Srikanth Sridharan

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.

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.

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.

Performance Based Control-Relevant Design for Scramjet-Powered Hypersonic Vehicles

In this paper we consider limits of achievable performance for a class of scramjet-powered hypersonic aircraft. A simple 3-DOF model is used to illustrate the main ideas. The vehicle is characterized by unstable and non-minimum phase dynamics. The limitations introduced by the right-half plane zero and actuator saturation on achievable trajectories has been examined. In addition, we examine several vehicle configurations and consider fundamental limitations for the plant and closed loop performance. An optimization methodology that explicitly incorporates performance specifications into the design of vehicle is explored. The advantages of such an approach is illustrated with examples.

Integrated design and control of hypersonic vehicles

In this paper we consider the design and control of an airbreathing hypersonic vehicle. Such vehicles are characterized by non-minimum phase characteristics, instability, actuator saturation constraints, and lightly damped flexible modes. While traditional vehicle design has followed an iterative sequential procedure (with the controller design following an aero-centric vehicle design phase), an integrated vehicle-control design process (based on bilinear matrix inequalities) is considered in this paper. We consider several example problems to illustrate the advantages of such an approach.

A receding horizon control approach to portfolio optimization using a risk-minimax objective for wealth tracking

In this paper, we consider the problem of financial portfolio optimization. A hierarchical framework is used, and receding horizon control (RHC) ideas are exploited to pose and solve two relevant constrained optimization problems. We first present the classic problem of wealth maximization subject to risk constraints. We also formulate a new approach to portfolio optimization which attempts to minimize the peak risk over the prediction horizon, while trying to track a wealth objective. This approach is designed to assist investors that might be unable to precisely specify their risk tolerance. We compare this methodology with the classical approach. It is concluded that this approach may be particularly beneficial during downturns — appreciably limiting losses during downturns while providing most of the upturn benefits.

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.

Constraint enforcement and robust tube-based control for scramjet-powered hypersonic vehicles with significant uncertainties

This paper examines the issues involved in controlling an air-breathing hypersonic vehicle (characterized by their unstable, non-minimum phase dynamics) in the presence of significant modeling uncertainty and nonlinearities (control saturations). Modeling of the vehicle exhaust (plume) is complicated, often requiring computational fluid dynamic (CFD) simulations to capture all relevant effects. The focus of this paper is on obtaining a control law that maintains the vehicle trajectory within an acceptable tube while enforcing control constraints in the presence of modeling uncertainty. A robust domain of attraction based approach is used to generate/validate a feasible tube. The computational aspects of such an approach is examined, and the benefits of a decentralized control technique is considered. This approach is compared with other techniques such as linear matrix inequalities based controller design. These approaches are applied to a command following scenario in order to illustrate the performance of the proposed approach.