from the CHANDRA Deep Fields

We report on the X-ray evolution over the last approx.9 Gyr of cosmic history (i.e., since z = 1.4) of late-type galaxy populations in the Chandra Deep Field-North and Extended Chandra Deep Field-South (CDF-N and E-CDF-S. respectively; jointly CDFs) survey fields. Our late-type galaxy sample consists of 2568 galaxies. which were identified using rest-frame optical colors and HST morphologies. We utilized X-ray stacking analyses to investigate the X-ray emission from these galaxies, emphasizing the contributions from normal galaxies that are not dominated by active galactic nuclei (AGNs). Over this redshift range, we find significant increases (factors of approx. 5-10) in the X-ray-to-optical mean luminosity ratio (L(sub x)/L(sub B)) and the X-ray-to-stellar-mass mean ratio (L(sub x)/M(sub *)) for galaxy populations selected by L(sub B) and M(sub *), respectively. When analyzing galaxy samples selected via SFR, we find that the mean X-ray-to-SFR ratio (L(sub x)/SFR) is consistent with being constant over the entire redshift range for galaxies with SFR = 1-100 Solar Mass/yr, thus demonstrating that X-ray emission can be used as a robust indicator of star-formation activity out to z approx. 1.4. We find that the star-formation activity (as traced by X-ray luminosity) per unit stellar mass in a given redshift bin increases with decreasing stellar mass over the redshift range z = 0.2-1, which is consistent with previous studies of how star-formation activity depends on stellar mass. Finally, we extend our X-ray analyses to Lyman break galaxies at z approx. 3 and estimate that L(sub x)/L(sub B) at z approx. 3 is similar to its value at z = 1.4.

Lehmer, B.D↗

Association of American Geographers, Remote Sensing Specialty Group Special Issue of Geocarto International

This special issue continues the precedence of the Association of American Geographers (AAG), Remote Sensing Specialty Group (RSSG) for publishing selected articles in Geocarto International as a by-product from the AAG annual meeting. As editors, we issued earlier this year, a solicitation for papers to be published in a special issue of Geocarto International that were presented in RSSG-sponsored sessions at the 2001 AAG annual meeting held in New York City on February 27-March 3. Although not an absolute requisite for publication, the vast majority of the papers in this special issue were presented at this year's AAG meeting in New York. Other articles in this issue that were not part of a paper or poster session at the 2001 AAG meeting are authored by RSSG members. Under the auspices of the RSSG, this special Geocarto International issue provides even more compelling evidence of the inextricable linkage between remote sensing and geography. The papers in this special issue fall into four general themes: 1) Urban Analysis and Techniques for Urban Analysis; 2) Land Use/Land Cover Analysis; 3) Fire Modeling Assessment; and 4) Techniques. The first four papers herein are concerned with the use of remote sensing for analysis of urban areas, and with use or development of techniques to better characterize urban areas using remote sensing data. As the lead paper in this grouping, Rashed et al., examine the usage of spectral mixture analysis (SMA) for analyzing satellite imagery of urban areas as opposed to more 'standard' methods of classification. Here SMA has been applied to IRS-1C satellite multispectral imagery to extract measures that better describe the 'anatomy' of the greater Cairo, Egypt region. Following this paper, Weng and Lo describe how Landsat TM data have been used to monitor land cover types and to estimate biomass parameters within an urban environment. The research reported in this paper applies an integrated GIS (Geographic Information System) approach for detecting urban growth and assessing its impact on biomass in the Zhujiang Delta, China. The remaining two papers in this first grouping deal with improved techniques for characterizing and analyzing urban areas using remote sensing data. Myint examines the use of texture analysis to better classify urban features. Here wavelet analysis has been employed to assist in deriving a more robust classification of the urban environment from high spatial resolution, multispectral aircraft data. Mesev provides insight on how through the modification of the standard maximum likelihood image analysis technique, population census data can be used enhance the overall robustness of urban image classification through the modification of the standard maximum likelihood image analysis technique.

Allen, Thomas R.↗

Exploiting Satellite Remote-Sensing Data in Fine Particulate Matter Characterization for Serving the Environmental Public Health Tracking Network (EPHTN): The HELIX-Atlanta Experience and NPOESS Implications

As part of the U.S. National Environmental Public Health Tracking Network (EPHTN), the National Center for Environmental Health (NCEH) at the U.S. Centers for Disease Control and Prevention (CDC) led a project in collaboration with the National Aeronautics and Space Administration (NASA) Marshall Space Flight Center (MSFC) called Health and Environment Linked for Information Exchange (HELIX-Atlanta). Under HELIX-Atlanta, pilot projects were conducted to develop methods to better characterize exposure; link health and environmental datasets; and analyze spatial/temporal relationships. This paper describes and demonstrates different techniques for surfacing daily environmental hazards data of particulate matter with aerodynamic diameter less than or equal to 2.5 micrometers (PM(sub 2.5) for the purpose of integrating respiratory health and environmental data for the CDC's pilot study of HELIX-Atlanta. It describes a methodology for estimating ground-level continuous PM(sub 2.5) concentrations using spatial surfacing techniques and leveraging NASA Moderate Resolution Imaging Spectrometer (MODIS) data to complement the U.S. Environmental Protection Agency (EPA) ground observation data. The study used measurements of ambient PM(sub 2.5) from the EPA database for the year 2003 as well as PM(sub 2.5) estimates derived from NASA's MODIS data. Hazard data have been processed to derive the surrogate exposure PM(sub 2.5) estimates. The paper has shown that merging MODIS remote sensing data with surface observations of PM(sub 2.5), may provide a more complete daily representation of PM(sub 2.5), than either data set alone would allow, and can reduce the errors in the PM(sub 2.5) estimated surfaces. Future work in this area should focus on combining MODIS column measurements with profile information provided by satellites like the National Polar-orbiting Operational Environmental Satellite System (NPOESS). The Visible Infrared Imager/Radiometer Suite (VIIRS) and the Aerosol Polarimeter Sensor (APS) NPOESS sensors will provide first-order information on aerosol particle size and are anticipated to provide information on aerosol products at higher resolution and accuracy than MODIS. Use of the NPOESS remote sensing data should result in more robust remotely sensed data that can be coupled with the methods discussed in this paper to generate surface concentrations of PM(2.5) for linkage with health data in Environmental Public Health Tracking.

Al-Hamdan, Mohammad Z.↗

Preliminary Design, Testing, and Performance of the LOFTID Navigation System

The Low Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) involves the first orbital test of an inflatable decelerator. This test involves the LOFTID re-entry vehicle using an inflatable decelerator to re-enter the atmosphere after flying to orbit as a secondary payload. Due to system constraints, including spin stabilization, unknown time of day, a limited space available for antennas, and a heat shield which blocks magnetic fields, the navigation system includes only an inertial measurement unit and a single GPS receiver. As the vehicle is turned off for the first part of the mission and will not receive commands or data from the ground, the navigation system will not have accurate initialization, and will in-stead rely on pre-flight estimates or first measurement estimation. This could result in significant unknown error in the initial state, resulting in needing to initialize the state on-orbit and requires using the single GPS antenna for attitude updates. These design considerations led to using an Extended Kalman filter, modified to perform with these design constraints. A streamlined testing approach, including tests with flight-like rotations, is being used to limit the time and resources needed to test the navigation system while still fully testing the performance and robustness of the navigation system. This testing approach follows the NASA test-as-you-fly principle and allows for early detection of errors and changes that are needed in the software. This results in a navigation system that, even within the design constraints of the mission architecture, will provide the performance and robustness needed of the mission.

Joel Amert↗

Digital active control law synthesis for aeroservoelastic systems

This paper presents a formulation for synthesis of digital active control laws for aeroservoelastic systems, which are typically modeled by large order equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics, and gust spectra. The control law is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented by an onboard digital microprocessor. The synthesis procedure minimizes a linear quadratic Gaussian type cost function, by updating selected free parameters of the control law, while satisfying a set of inequality constraints on the design loads, responses and stability margins. A stable classical control law or an estimator based full or reduced order control law can be used as an initial design starting point. The gradients of the cost function and the constraints, with respect to the digital control law design variables are derived analytically, to facilitate rapid convergence. Selected design responses can be treated as constraints instead of lumping them into the cost function, in order to satisfy individual root-mean-square load and response limitations. Constraints are also imposed on the minimum singular value requirements for stability robustness improvement.

Mukhopadhyay, Vivekananda↗