This paper describes the design of a nonlinear robust adaptive controller for a flexible air-breathing hypersonic vehicle model. Because of the complexity of a first-principle model of the vehicle dynamics, a control-oriented model is adopted for design and stability analysis. This simplified model retains the dominant features of the higher-fidelity model, including the nonminimum phase behavior of the flight-path angle dynamics, the flexibility effects, and the strong coupling between the engine and flight dynamics. A combination of nonlinear sequential loop closure and adaptive dynamic inversion is adopted for the design of a dynamic state-feedback controller that provides stable tracking of the velocity and altitude reference trajectories and imposes a desired set point for the angle of attack. A complete characterization of the internal dynamics of the model is derived for a Lyapunov-based stability analysis of the closed-loop system, which includes the structural dynamics. The proposed methodology addresses the issue of stability robustness with respect to both parametric model uncertainty, which naturally arises when adopting reduced-complexity models for control design, and dynamic perturbations due to the flexible dynamics. Simulation results from the full nonlinear model show the effectiveness of the controller.

Nonlinear Robust Adaptive Control of Flexible Air-Breathing Hypersonic Vehicles

The current air-breathing hypersonic flight (AHF) technology programs focus on development of flight test vehicles and operational vehicle prototypes that utilize airframe-integrated scramjet engines. A key issue in making AHF feasible and efficient is the control design. The non-standard dynamic characteristics of air-breathing hypersonic flight vehicles (AHFVs) together with the aerodynamic effects of hypersonic flight make the system modeling and controller design highly challenging. Moreover the wide range of speed during operation and the lack of a broad flight dynamics database add significant plant parameter variations and uncertainties to the AHF modeling and control problem. In this paper, first, different approaches to this challenging problem presented in the literature are reviewed. Basic dynamic characteristics of AHFVs are described and various mathematical models developed for the flight dynamics of AHFVs are presented. Major nonlinearity and uncertainty sources in the AHF dynamics are explained. The theoretical and practical AHF control designs in the literature, including the control schemes in use at NASA research centers, are examined and compared. The review is supported by a brief history of the scramjet and AHF research in order to give a perspective of the AHF technology. Next, the existing gaps in AHF control and the emerging trends in the air-breathing hypersonic transportation are discussed. Potential control design directions to fill these gaps and meet the trends are addressed. The major problem in AHF control is the handling of the various coupling effects, nonlinearities, uncertainties, and plant parameter variations. As a potential solution, the use of integrated robust (adaptive) nonlinear controllers based on time varying decentralized/triangular models is proposed. This specific approach is motivated by the promise of novel techniques in control theory developed in recent years. ∗This work was supported in parts by Air Force Office of Scientific Research under Grant #F49620-01-1-0489 and by NASA under grant URC Grant #NCC4-158. †Student Member AIAA, graduate student, Electrical Engineering Department. ‡Member AIAA, professor, Mechanical Engineering Department. §Professor, Electrical Engineering Department Nomenclature The following notation is used throughout the paper, unless otherwise stated. a∞ : free stream velocity of sound ĀD : diffuser exit/inlet (area) ratio c : reference length CD : drag coefficient CL : lift coefficient Cm : pitching moment coefficient (pmc) Cm(q) : pmc due to pitch rate Cm(α) : pmc angle of attack Cmα : ∂Cm/∂α Cm(δe): pmc due to δe CT : thrust coefficient fs : stoichiometric ratio for hydrogen, 0.029 h : vehicle altitude I (In) : the (n× n) identity matrix Iyy : vehicle y-axis inertia per unit width m : vehicle mass m : vehicle mass per unit width ṁair : air mass flow rate ṁf : fuel mass flow rate M : pitching moment M∞ : vehicle flight Mach Number nx : acceleration along the vehicle x-axis nz : acceleration along the vehicle z-axis P : pressure q : pitch rate Q : generalized elastic force re : radial distance from Earth’s center Re : radius of the Earth, 20,903,500 ft S : reference area T0 : temperature across the combustor Th : thrust u : speed along the vehicle x-axis V : vehicle velocity X : force along the vehicle x-axis Z : force along the vehicle z-axis α : angle of attack γ : flight path angle (γ = θ − α) δe : pitch control surface deflection δt : throttle setting ∆τ1 : fore-body elastic mode shape ∆τ2 : after-body elastic mode shape ζ1 : damping ratio of the first vibration mode η : generalized elastic coordinate 1 American Institute of Aeronautics and Astronautics 12th AIAA International Space Planes and Hypersonic Systems and Technologies 15 19 December 2003, Norfolk, Virginia AIAA 2003-7081 Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. ηf : fuel equivalence ratio, ṁf fsṁair θ : pitch angle μg : gravitational constant ρ : density of air ω1 : natural frequency of the first vibration mode 0n×m: the n×m zero matrix Subscripts A : due to aerodynamics E : due to external nozzle T : due to engine thrust 0 : trim condition ∞ : free stream condition

Flight Dynamics and Control of Air-Breathing Hypersonic Vehicles: Review and New Directions

Description, capabilities, recent upgrades, and utilization of the NASA Langley Research Center (LaRC) Aerothermodynamic Facilities Complex (AFC) are presented. The AFC consists of five hypersonic, blow-down-to-vacuum wind tunnels that collectively provide a range of Mach number from 6 to 20, unit Reynolds number from 0.04 to 22 million per foot and, most importantly for blunt configurations, normal shock density ratio from 4 to 12. These wide ranges of hypersonic simulation parameters are due, in part, to the use of three different test gases (air, helium, and tetrafluoromethane), thereby making several of the facilities unique. The Complex represents nearly three-fourths of the conventional (as opposed to impulse)-type hypersonic wind tunnels operational in this country. AFC facilities are used to assess and optimize the hypersonic aerodynamic performance and aeroheating characteristics of aerospace vehicle concepts and to provide benchmark aerodynamic/aeroheating data fr generating the flight aerodynamic databook and final design of the thermal protection system (TPS) (e.g., establishment of flight limitations not to exceed TPS design limits). Modifications and enhancements of AFC hardware components and instrumentation have been pursued to increase capability, reliability, and productivity in support of programmatic goals. Examples illustrating facility utilization in recent years to generate essentially all of the experimental hypersonic aerodynamic and aeroheating information for high-priority, fast-paced Agency programs are presented. These programs include Phase I of the Reusable Launch Vehicle (RLV) Advanced Technology Demonstrator, X-33 program, PHase II of the X-33 program, X-34 program, the Hyper-X program ( a Mach 5,7, and 10 airbreathing propulsion flight experiment), and the X-38 program (Experimental Crew Return Vehicle, X-CRV). Current upgrades/enchancements and future plans for the AFC are discussed.

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Langley Aerothermodynamic Facilities Complex: Enhancements and Testing Capabilities

A maneuver design method that is particularly well-suited for determining the stability and control characteristics of hypersonic vehicles is described in detail. Analytical properties of the maneuver design are explained. The importance of these analytical properties for maximizing information content in flight data is discussed, along with practical implementation issues. Results from flight tests of the X-43A hypersonic research vehicle (also called Hyper-X) are used to demonstrate the excellent modeling results obtained using this maneuver design approach. A detailed design procedure for generating the maneuvers is given to allow application to other flight test programs.

Flight-Test Experiment Design for Characterizing Stability and Control of Hypersonic Vehicles

Aerothermodynamic design environments are presented for the Mars Science Laboratory entry capsule heatshield. The design conditions are based on Navier-Stokes flowfield simulations on shallow (maximum total heat load) and steep (maximum heat flux, shear stress, and pressure) entry trajectories from a 2009 launch. Boundary layer transition is expected prior to peak heat flux, a first for Mars entry, and the heatshield environments were defined for a fully-turbulent heat pulse. The effects of distributed surface roughness on turbulent heat flux and shear stress peaks are included using empirical correlations. Additional biases and uncertainties are based on computational model comparisons with experimental data and sensitivity studies. The peak design conditions are 197 W/sq cm for heat flux, 471 Pa for shear stress, 0.371 Earth atm for pressure, and 5477 J/sq cm for total heat load. Time-varying conditions at fixed heatshield locations were generated for thermal protection system analysis and flight instrumentation development. Finally, the aerothermodynamic effects of delaying launch until 2011 are previewed.

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Aerothermodynamic Design of the Mars Science Laboratory Heatshield

This paper provides an overview of the activities associated with the aerodynamic database which is being developed in support of NASA''s Hyper-X scramjet flight experiments. Three flight tests are planned as part of the Hyper-X Program. Each will utilize a small, non-recoverable research vehicle with an airframe integrated scramjet propulsion engine. The research vehicles will be individually rocket boosted to the scramjet engine test points at Mach 7 and Mach 10. The research vehicles will then separate from the first stage booster vehicle and the scramjet engine test will be conducted prior to the terminal decent phase of the flight. An overview is provided of the activities associated with the development of the Hyper-X aerodynamic database, including wind tunnel test activities and parallel CFD analysis efforts for all phases of the Hyper-X flight tests. A brief summary of the Hyper-X research vehicle aerodynamic characteristics is provided, including the direct and indirect effects of the airframe integrated scramjet propulsion system operation on the basic airframe stability and control characteristics. Brief comments on the planned post flight data analysis efforts are also included.

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Aerodynamic Database Development for the Hyper-X Airframe Integrated Scramjet Propulsion Experiments

Postflight analysis of the Mars Pathfinder hypersonic, continuum aerodynamic data base is presented. Measured data include accelerations along the body axis and axis normal directions. Comparisons of preflight simulation and measurements show good agreement. The prediction of two static instabilities associated with movement of the sonic line from the shoulder to the nose and back was confirmed by measured normal accelerations. Reconstruction of atmospheric density during entry has an uncertainty directly proportional to the uncertainty in the predicted axial coefficient. The sensitivity of the moment coefficient to freestream density, kinetic models and center-of-gravity location are examined to provide additional consistency checks of the simulation with flight data. The atmospheric density as derived from axial coefficient and measured axial accelerations falls within the range required for sonic line shift and static stability transition as independently determined from normal accelerations.

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Prediction and Validation of Mars Pathfinder Hypersonic Aerodynamic Data Base

The present study performs a six degree-of-freedom entry dispersion analysis for the Multiple Experiment Transporter to Earth Orbit and Return (METEOR) mission. METEOR offered the capability of flying a recoverable science package in a microgravity environment. However, since the Recovery Module has no active control system, an accurate determination of the splashdown position is difficult because no opportunity exists to remove any errors. Hence, uncertainties in the initial conditions prior to deorbit burn initiation, during deorbit burn and exo-atmosphperic coast phases, and during atmospheric flight impact the splashdown location. This investigation was undertaken to quantify the impact of the various exo-atmospheric and atmospheric uncertainties. Additionally, a Monte-Carlo analysis was performed to statistically assess the splashdown dispersion footprint caused by the multiple mission uncertainties. The Monte-Carlo analysis showed that a 3-sigma splashdown dispersion footprint with axes of 43.3 nm (long), -33.5 nm (short), and 10.0 nm (crossrange) can be constructed. A 58 percent probability exists that the Recovery Module will overshoot the nominal splashdown site.

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Six Degree-of-Freedom Entry Dispersion Analysis for the METEOR Recovery Module

NASA''s Hyper-X Research Vehicle will provide a unique opportunity to obtain data on an operational airframe integrated scramjet propulsion system at true flight conditions. The airframe integrated nature of the scramjet engine with the Hyper-X vehicle results in a strong coupling effect between the propulsion system operation and the airframe''s basic aerodynamic characteristics. Comments on general airframe integrated scramjet propulsion system effects on vehicle aerodynamic performance, stability, and control are provided, followed by examples specific to the Hyper-X research vehicle. An overview is provided of the current activities associated with the development of the Hyper-X aerodynamic database, including wind tunnel test activities and parallel CFD analysis efforts. A brief summary of the Hyper-X aerodynamic characteristics is provided, including the direct and indirect effects of the airframe integrated scramjet propulsion system operation on the basic airframe stability and control characteristics.

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Propulsion System Airframe Integration Issues and Aerodynamic Database Development for the Hyper-X Flight Research Vehicle

Computational fluid dynamics (CFD) tools have been used extensively in the analysis and development of the X-43 Hyper-X Research Vehicle (HXRV). A significant element of this analysis is the prediction of integrated vehicle aero-propulsive performance, which includes an integration of aerodynamic and propulsion flow fields. This paper describes analysis tools used and the methodology for obtaining pre-flight predictions of longitudinal performance increments. The use of higher-fidelity methods to examine flow-field characteristics and scramjet flowpath component performance is also discussed. Limited comparisons with available ground test data are shown to illustrate the approach used to calibrate methods and assess solution accuracy. Inviscid calculations to evaluate lateral-directional stability characteristics are discussed. The methodology behind 3D tip-to-tail calculations is described and the impact of the 3D exhaust plume expansion in the aftbody region is illustrated. Finally, future technology development needs in the area of hypersonic propulsion-airframe integration analysis are discussed.

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C Engelund Walter

Papers

Aerodynamic Database Development for the Hyper-X Airframe Integrated Scramjet Propulsion Experiments

Prediction and Validation of Mars Pathfinder Hypersonic Aerodynamic Data Base

Six Degree-of-Freedom Entry Dispersion Analysis for the METEOR Recovery Module

Propulsion System Airframe Integration Issues and Aerodynamic Database Development for the Hyper-X Flight Research Vehicle

Integrated Aero-Propulsive CFD Methodology for the Hyper-X Flight Experiment