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NASA NTRS1992

Hybrid suboptimal control of multi-rate multi-loop sampled-data systems

A hybrid state-space controller is developed for suboptimal digital control of multirate multiloop multivariable continuous-time systems. First, an LQR is designed for a continuous-time subsystem which has a large bandwidth and is connnected in the inner loop of the overall system. The designed LQR would optimally place the eigenvalues of a closed-loop subsystem in the common region of an open sector bounded by sector angles + or - pi/2k for k = 2 or 3 from the negative real axis and the left-hand side of a vertical line on the negative real axis in the s-plane. Then, the developed continuous-time state-feedback gain is converted into an equivalent fast-rate discrete-time state-feedback gain via a digital redesign technique (Tsai et al. 1989, Shieh et al. 1990) reviewed here. A real state reconstructor is redeveloped utilizing the fast-rate input-output data of the system of interest. The design procedure of multiloop multivariable systems using multirate samplers is shown, and a terminal homing missile system example is used to demonstrate the effectiveness of the proposed method.

Shieh, Leang S.↗

NASA NTRS1988

An adaptive identification and control scheme for large space structures

A unified identification and control scheme capable of achieving space at form performance objectives under nominal or failure conditions is described. Preliminary results are also presented, showing that the methodology offers much promise for effective robust control of large space structures. The control method is a multivariable, adaptive, output predictive controller called Model Predictive Control (MPC). MPC uses a state space model and input reference trajectories of set or tracking points to adaptively generate optimum commands. For a fixed model, MPC processes commands with great efficiency, and is also highly robust. A key feature of MPC is its ability to control either nonminimum phase or open loop unstable systems. As an output controller, MPC does not explicitly require full state feedback, as do most multivariable (e.g., Linear Quadratic) methods. Its features are very useful in LSS operations, as they allow non-collocated actuators and sensors. The identification scheme is based on canonical variate analysis (CVA) of input and output data. The CVA technique is particularly suited for the measurement and identification of structural dynamic processes - that is, unsteady transient or dynamically interacting processes such as between aerodynamics and structural deformation - from short, noisy data. CVA is structured so that the identification can be done in real or near real time, using computationally stable algorithms. Modeling LSS dynamics in 1-g laboratories has always been a major impediment not only to understanding their behavior in orbit, but also to controlling it. In cases where the theoretical model is not confirmed, current methods provide few clues concerning additional dynamical relationships that are not included in the theoretical models. CVA needs no a priori model data, or structure; all statistically significant dynamical states are determined using natural, entropy-based methods. Heretofore, a major limitation in applying adaptive controllers to LSS problems has been the requirement for accurate models. We feel that MPC coupled with the CVA identification scheme will resolve this limitation. The results are based on research performed under an SBIR grant, administered by the Air Force Office of Scientific Research.

Carroll, J. V.↗

NASA NTRS1993

Rotorcraft flying qualities improvement using advanced control

We report on recent experience gained when a multivariable helicopter flight control law was tested on the Large Motion Simulator (LMS) at DRA Bedford. This was part of a study into the application of multivariable control theory to the design of full-authority flight control systems for high-performance helicopters. In this paper, we present some of the results that were obtained during the piloted simulation trial and from subsequent off-line simulation and analysis. The performance provided by the control law led to level 1 handling quality ratings for almost all of the mission task elements assessed, both during the real-time and off-line analysis.

Walker, D.↗

NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗

NASA NTRS1993

On-line evaluation of multiloop digital controller performance

The purpose of this presentation is to inform the Guidance and Control community of capabilities which were developed by the Aeroservoelasticity Branch to evaluate the performance of multivariable control laws, on-line, during wind-tunnel testing. The capabilities are generic enough to be useful for all kinds of on-line analyses involving multivariable control in experimental testing. Consequently, it was decided to present this material at this workshop even though it has been presented elsewhere. Topics covered include: essential on-line analysis requirements; on-line analysis capabilities; on-line analysis software; frequency domain procedures; controller performance evaluation frequency-domain flutter suppression; and plant determination.

Wieseman, Carol D.↗

NASA NTRS1994

Noise and drift analysis of non-equally spaced timing data

Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators is then performed by using a variance (Allan variance, modified Allan variance, or time variance) or a system of several variances (multivariance method). However, in some cases, several samples, or even several sets of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (one minute) and since the timing data sequence is very long (more than ten years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. Different interpolation algorithms (linear interpolation, cubic spline) are used to calculate variances in order to verify that they neither lose information nor add erroneous information. A comparison of the results of the different algorithms is given. Finally, the multivariance method was adapted to the measurement sequence of the millisecond pulsar timing data: the responses of each variance of the system are calculated for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics, and separability of this method is given.

Vernotte, F.↗

NASA NTRS1995

Computerized design of controllers using data models

The major contributions of the grant effort have been the enhancement of the Compensator Improvement Program (CIP), which resulted in the Ohio University CIP (OUCIP) package, and the development of the Model and Data-Oriented Computer Aided Design System (MADCADS). Incorporation of direct z-domain designs into CIP was tested and determined to be numerically ill-conditioned for the type of lightly damped problems for which the development was intended. Therefore, it was decided to pursue the development of z-plane designs in the w-plane, and to make this conversion transparent to the user. The analytical development needed for this feature, as well as that needed for including compensator damping ratios and DC gain specifications, closed loop stability requirements, and closed loop disturbance rejection specifications into OUCIP are all contained in Section 3. OUCIP was successfully tested with several example systems to verify proper operation of existing and new features. The extension of the CIP philosophy and algorithmic approach to handle modern multivariable controller design criteria was implemented and tested. Several new algorithms for implementing the search approach to modern multivariable control system design were developed and tested. This analytical development, most of which was incorporated into the MADCADS software package, is described in Section 4, which also includes results of the application of MADCADS to the MSFC ACES facility and the Hubble Space Telescope.

Irwin, Dennis↗

NASA NTRS1995

A diagnostic analysis of the VVP single-doppler retrieval technique

A diagnostic analysis of the VVP (volume velocity processing) retrieval method is presented, with emphasis on understanding the technique as a linear, multivariate regression. Similarities and differences to the velocity-azimuth display and extended velocity-azimuth display retrieval techniques are discussed, using this framework. Conventional regression diagnostics are then employed to quantitatively determine situations in which the VVP technique is likely to fail. An algorithm for preparation and analysis of a robust VVP retrieval is developed and applied to synthetic and actual datasets with high temporal and spatial resolution. A fundamental (but quantifiable) limitation to some forms of VVP analysis is inadequate sampling dispersion in the n space of the multivariate regression, manifest as a collinearity between the basis functions of some fitted parameters. Such collinearity may be present either in the definition of these basis functions or in their realization in a given sampling configuration. This nonorthogonality may cause numerical instability, variance inflation (decrease in robustness), and increased sensitivity to bias from neglected wind components. It is shown that these effects prevent the application of VVP to small azimuthal sectors of data. The behavior of the VVP regression is further diagnosed over a wide range of sampling constraints, and reasonable sector limits are established.

Boccippio, Dennis J.↗

NASA NTRS1995

Chemical studies of H chondrites. 6: Antarctic/non-Antarctic compositional differences revisited

We report data for the trace elements Au, Co, Sb, Ga, Rb, Ag, Se, Cs, Te, Zn, Cd, Bi, T1, and In (ordered by putative volatility during nebular condensation and accretion) determined by radiochemical neutron activation analysis of 14 additional H5 and H6 chondrite falls. Data for the 10 most volatile elements (Rb to In) treated by the multivariate techniques of linear discriminant analysis and logistic regression in these and 44 other falls are compared with those of 59 H4-6 chondrites from Antarctica. Various populations are tested by the multivariate techniques, using the previously developed method of randomization-simulation to assess significance levels. An earlier conclusion, based on fewer examples, that H4-6 chondrite falls are compositionally distinguishable from the Antarctic suite is verified by the additional data. This distinctiveness is highly significant because of the presence of samples from Victoria Land in the Antarctic population, which differ compositionally from falls beyond any reasonable doubt. However, it cannot be proven unequivocally that falls and Antarctic samples from Queen Maud Land are compositionally distinguishable. Trivial causes (e.g., analyst bias, weathering) cannot explain the Victoria Land (Antarctic)/non-Antarctic compositional difference for paradigmatic H4-6 chondrites. This seems to reflect a time-dependent variation of near-Earth meteoroid source regions differing in average thermal history.

Wolf, Stephen F.↗

NASA NTRS1995

Cooperative control theory and integrated flight and propulsion control

The major contribution of this research was the exposition of the fact that airframe and engine interactions could be present, and their effects could include loss of stability and performance of the control systems. Also, the significance of two directional, as opposed to one-directional, coupling was identified and explained. A multivariable stability and performance analysis methodology was developed, and applied to several candidate aircraft configurations. In these example evaluations, the significance of these interactions was underscored. Also exposed was the fact that with interactions present along with some integrated control approaches, the engine command/limiting logic (which represents an important nonlinear component of the engine control system) can impact closed-loop airframe/engine system stability. Finally, a brief investigation of control-law synthesis techniques appropriate for the class of systems was pursued, and it was determined that multivariable techniques, including model-following formulations of LQG and/or H infinity methods, showed promise. However, for practical reasons, decentralized control architectures are preferred, which is an architecture incompatible with these synthesis methods. The major contributions of the second phase of the grant was the development of conditions under which no decentralized controller could achieve closed loop system requirements on stability and/or performance. Sought were conditions that depended only on properties of the plant and the requirement, and independent of any particular control law or synthesis approach. Therefore, they could be applied a priori, before synthesis of a candidate control law. Under this grant, such conditions were found regarding stability, and encouraging initial results were obtained regarding performance.

Schmidt, David K.↗

NASA NTRS1996

Balanced Placement Of Vibration Sensors And Actuators

Mathematical approach that involves Hankel singular values leads to method for estimation of optimal placement of relatively few vibration sensors and actuators in multivariable flexible structure. Approach extends and complements previous developments regarding approximate decomposition, to Hankel singular values, of singular values of controllability and observability grammian matrices of multivariable flexible structure. Mathematical constructs also described in "Designing An Approximately Balanced LQG Compensator" (NPO-19000).

Gawronski, Wodek↗

NASA NTRS1994

Empirical Modeling of Plant Gas Fluxes in Controlled Environments

As humans extend their reach beyond the earth, bioregenerative life support systems must replace the resupply and physical/chemical systems now used. The Controlled Ecological Life Support System (CELSS) will utilize plants to recycle the carbon dioxide (CO2) and excrement produced by humans and return oxygen (O2), purified water and food. CELSS design requires knowledge of gas flux levels for net photosynthesis (PS(sub n)), dark respiration (R(sub d)) and evapotranspiration (ET). Full season gas flux data regarding these processes for wheat (Triticum aestivum), soybean (Glycine max) and rice (Oryza sativa) from published sources were used to develop empirical models. Univariate models relating crop age (days after planting) and gas flux were fit by simple regression. Models are either high order (5th to 8th) or more complex polynomials whose curves describe crop development characteristics. The models provide good estimates of gas flux maxima, but are of limited utility. To broaden the applicability, data were transformed to dimensionless or correlation formats and, again, fit by regression. Polynomials, similar to those in the initial effort, were selected as the most appropriate models. These models indicate that, within a cultivar, gas flux patterns appear remarkably similar prior to maximum flux, but exhibit considerable variation beyond this point. This suggests that more broadly applicable models of plant gas flux are feasible, but univariate models defining gas flux as a function of crop age are too simplistic. Multivariate models using CO2 and crop age were fit for PS(sub n), and R(sub d) by multiple regression. In each case, the selected model is a subset of a full third order model with all possible interactions. These models are improvements over the univariate models because they incorporate more than the single factor, crop age, as the primary variable governing gas flux. They are still limited, however, by their reliance on the other environmental conditions under which the original data were collected. Three-dimensional plots representing the response surface of each model are included. Suitability of using empirical models to generate engineering design estimates is discussed. Recommendations for the use of more complex multivariate models to increase versatility are included.

Cornett, Jessie David↗

NASA NTRS1997

Areal Distribution of the Oxygen-Isotope Ratio in Greenland

Mean values of the oxygen-isotope ratio relative to standard mean ocean water reported for 46 sites on the Greenland ice sheet are compiled together with data on mean annual surface temperature, latitude, 6180 elevation, and mean annual shortest distance to the open ocean denoted by the 10% sea-ice concentration boundary. Stepwise regression analyses, with 6180 as the dependent variable, define two robust models. In the forward mode at the 99.9% confidence level, only temperature enters the model. In the backward mode at the 95% confidence level, only temperature, latitude, and distance to the open ocean remain in the model. Inversions of the models on the basis of 160 gridpoint locations 100 km apart in the area delimited by the surface equilibrium line produce four contoured distributions of 6"0. Two distributions are based on the bivariate model and two on the multivariate model. The second distribution for each model is obtained substituting mean annual surface-temperature values obtained from the Nimbus-7 Temperature Humidity Infrared Radiometer (THIR) database. All four distributions are considered valid, and differences between them are evaluated using contoured anomaly maps. It is suggested that the inversion of the multivariate model using THIR data provides the more reliable pattern for studies of atmospheric advection or for the derivation of ice-flow adjustments for 6180 series obtained from deep-core or ablation-zone sites.

Zwally, H. Jay↗

NASA NTRS2001

Robust Nonlinear Feedback Control of Aircraft Propulsion Systems

This is the final report on the research performed under NASA Glen grant NASA/NAG-3-1975 concerning feedback control of the Pratt & Whitney (PW) STF 952, a twin spool, mixed flow, after burning turbofan engine. The research focussed on the design of linear and gain-scheduled, multivariable inner-loop controllers for the PW turbofan engine using H-infinity and linear, parameter-varying (LPV) control techniques. The nonlinear turbofan engine simulation was provided by PW within the NASA Rocket Engine Transient Simulator (ROCETS) simulation software environment. ROCETS was used to generate linearized models of the turbofan engine for control design and analysis as well as the simulation environment to evaluate the performance and robustness of the controllers. Comparison between the H-infinity, and LPV controllers are made with the baseline multivariable controller and developed by Pratt & Whitney engineers included in the ROCETS simulation. Simulation results indicate that H-infinity and LPV techniques effectively achieve desired response characteristics with minimal cross coupling between commanded values and are very robust to unmodeled dynamics and sensor noise.

Garrard, William L.↗

NASA NTRS2002

Using Clustering to Establish Climate Regimes from PCM Output

A multivariate statistical clustering technique--based on the k-means algorithm of Hartigan has been used to extract patterns of climatological significance from 200 years of general circulation model (GCM) output. Originally developed and implemented on a Beowulf-style parallel computer constructed by Hoffman and Hargrove from surplus commodity desktop PCs, the high performance parallel clustering algorithm was previously applied to the derivation of ecoregions from map stacks of 9 and 25 geophysical conditions or variables for the conterminous U.S. at a resolution of 1 sq km. Now applied both across space and through time, the clustering technique yields temporally-varying climate regimes predicted by transient runs of the Parallel Climate Model (PCM). Using a business-as-usual (BAU) scenario and clustering four fields of significance to the global water cycle (surface temperature, precipitation, soil moisture, and snow depth) from 1871 through 2098, the authors' analysis shows an increase in spatial area occupied by the cluster or climate regime which typifies desert regions (i.e., an increase in desertification) and a decrease in the spatial area occupied by the climate regime typifying winter-time high latitude perma-frost regions. The patterns of cluster changes have been analyzed to understand the predicted variability in the water cycle on global and continental scales. In addition, representative climate regimes were determined by taking three 10-year averages of the fields 100 years apart for northern hemisphere winter (December, January, and February) and summer (June, July, and August). The result is global maps of typical seasonal climate regimes for 100 years in the past, for the present, and for 100 years into the future. Using three-dimensional data or phase space representations of these climate regimes (i.e., the cluster centroids), the authors demonstrate the portion of this phase space occupied by the land surface at all points in space and time. Any single spot on the globe will exist in one of these climate regimes at any single point in time. By incrementing time, that same spot will trace out a trajectory or orbit between and among these climate regimes (or atmospheric states) in phase (or state) space. When a geographic region enters a state it never previously visited, a climatic change is said to have occurred. Tracing out the entire trajectory of a single spot on the globe yields a 'manifold' in state space representing the shape of its predicted climate occupancy. This sort of analysis enables a researcher to more easily grasp the multivariate behavior of the climate system.

Oglesby, Robert↗

NASA NTRS1997

Anterior segment sparing to reduce charged particle radiotherapy complications in uveal melanoma

PURPOSE: The purpose of this investigation is to delineate the risk factors in the development of neovascular glaucoma (NVG) after helium-ion irradiation of uveal melanoma patients and to propose treatment technique that may reduce this risk. METHODS AND MATERIALS: 347 uveal melanoma patients were treated with helium-ions using a single-port treatment technique. Using univariate and multivariate statistics, the NVG complication rate was analyzed according to the percent of anterior chamber in the radiation field, tumor size, tumor location, sex, age, dose, and other risk factors. Several University of California San Francisco-Lawrence Berkeley National Laboratory (LBNL) patients in each size category (medium, large, and extralarge) were retrospectively replanned using two ports instead of a single port. By using appropriate polar and azimuthal gaze angles or by treating patients with two ports, the maximum dose to the anterior segment of the eye can often be reduced. Although a larger volume of anterior chamber may receive a lower dose by using two ports than a single port treatment. We hypothesize that this could reduce the level of complications that result from the irradiation of the anterior chamber of the eye. Dose-volume histograms were calculated for the lens, and compared for the single and two-port techniques. RESULTS: NVG developed in 121 (35%) patients. The risk of NVG peaked between 1 and 2.5 years posttreatment. By univariate and multivariate analysis, the percent of lens in the field was strongly correlated with the development of NVG. Other contributing factors were tumor height, history of diabetes, and vitreous hemorrhage. Dose-volume histogram analysis of single-port vs. two-port techniques demonstrate that for some patients in the medium and large category tumor groups, a significant decrease in dose to the structures in the anterior segment of the eye could have been achieved with the use of two ports. CONCLUSION: The development of NVG after helium-ion irradiation is correlated to the amount of lens, anterior chamber in the treatment field, tumor height, proximity to the fovea, history of diabetes, and the development of vitreous hemorrhage. Although the influence of the higher LET deposition of helium-ions is unclear, this study suggests that by reducing the dose to the anterior segment of the eye may reduce the NVG complications. Based on this retrospective analysis of LBNL patients, we have implemented techniques to reduce the amount of the anterior segment receiving a high dose in our new series of patients treated with protons using the cyclotron at the UC Davis Crocker Nuclear Laboratory (CNL).

NASA Discipline Radiation Health↗

NASA NTRS2005

Pre-biotic stage of life origin under non-photosynthetic conditions

Spontaneous assembling of a simplest bacterial cell even if all necessary molecules are present in a solution seems to be extremely rare event and from the scientific standpoint has to be considered as impossible. Therefore, a predecessor of a living cell has to be very simple for providing its self-assembling and at the same time it should be able of progressive increase in complexity. Now phase-separated particles, first of all micelles, are put forward as possible predecessors of living cell. According to the offered working concept only phase-separated particles possessing autocatalytic properties can be considered as predecessors of living cells. The first stage of evolution of these phase-separated autocatalytic systems is the appearance of pre-biotic metabolism providing synthesis of amphiphiles for formation of capsules of these systems. This synthesis is maintained by the energy of a base reaction being a component of a planet-chemical cycle. Catalytic system providing functioning of pre-biotic metabolism is based on multivariate oligomeric autocatalyst, which reproduces itself from monomers, penetrating the particles from the outside. Since the autocatalyst realizes random polymerization then a collection of other oligomers possessing different catalytic functions is produced. In the paper the functioning of multivariate oligomeric autocatalyst in flow reactor is analyzed. c2005 Published by Elsevier Ltd on behalf of COSPAR.

Biogenesis↗

NASA NTRS2010

Prediction Activities at NASA's Global Modeling and Assimilation Office

The Global Modeling and Assimilation Office (GMAO) is a core NASA resource for the development and use of satellite observations through the integrating tools of models and assimilation systems. Global ocean, atmosphere and land surface models are developed as components of assimilation and forecast systems that are used for addressing the weather and climate research questions identified in NASA's science mission. In fact, the GMAO is actively engaged in addressing one of NASA's science mission s key questions concerning how well transient climate variations can be understood and predicted. At weather time scales the GMAO is developing ultra-high resolution global climate models capable of resolving high impact weather systems such as hurricanes. The ability to resolve the detailed characteristics of weather systems within a global framework greatly facilitates addressing fundamental questions concerning the link between weather and climate variability. At sub-seasonal time scales, the GMAO is engaged in research and development to improve the use of land information (especially soil moisture), and in the improved representation and initialization of various sub-seasonal atmospheric variability (such as the MJO) that evolves on time scales longer than weather and involves exchanges with both the land and ocean The GMAO has a long history of development for advancing the seasonal-to-interannual (S-I) prediction problem using an older version of the coupled atmosphere-ocean general circulation model (AOGCM). This includes the development of an Ensemble Kalman Filter (EnKF) to facilitate the multivariate assimilation of ocean surface altimetry, and an EnKF developed for the highly inhomogeneous nature of the errors in land surface models, as well as the multivariate assimilation needed to take advantage of surface soil moisture and snow observations. The importance of decadal variability, especially that associated with long-term droughts is well recognized by the climate community. An improved understanding of the nature of decadal variability and its predictability has important implications for efforts to assess the impacts of global change in the coming decades. In fact, the GMAO has taken on the challenge of carrying out experimental decadal predictions in support of the IPCC AR5 effort.

Schubert, Siegfried↗