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

WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: (a) a thin boundary layer enveloping the body and dominated by viscous effects, and (b) a motion outside the boundary layer in which viscosity is much less important. It will be remembered that in the external motion occur the large pressure changes, which, transmitted through the boundary layer, account for nearly all the lift and for part of the drag. These pressures we observed to be calculable from the velocities without appreciable error by Bernoulli's equation. In the present Article we confine attention to this external flow, assuming it to be steady, incompressible, and inviscid. Its dependence upon (a), already discussed to some extent, we ignore; the boundary layer is conceived to be everywhere very thin, so that the only role it plays is to allow of relative velocity at the surface of the body. The assumptions made, excepting that of incompressibility, will appear drastic, and it will not be surprising if some of our deductions prove discordant with experimental fact. Nevertheless, they lead to a theory which finds many applications and uses in real fluid motion, and, in particular, gives an intimate view of aerofoil flow that is very close to the truth. It is convenient to develop our reasoning in analytical terms and for simplicity to restrict the flow to two dimensions (Article 1, §5). But the engineer will find special scope in this part of aerodynamics for graphical methods in the solution of particular problems.

Aerodynamics for Engineers

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

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

Review of combustion stabilization for hypersonic airbreathing propulsion

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

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

A computational study was conducted to better understand experimental results obtained from wind tunnel tests of a Mach 4 waverider model and a comparative reference configuration. The experimental results showed that the performance of the reference configuration was slightly better than that of the waverider model. These results con- tradict waverider design theory, which suggests that a waverider optimized for maximum lift-to-drag should provide better performance than any other non-waverider configuration at a given design point, especially at hypersonic speeds. The computational results showed that the predicted surface pressure values and the integrated lift and drag coefficients from the pressure distributions were much lower for the reference model than for the flat-top model, due to the reference model bottom surface having a slight expansion. The lift-to-drag ratios for the flat-top model were higher due to a relatively low drag for the same amount of lift. These results indicate that the performance advantage of the reference model was due to the shape of the bottom surface and not due to the flat top surface. The results also showed that the reference model exhibited the same shock attachment characteristics as the waverider because the planform shapes were identical. CFD predictions show that the planform shape gives the waverider an advantage in performance over conventional hypersonic vehicles and that altering the bottom surface of a waverider does not cause significant performance degradation.

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Interpretation of Waverider Performance Data Using Computational Fluid Dynamics

The component integration of a class of hypersonic high-lift configurations known as waveriders into hypersonic cruise vehicles was evaluated. A wind-tunnel model was developed which integrates realistic vehicle components with two waverider shapes, referred to as the "straight-wing" and "cranked-wing" shapes. Both shapes were conical- flow-derived waveriders for a design Mach number of 4.0. Experimental data and limited computational fluid dynamics (CFD) predictions were obtained over a Mach number range of 1.6 to 4.63 at a Reynolds number of 2.0x106 per foot. The CFD predictions and flow visualization data confirmed the shock attachment characteristics of the baseline waverider shapes and illustrated the waverider flow-field properties. Experimental data showed that no significant performance degradations, in terms of maximum lift-to-drag ratios, occur at off-design Mach numbers for the waverider shapes and the integrated configurations. A comparison of the fully-integrated waverider vehicles to the baseline shapes showed that the performance was significantly degraded when all of the components were added to the waveriders, with the most significant degradation resulting from aftbody closure and the addition of control surfaces. Both fully-integrated configurations were longitudinally unstable over the Mach number range studied with the selected center of gravity location and for unpowered conditions. The cranked-wing configuration provided better lateral-directional stability characteristics than the straight-wing configuration.

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Aerodynamic Performance and Flow-Field Characteristics of Two Waverider-Based Hypersonic Cruise Configurations

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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Jr Charles E. Cockrell

Papers

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

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

Interpretation of Waverider Performance Data Using Computational Fluid Dynamics

Aerodynamic Performance and Flow-Field Characteristics of Two Waverider-Based Hypersonic Cruise Configurations

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