Retrospective‐cost‐based model reference adaptive control of nonminimum‐phase systems
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Nima Mohseni↗
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On the Robustness Properties of M-MRAC
The paper presents performance and robustness analysis of the modified reference model MRAC (model reference adaptive control) or M-MRAC in short, which differs from the conventional MRAC systems by feeding back the tracking error to the reference model. The tracking error feedback gain in concert with the adaptation rate provides an additional capability to regulate not only the transient performance of the tracking error, but also the transient performance of the control signal. This differs from the conventional MRAC systems, in which we have only the adaptation rate as a tool to regulate just the transient performance of the tracking error. It is shown that the selection of the feedback gain and the adaptation rate resolves the tradeoff between the robustness and performance in the sense that the increase in the feedback gain improves the behavior of the adaptive control signal, hence improves the systems robustness to time delays (or unmodeled dynamics), while increasing the adaptation rate improves the tracking performance or systems robustness to parametric uncertainties and external disturbances.
Stepanyan, Vahram↗
Projection-Based Inter-Agent Collision Avoidance in Dual Agent Systems
Inter-agent collisions can occur in otherwise dynamically-stable (i.e., Lyapunov stable) dual-agent leaderfollower systems. These inter-agent collisions between the leader and the follower happen during the transient phase of the system’s evolution, although the steady-state behavior of the system is asymptotically/exponentially stable. Therefore, to avoid such inter-agent collisions, it is essential to control the relative error trajectory between the leader and the follower during the transient phase of the system’s evolution. In this paper, we introduce a novel projection operator based modelreference control architecture that can mitigate impending inter-agent collisions by modifying the transient dynamics of relative trajectories. This controller augments the follower’s baseline controller and consists of two essential components: a collision-free reference model based on the projection operator and a model reference tracking controller to guide the follower to follow the reference-model. This paper defines the concept of transient-instability in leader-follower systems, introduces collision mitigation controller architecture, and presents an illustrative example demonstrating its effectiveness.
Bayard, David S.↗
The NASA MSFC Earth Global Reference Atmospheric Model-2007 Version
Reference or standard atmospheric models have long been used for design and mission planning of various aerospace systems. The NASA/Marshall Space Flight Center (MSFC) Global Reference Atmospheric Model (GRAM) was developed in response to the need for a design reference atmosphere that provides complete global geographical variability, and complete altitude coverage (surface to orbital altitudes) as well as complete seasonal and monthly variability of the thermodynamic variables and wind components. A unique feature of GRAM is that, addition to providing the geographical, height, and monthly variation of the mean atmospheric state, it includes the ability to simulate spatial and temporal perturbations in these atmospheric parameters (e.g. fluctuations due to turbulence and other atmospheric perturbation phenomena). A summary comparing GRAM features to characteristics and features of other reference or standard atmospheric models, can be found Guide to Reference and Standard Atmosphere Models. The original GRAM has undergone a series of improvements over the years with recent additions and changes. The software program is called Earth-GRAM2007 to distinguish it from similar programs for other bodies (e.g. Mars, Venus, Neptune, and Titan). However, in order to make this Technical Memorandum (TM) more readable, the software will be referred to simply as GRAM07 or GRAM unless additional clarity is needed. Section 1 provides an overview of the basic features of GRAM07 including the newly added features. Section 2 provides a more detailed description of GRAM07 and how the model output generated. Section 3 presents sample results. Appendices A and B describe the Global Upper Air Climatic Atlas (GUACA) data and the Global Gridded Air Statistics (GGUAS) database. Appendix C provides instructions for compiling and running GRAM07. Appendix D gives a description of the required NAMELIST format input. Appendix E gives sample output. Appendix F provides a list of available parameters to enable the user to generate special output. Appendix G gives an example and guidance on incorporating GRAM07 as a subroutine in other programs such as trajectory codes or orbital propagation routines.
Leslie, F.W.↗
The NASA Marshall Space Flight Center Earth Global Reference Atmospheric Model-2010 Version
Reference or standard atmospheric models have long been used for design and mission planning of various aerospace systems. The NASA Marshall Space Flight Center Global Reference Atmospheric Model was developed in response to the need for a design reference atmosphere that provides complete global geographical variability and complete altitude coverage (surface to orbital altitudes), as well as complete seasonal and monthly variability of the thermodynamic variables and wind components. In addition to providing the geographical, height, and monthly variation of the mean atmospheric state, it includes the ability to simulate spatial and temporal perturbations.
Leslie, F. W.↗
The global reference atmospheric model, mod 2 (with two scale perturbation model)
The Global Reference Atmospheric Model was improved to produce more realistic simulations of vertical profiles of atmospheric parameters. A revised two scale random perturbation model using perturbation magnitudes which are adjusted to conform to constraints imposed by the perfect gas law and the hydrostatic condition is described. The two scale perturbation model produces appropriately correlated (horizontally and vertically) small scale and large scale perturbations. These stochastically simulated perturbations are representative of the magnitudes and wavelengths of perturbations produced by tides and planetary scale waves (large scale) and turbulence and gravity waves (small scale). Other new features of the model are: (1) a second order geostrophic wind relation for use at low latitudes which does not "blow up" at low latitudes as the ordinary geostrophic relation does; and (2) revised quasi-biennial amplitudes and phases and revised stationary perturbations, based on data through 1972.
Justus, C. G.↗
Improvements in the perturbation simulations of the global reference atmospheric model
The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs.
Justus, C. G.↗
Venus Global Reference Atmospheric Model
Venus Global Reference Atmospheric Model (Venus-GRAM) is an engineering-level atmospheric model developed by MSFC that is widely used for diverse mission applications including: Systems design; Performance analysis; Operations planning for aerobraking, Entry, Descent and Landing, and aerocapture; Is not a forecast model; Outputs include density, temperature, pressure, wind components, and chemical composition; Provides dispersions of thermodynamic parameters, winds, and density; Optional trajectory and auxiliary profile input files Has been used in multiple studies and proposals including NASA Engineering and Safety Center (NESC) Autonomous Aerobraking and various Discovery proposals; Released in 2005; Available at: https://software.nasa.gov/software/MFS-32314-1.
Justh, Hilary L.↗
Interpretation of waverider performance data using computational fluid dynamics
A computational study was conducted to better understand experimental results obtained from wind-tunnel tests of a Mach 4 conical-flow-derived waverider and a comparative reference configuration, which showed that the aerodynamic performance of the reference configuration was slightly better than that of the waverider. The computational results showed that the predicted surface pressure values and the integrated lift and drag coefficients were much lower for the reference model because the reference model bottom is an expansion surface. However, the lift-drag ratios for the reference model were higher due to a relatively low drag for a comparable amount of lift. The results also showed that the reference model exhibited the same shock attachment characteristics as the conical-flow-derived waverider, and is therefore also a waverider. The shock attachment characteristic gives the waverider a performance advantage over conventional hypersonic vehicles, and the results suggest that altering the bottom surface does not cause significant performance degradation. Flowfield solutions also show that the conical-flow waverider model has better propulsion/airframe integration characteristics than the reference configuration. The results also suggest that generating flowfields other than conical ones may be used to design waveriders with improved aerodynamic performance.
COMPUTATIONAL FLUID DYNAMICS↗
Planned Improvements to the Venus Global Reference Atmospheric Model
The Venus Global Reference Atmospheric Model (Venus-GRAM) is an engineering-level atmospheric model applicable for engineering design analyses, mission planning, and operational decision making. Missions to Venus have generated a wealth of atmospheric data, however, Venus-GRAM has not been updated since its development and release in 2005. GRAM upgrades and maintenance have depended on inconsistent and waning project-specific support. The NASA Science Mission Directorate (SMD) has agreed to provide funding support in Fiscal Year 2018 and 2019 to upgrade the GRAMs. This presentation will provide an overview of Venus-GRAM and the objectives, tasks, and milestones related to the GRAM upgrades.
Justh, H. L.↗
Improvements in the Global Reference Atmospheric Model and comparisons with a global 3-D numerical model
The status of the Global Reference Atmospheric Model (GRAM) and the Mars Global Reference Atmospheric Model (MARS-GRAM) is reviewed. The wavelike perturbations observed in the Viking 1 and 2 surface pressure data, in the Mariner 9 IR spectroscopy data, and in the Viking 1 and 2 lander entry profiles were studied and the results interpreted.
Justus, C. G.↗
Upgrades to the Mars Global Reference Atmospheric Model (Mars-GRAM)
The inability to test planetary spacecraft in the flight environment prior to a mission requires engineers to rely on ground-based testing and models of the vehicle and expected environments. One of the most widely used engineering reference models of planetary atmospheres are the Global Reference Atmospheric Models (GRAMs). The NASA Science Mission Directorate (SMD) has provided funding support to upgrade the GRAMs since Fiscal Year 2018. The GRAM upgrades are being developed by NASA Marshall Space Flight Center and NASA Langley Research Center. This poster provides details regarding recent MarsGRAM upgrades.
atmospheric models↗
Global Reference Atmospheric Model and Trace Constituents
Global Reference Atmospheric Model (GRAM-99) is an engineering-level model of the Earth's atmosphere. It provides both mean values and perturbations for density, temperature, pressure, and winds, as well as monthly- and geographically-varying trace constituent concentrations. From 0-27 km, thermodynamics and winds are based on National Oceanic and Atmospheric Administration Global Upper Air Climatic Atlas (GUACA) climatology. Above 120 km, GRAM is based on the NASA Marshall Engineering Thermosphere (MET) model. In the intervening altitude region, GRAM is based on Middle Atmosphere Program (MAP) climatology that also forms the basis of the 1986 COSPAR Intemationa1 Reference Atmosphere (CIRA). MAP data in GRAM are augmented by a specially-derived longitude variation climatology. Atmospheric composition is represented in GRAM by concentrations of both major and minor species. Above 120 km, MET provides concentration values for N2, O2, Ar, O, He, and H. Below 120 km, species represented also include H2O, O3, N2O, CO, CH, and CO2. Water vapor in GRAM is based on a combination of GUACA, Air Force Geophysics Laboratory (AFGL), and NASA Langley Research Center climatologies. Other constituents below 120 km are based on a combination of AFGL and h4AP/CIRA climatologies. This report presents results of comparisons between GRAM Constituent concentrations and those provided by the Naval Research Laboratory (NRL) climatology of Summers (NRL,/MR/7641-93-7416, 1993). GRAM and NRL concentrations were compared for seven species (CH4, CO, CO2, H2O, N2O, O2, and O3) for months January, April, July, and October, over height range 0-115 km, and latitudes -90deg to + 90deg at 10deg increments. Average GRAM-NRL correlations range from 0.878 (for CO) to 0.975 (for O3), with an average over all seven species of 0.936 (standard deviation 0.049).
Justus, C.↗
The NASA/MSFC global reference atmospheric model: MOD 3 (with spherical harmonic wind model)
Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.
Justus, C. G.↗
Four-Dimensional Global Reference-Atmosphere Model
Four-Dimensional Global Reference Atmosphere Model (GRAM) computer program developed from empirical atmospheric model generating values for pressure, density, temperature, and winds, from ground to orbital altitudes. Is amalgamation of two empirical atmospheric models for low and high atmosphere with newly-developed latitude-and longitude-dependent model for middle atmosphere. UNIVAC version written in UNIVAC FORTRAN. DEC VAX version of GRAM written in FORTRAN 77. Applications include simulation of reentry trajectories of external tanks, studies of global circulation and diffusion and generation of plots or data for comparison.
Johnson, Dale↗
Extensive middle atmosphere (20-120 KM) modification in the Global Reference Atmospheric Model (GRAM-90)
The Global Reference Atmospheric Model (GRAM) is currently available in the 'GRAM-88' version (Justus, et al., 1986; 1988), which includes relatively minor upgrades and changes from the 'MOD-3' version (Justus, et al., 1980). Currently a project is underway to use large amounts of data, mostly collected under the Middle Atmosphere Program (MAP) to produce a major upgrade of the program planned for release as the GRAM-90 version. The new data and program revisions will particularly affect the 25-90 km height range. Sources of data and preliminary results are described here in the form of cross-sectional plots.
Justus, C. G.↗
Middle atmosphere trace constituents; Proceedings of Workshop 9 of the Twenty-sixth COSPAR Plenary Meeting, Toulouse, France, June 30-July 11, 1986
Papers are presented on a reference model for stratospheric NO2, a proposed reference model for nitric acid, proposed reference models for ozone, and a background stratospheric aerosol reference model. Other topics include a comparison between the observed and calculated distributions of trace species in the middle atmosphere, recent measurements of trace constituents from rocket and balloon probes, NO2 field observations in the stratosphere during the MAP/GLOBUS Campaign in 1983 and 1985, and the vertical distribution of ozone in the equatorial zone. Also considered are precision measurements of stratospheric ozone profiles by rocket-borne optical ozonesondes, vertical profiles of source gases at tropical latitudes, and measurements of stratospheric trace constituent distributions from balloon-borne far infrared observations.
Keating, G. M.↗
Outer Planet Global Reference Atmospheric Model (GRAM) Upgrades
Introduction: The Global Reference Atmospheric Model (GRAM) is one of the most widely used engineering models of planetary atmospheres. The GRAM upgrades are being developed by NASA Marshall Space Flight Center and NASA Langley Research Center. This presentation will provide details regarding the upgrades to the existing GRAMs, the development of new GRAMs, and the ongoing objectives, tasks, and milestones related to the GRAM upgrades funded by the NASA Science Mission Directorate (SMD). GRAM: The GRAMs are engineering-oriented atmospheric models that estimate mean values and statistical variations of the atmospheric properties for numerous planetary destinations. They provide mean values and variability for any point in the atmosphere as well as seasonal, geographic, and altitude variations. GRAM outputs include atmospheric density, temperature, pressure, winds, and chemical composition along a user-defined path. They are extensively used by the engineering community because of their ability to create realistic dispersions. GRAMs have been integrated into high fidelity flight dynamic simulations of launch, entry, descent and landing (EDL), aerobraking and aerocapture. GRAMs are currently available for Earth, Mars, Venus, Neptune, Titan, and Uranus. Outer Planet GRAM Upgrade Status: Code Modernization. The outer planet GRAMs have been rearchitected from Fortran to a common object-oriented C++ framework called the GRAM Suite. This new architecture creates a common GRAM library of data models and utilities. The first C++ releases of the rearchitected legacy outer planet GRAMs (Neptune and Titan-GRAM) are straight conversions from the latest Fortran version. Model Upgrades. The focus of the model upgrade task is to improve the atmosphere models in the existing GRAMs and to establish a foundation for developing GRAMs for additional destinations. The GRAM ephemeris has been upgraded to the NASA Navigation and Ancillary Information Facility (NAIF) SPICE toolkit (version N0066). The calculation of the speed of sound has also been improved in the GRAMs. In FY20, the GRAM project established a contract with Hampton University to develop empirical global models for Jupiter, Saturn, Uranus, Neptune, and Titan. Upgraded Outer Planet GRAM Releases. GRAM Suite Version 1.0 was released in May 2020 and contains the rearchitected Neptune-GRAM, including the common GRAM framework and planet–specific code. GRAM Suite Version 1.1 was released in September 2020 and added the rearchitected Titan-GRAM to the GRAM Suite. A User Guide and Programmer’s Manual are released with all GRAMs. New Outer Planet GRAM Releases. New GRAMs have been developed for Uranus and Jupiter. Uranus-GRAM is based on the NASA Ames Research Center (ARC) Uranus Atmospheric Model [1,2] and was released in GRAM Suite Version 1.2 in July 2021. Jupiter-GRAM is based on Galileo probe Atmospheric Structure Instrument (ASI) data from Seiff et al. [3] Saturn-GRAM is also under development. Both Jupiter and Saturn-GRAM will be released in future versions of the GRAM Suite. Conclusions: GRAMs are vital and frequently used toolsets. Releases of the GRAM Suite, upgrades of the existing planetary GRAMs, and development of new planetary GRAMs are ongoing. Titan-GRAM atmosphere model upgrades will be included in the next phase of GRAM tasks. References: [1] Allen Jr., G.A. et al. (2014) 11th International Planetary Probe Workshop, Abstract #8023. [2] Allen Jr., G.A. et al. (2014) Workshop on the Study of the Ice Giant Planets, Abstract #2001. [3] Seiff, A. et al. (1998) JGR, 103, 22,857 -22,889. Acknowledgments: The authors gratefully acknowledge support from the NASA SMD.
atmospheric models↗