Jeffrey J. Dickeson

Modeling and Control of Scramjet-Powered Hypersonic Vehicles: Challenges, Trends, & Tradeoffs

In this paper, we provide an overview of scramjet-powered hypersonic vehicle modeling and control challenges. Such vehicles are characterized by unstable non-minimum phase dynamics with significant coupling and low thrust or FER (normalized fuel equivalency ratio) margins. Recent trends in hypersonic vehicle research is summarized. To illustrate control system design issues and tradeoffs, a generic nonlinear 3DOF longitudinal dynamics model capturing aero-elastic-propulsive interactions for wedge-shaped vehicle is used. The model is analyzed over a broad range of hypersonic flight conditions (i.e. operating points). The paper highlights how vehicle level-flight static (trim) and dynamic properties change over the trimmable air-breathing corridor (∼ Mach 4.75-12.6, 70-115 kft). Particular attention is paid to thermal choking constraints imposed on control system design as a direct consequence of having a finite FER margin. The dependence of FER margin on altitude, Mach, and the bow flow turning angle is discussed. The latter depends on Mach, altitude, angle-of-attack (AOA), and forebody flexing. It is (briefly) discussed how FER margin can be estimated on the basis of Mach, altitude, and AOA if a flexing upper bound is assumed. The implication of this state-dependent nonlinear FER margin constraint as well as that of the right half plane (RHP) zero, associated with the elevator-flight path angle (FPA) map, on control system bandwidth (BW) and FPA tracking are discussed. It is argued that while the non-minimum phase zero limits the achievable closed loop FPA BW, FER coupling into FPA can be used to address this. This, however, is limited by FER margin limits and may impose constraints on the size of the FPA (and velocity) commands that can be followed. This is particularly important because the vehicle is inherently unstable which implies a closed loop system (with a finite downward gain margin) that can become destabilized if driven sufficiently deep into control saturation. A consequence of this is that designers must take note of the fact that FPA commands which are sufficiently large and/or rapid may be impossible to follow with the desired level of fidelity. This is quantified within the paper. Speed command following issues are also discussed.

Constraint enforcement for scramjet-powered hypersonic vehicles with significant aero-elastic-propulsion interactions

In this paper, we examine the control of a scramjet-powered hypersonic vehicle with significant aero-elastic-propulsion interactions. Such vehicles are characterized by open loop unstable non-minimum phase dynamics, low frequency aero-elastic modes, significant coupling, and hard constraints (e.g. control surface deflection limits, thrust margin). Within this paper, attention is placed on maintaining acceptable closed loop performance (i.e. tracking of speed and flight path angle commands) while satisfying hard control surface deflection constraints as well as stoichiometrically normalized fuel-equivalency-ratio (FER) margin constraints. Control surface constraints are a consequence of maximum permissible aerodynamic loading. FER margin constraints are a consequence of thermal choking (i.e. unity combustor exit Mach number) and the fact that thrust loss may not be captured for FER greater than unity. Such limits are particularly important since the vehicle is open loop unstable and “saturation” can result in instability. To address these issues, one can design conservative (i.e. less aggressive or lower bandwidth) controllers that maintain operation below saturation levels for anticipated reference commands (and disturbances). Doing so, however, unnecessarily sacrifices performance - particularly when small reference commands are issued. Within this paper, the above issues are addressed using generalized predictive control (GPC). A 3DOF longitudinal model for a generic hypersonic vehicle, which includes aero-elastic-propulsion interactions, is used to illustrate the ideas.

Robust LPV H Gain-Scheduled Hover-to-Cruise Conversion for a Tilt-Wing Rotorcraft in the Presence of CG Variations

This paper describes the development and analysis of gain-scheduled, multi-variable Hinfin control law for the conversion of a linear parameter varying (LPV) model of a high-speed autonomous rotorcraft vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing aircraft combine the high-speed cruise capabilities of a conventional airplane with the vertical takeoff and station keeping abilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An Hinfin design methodology was used to develop linear controllers along various operating points of a conversion trajectory. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. Performance robustness with respect to variation in the location of the center of gravity (eg) has been studied.

Decentralized Control of an Airbreathing Scramjet-Powered Hypersonic Vehicle

In this paper, an overview is provided of control efforts implemented using the scramjetpowered hypersonic vehicle model developed by Bolender, Doman, et.al. (2005-2009). The nonlinear model is characterized by unstable non-minimum phase dynamics with aeroelastic-propulsion coupling and nonlinear propulsion constraints. The viability of simple inner-outer loop single-input single-output (SISO) control structures is examined and quantified. Reference command and control amplitude and bandwidth tradeoffs are addressed. A simple (non-scheduled ) inner-outer loop control law is shown to yield excellent tracking of a constant (q = 2076 psf) dynamic pressure guidance command profile from Mach 5.7 to Mach 12. Robustness, gain scheduling as well as multivariable control issues are also addressed.

Control-relevant modeling, analysis, and design for scramjet-powered hypersonic vehicles

Within this paper, control-relevant vehicle design concepts are examined using a widely used 3 DOF (plus flexibility) nonlinear model for the longitudinal dynamics of a generic carrot-shaped scramjet powered hypersonic vehicle. Trade studies associated with vehicle/engine parameters are examined. The impact of parameters on control-relevant static properties (e.g. level-flight trimmable region, trim controls, AOA, thrust margin) and dynamic properties (e.g. instability and right half plane zero associated with flight path angle) are examined. Specific parameters considered include: inlet height, diffuser area ratio, lower forebody compression ramp inclination angle, engine location, center of gravity, and mass. Vehicle optimizations is also examined. Both static and dynamic considerations are addressed. The gap-metric optimized vehicle is obtained to illustrate how this controlcentric concept can be used to “reduce” scheduling requirements for the final control system. A classic inner-outer loop control architecture and methodology is used to shed light on how specific vehicle/engine design parameter selections impact control system design. In short, the work represents an important first step toward revealing fundamental tradeoffs and systematically treating control-relevant vehicle design.

Robust LPV H ∞ gain-scheduled hover-to-cruise conversion for a tilt-wing rotorcraft in the presence of CG variations

This paper describes the development and analysis of gain-scheduled, multi-variable Hinfin control law for the conversion of a linear parameter varying (LPV) model of a high-speed autonomous rotorcraft vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing aircraft combine the high-speed cruise capabilities of a conventional airplane with the vertical takeoff and station keeping abilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An Hinfin design methodology was used to develop linear controllers along various operating points of a conversion trajectory. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. Performance robustness with respect to variation in the location of the center of gravity (eg) has been studied.

Elevator Sizing, Placement, and Control-Relevant Tradeoffs for Hypersonic Vehicles

Within this paper, control-relevant vehicle design concepts are examined using a widely used 3 DOF (plus flexibility) nonlinear model for the longitudinal dynamics of a generic carrot-shaped scramjet powered hypersonic vehicle. The impact of elevator size and placement on control-relevant static properties (e.g. level-flight trimmable region, trim controls, Angle of Attack (AOA), thrust margin) and dynamic properties (e.g. instability and right half plane zero associated with flight path angle) are examined. Elevator usage has been examine for a class of typical hypersonic trajectories.

Impact of Plume Modeling on the Design and Control for a Class of Air-Breathing Hypersonic Vehicles

This paper examines control-relevant modeling issues for a class of scramjet-powered hypersonic vehicles. A simple nonlinear 3DOF model is used to illustrate the main ideas. Two different plume modeling methodologies from previous literature are compared to a newly developed methodology. The impact of the modeling method on vehicle design has been examined. Nominal control design robustness issues are also addressed.

H ∞ Hover-to-Cruise Conversion for a Tilt-Wing Rotorcraft

This paper describes the development of robust, multi-variable H∞ control systems for the conversion of the High-Speed Autonomous Rotorcraft Vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing rotorcraft combine the high-speed cruise capabilities of a conventional airplane with the hovering capabilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An H∞design methodology was used to develop cruise and hover control systems because it directly addresses multi-variable and robust design issues. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The cruise and hover control designs form the basis for the conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. A tilt-wing rotorcraft Modeling, Simulation, Animation, and Real-Time Control (MoSART) software environment provides 3D visualization of the vehicle’s dynamics. The environment is useful for conceptualizing the natural rotorcraft dynamics and for gaining an intuitive understanding of the closed-loop system performance.

H ∞ mixed-sensitivity optimization for distributed parameter plants subject to convex constraints

This paper focuses on Hinfin near-optimal finite- dimensional compensator design for linear time invariant (LTI) distributed parameter plants subject to convex constraints. The distributed parameter plant is first approximated by a finite dimensional approximant. For unstable plants, the coprime factors are approximated by their finite dimensional approximants. The Youla parameterization is then used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity Hinfin optimization that is convex in the Youla Q-parameter. A finite-dimensional (real- rational) stable basis is used to approximate the Q-parameter. By so doing, the associated infinite-dimensional optimization problem is transformed to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity Hinfin control system design problems, subgradient concepts are used to directly accommodate time-domain specifications (e.g. peak value of control action, overshoot) in the design process. As such, a systematic design methodology is provided for a large class of distributed parameter plant control system design problems. Convergence results are presented. An illustrative examples for a hypersonic vehicle is provided. In short, the approach taken permits a designer to address control system design problems for which no direct method exists.