Control of Aerothermoelastic Effects in Hypersonic Vehicles

1. Introduction

 Aeroservoelasticity considers the interaction between aerodynamics, inertial, structural, actuation, and control system dynamics. Flight controllers are usually designed for a rigid-body model and any aeroservoelastic issues are eliminated by including notch filters to eliminate observability of structural modes. This approach may not be acceptable for future aircraft that have lightweight and flexible components with low natural frequencies. Thus, modeling and control of both rigid-body and structural dynamics must be used. Structural dynamics has been extensively studied for modeling and control at transonic and high dynamic pressure regimes for limited applications such as flutter and buffet suppression; however, there are several aircraft that must consider aeroservoelastic dynamics within a standard flight envelope. The first-bending mode of the SR-71 fuselage has a natural frequency near 3 Hz that is easily excited by pilot maneuvers. Several uninhabited aerial vehicles such as Theseus and APEX with lightweight and high aspect-ratio wings have several structural modes less than 2 Hz that affect flight characteristics. Also, the proposed high-speed civil transport anticipates a fuselage bending mode near 1.5 Hz that must be actively controlled to attain acceptable ride quality.
 Modeling and control of aeroservoelasticity must also be considered for a proposed class of hypersonic aerospacecraft. These vehicles are being investigated for economic competitiveness of access to space missions such as payload delivery to low Earth orbit, reconnaissance, and cruise flight. The main aeroservoelastic feature is a coupling between the wedge-shape body and an air-breathing propulsion system that causes aerodynamic, inertial, structural, control, and even thermal dynamics to interact.

 Aeropropulsive and aeroelastic models and associated controllers were extensively developed for several models that generally describe the proposed aerospacecraft. The strong interactions between the coupled dynamics of these models present many challenges for control design to achieve acceptable closed-loop properties. These interactions are a direct result of the scramjet engine which essentially uses the fuselage as part of the propulsion system. Thus, the aerodynamics and elastic dynamics can affect and respond to the propulsive dynamics. Several control synthesis methodologies have been considered for hypersonic models including classical control, H-infinity, mu, and a linear parameter-varying approach.

 The effects of aerothermoelasticity were studied for a hypersonic vehicle known as the National AeroSpace Plane (NASP) and shown to significantly affect the open-loop dynamics; however, these effects were generally not considered for controller synthesis. A computational analysis was performed to show a large range of surface temperatures that can be reached during a typical ascent profile. Correspondingly, the structural dynamics show large variations in modal parameters and mode shapes as a result from temperature-induced stiffness changes.

 An explicit model-following approach is used for the control design such that the closed-loop dynamics approximate a desired model. This desired model is chosen as a highly-damped structural mode with a natural frequency near the open-loop structural frequency for the cold model. Specifically, the desired dynamics have natural frequency of 2.6 Hz and damping of 0.23. The open-loop transfer functions of the hot and cold plant models and the desired actively damped structural dynamics are shown in the figure.

 The dynamics used for control synthesis are a single-input and single-output subset of the full open-loop model. The only measurement from the physical plant used for feedback is the angle of attack because this variable is strongly dependent on the elastic response and it provides sufficient information for control design. Also, the only control effector commanded from the inner-loop controller is the elevator deflection. The control surface is chosen because the bandwidth should be high enough to control the structural modes whereas it is doubtful the engine effectors can be effective. A linear parameter-varying controller is synthesized for the inner-loop model. This controller is originally formulated with 27 states; however, reduced-order controllers may be derived using standard model reduction methods.

 The angle of attack measurements in response to a command elevator deflection are shown in the figure to the right. The open-loop response clearly shows a large oscillatory component because the deflection excites the low damped structural mode. The closed-loop response does not show this oscillatory component because the controller actively damps the structural mode and thus the elevator deflection does not strongly excite structural motion. Also, this response is computed along a parameter-varying trajectory with temperatures ranging from cold to hot in 10 seconds. This trajectory is unrealistically fast; however, it shows the response is damped over the wide range of temperatures with arbitrarily fast time variation.

 5. Outer-Loop Controller An outer-loop controller is designed to stabilize the vehicle and achieve desired handling qualities for maneuvering. This controller is the flight mechanics controller that is commonly designed for aircraft that do not require active structural damping. A robust design approach is chosen to compute the outer-loop gains and account for modeling errors of the rigid-body dynamics and performance errors of the inner-loop controller. This controller would ideally be gain scheduled over flight conditions such as Mach and dynamic pressure;however, the model was not sufficiently complex to account for a range of flight conditions. Thus, mu-synthesis is used to design the controller at a single-point flight condition. A Mach regulation loop is included with the outer-loop dynamics to track commands to the Mach variable. The feedback law for this loop is chosen based on classical design arguments and is realized as a simple proportional controller. The commands from the regulator are changes to the fuel flow rate only because a preliminary study indicated this variable is convenient for Mach regulation. The change in fuel flow is simply the difference between the measured and desired Mach numbers. The outer-loop controller is allowed to use all control effectors which are the elevator surface, the engine diffuser area ratio, and the engine fuel flow ratio; however, only the elevator surface is used. The engine fuel flow ratio is not commanded by the outer-loop controller because the Mach regulation commands this variable. The diffuser area ratio is not used because it is not clear that such a parameter of a physical engine would have an appreciable bandwidth without an unreasonable time delay. Also, all sensors are available as feedback measurements to the controller. The model used for control design of the outer-loop gains includes some knowledge of the inner-loop dynamics. Some methods of multi-loop control design, such as robust dynamic inversion~\cite{reiner}, replace the actual inner-loop dynamics with the desired inner-loop dynamics so the synthesis model has linear elements; however, this approach may not be suitable here. The problem arises mainly because the rigid-body instability. The inner-loop design was formulated without explicit knowledge of this instability because the LPV synthesis algorithm would automatically try to stabilize the closed-loop system but the inner-loop controller was not supposed to affect the rigid-body dynamics. Thus, the effects of the inner-loop controller on the rigid-body instability are not known so the outer-loop design must consider the true unstable inner-loop system. A representative model of the linear parameter-varying inner-loop dynamics must be chosen for outer-loop synthesis model. The $\mu$-synthesis approach used for control design requires the model to have linear time-invariant dynamics with no parameter-varying dependencies so the gain-scheduled nature of the inner-loop dynamics must be ignored. The model chosen for outer-loop synthesis is computed by isolating the dynamics for the parameter representing the extreme hot temperature. This model is chosen because it is essentially a worst-case model in the sense that the inner-loop controller provides less active damping at hot temperatures than at cold temperatures.

 The figure on the right demonstrates the Mach number measured in response to a commanded filtered-step increase in Mach. The response is slightly faster than the commanded increase but the outer-loop dynamics track the command reasonably well. This response demonstrates the Mach regulation loop coupled with the outer-loop controller provides acceptable tracking.

 The measured angle of attack is also computed in response to the step increase in Mach and presented on the right. The magnitude of the angle of attack is relatively small and indicates the outer-loop controller is able to limit the effects of the Mach command. Also, the outer-loop and inner-loop controllers can simultaneously generate commands for the elevator deflection to achieve rigid-body performance and active damp the structural dynamics.

6. Information

• Project Team
 - Kristin Fitzpatrick graduate student University of Florida - MAE Department - Rick Lind assistant professor University of Florida - MAE Department
• Publications
 - R. Lind, Linear Parameter-Varying Modeling and Control of Structural Dynamics with Aerothermoelastic Effects,'' Journal of Guidance, Control, and Dynamics, Vol. 25, No. 2, July-August 2002, pp. 733-739. - R. Lind, Linear Parameter-Varying Modeling and Control of Structural Dynamics with Aerothermoelastic Effects,'' AIAA Structures, Structural Dynamics, and Materials Conference, St. Louis, MO, AIAA-99-1393, April 1999. - R. Lind, J.L. Buffington, and A.K. Sparks, Multi-Loop Aeroservoelastic Control of a Hypersonic Vehicle,'' AIAA Guidance, Navigation, and Control Conference, Portland, OR, AIAA-99-4123, August 1999.