David B. Doman

Nonlinear Longitudinal Dynamical Model of an Air-Breathing Hypersonic Vehicle

A nonlinear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures a number of complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, air-breathing hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, full-scale hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important, as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derivedusingLagrange’sequations.Theequationsof motioncaptureinertial couplingeffectsbetween thepitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are found to be unstableand,inmostcases,exhibitnonminimumphasebehavior.Thelinearizedmodelalsoindicatesthatthereisan aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode, and the short-period mode is very strongly coupled with the bending mode of the fuselage.

Control-Oriented Modeling of an Air-Breathing Hypersonic Vehicle

Full simulation models for flexible air-breathing hypersonic vehicles include intricate couplings between the engine and flight dynamics, along with complex interplay between flexible and rigid modes, resulting in intractable systems for nonlinear control design. In this paper, starting from a high-fidelity model, a control-oriented model in closed form is obtained by replacing complex force and moment functions with curve-fitted approximations, neglecting certain weak couplings, and neglecting slower portions of the system dynamics. The process itself allows an understanding of the system-theoretic properties of the model, and enables the applicability of model-based nonlinear control techniques. Although the focus of this paper is on the development of the control-oriented model, an example of control design based on approximate feedback linearization is provided. Simulation results demonstrate that this technique achieves excellent tracking performance, even in the presence of moderate parameter variations. The fidelity of the truth model is then increased by including additional flexible effects, which render the original control design ineffective. A more elaborate model with an additional actuator is then employed to enhance the control authority of the vehicle, required to compensate for the new flexible effects, and a new design is provided.

Nonlinear Robust Adaptive Control of Flexible Air-Breathing Hypersonic Vehicles

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.

Robust Linear Output Feedback Control of an Airbreathing Hypersonic Vehicle

This paper addresses issues related to robust output-feedback control for a model of an airbreathing hypersonic vehicle. The control objective is to provide robust velocity and altitude tracking in the presence of model uncertainties and varying flight conditions, using only limited state information. A baseline control design based on a robust full-order observer is shown to provide, in nonlinear simulations, insufficient robustness with respect to variations of the vehicle dynamics due to fuel consumption. An alternative approach to robust output-feedback design, which does not employ state estimation, is presented and shown to provide an increased level of performance. The proposed methodology reposes upon robust servomechanism theory and makes use of a novel internal model design. Robust compensation of the unstable zero dynamics of the plant is achieved by using measurements of pitch rate. The selection of the plants output map by sensor placement is an integral part of the control design procedures, accomplished by preserving certain system structures that are favorable for robust control design. The performance of each controller is comparatively evaluated by means of simulations of a full nonlinear model of the vehicle dynamics and is tested on a given range of operating conditions.

A Non-Linear Model for the Longitudinal Dynamics of a Hypersonic Air-breathing Vehicle

Abstract : A non-linear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures the complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derived using Lagranges Equations. The equations-of-motion capture inertial coupling effects between the pitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are shown to be unstable, and in most cases, exhibit non-minimum, phase behavior. The linearized model also indicates that there is an aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode. Furthermore, the short-period mode is very strongly coupled with the bending mode of the fuselage.

Wingbeat Shape Modulation for Flapping-Wing Micro-Air-Vehicle Control During Hover

Abstract : A new method of controlling a flapping-wing micro air vehicle by varying the velocity profiles of the wing strokes is presented in this manuscript. An exhaustive theoretical analysis along with simulation results show that this new method, called split-cycle constantperiod frequency modulation, is capable of providing independent control over vertical and horizontal body forces as well as rolling and yawing moments using only two physical actuators, whose oscillatory motion is defined by four parameters. An actuated bobweight is introduced to enable independent control of pitching moment. A general method for deriving sensitivities of cycle-averaged forces and moments to changes in wingbeat kinematic parameters is provided, followed by an analytical treatment for a case where the angle of attack of each wing is passively regulated and the motion of the wing spar in the stroke plane is driven by a split-cycle waveform. These sensitivities are used in the formulation of a cycle-averaged control law that successfully stabilizes and controls two different simulation models of the aircraft. One simulation model is driven by instantaneous aerodynamic forces derived from bladeelement theory, while the other is driven by an empirical representation of an unsteady aerodynamic model that was derived from experiments.

Integrated Adaptive Guidance and Control for Re-Entry Vehicles with Flight Test Results

To enable autonomous operation of future reusable launch vehicles, reconfiguration technologies will be needed to facilitate mission recovery following a major anomalous event. The Air Force’s Integrated Adaptive Guidance and Control program developed such a system for Boeing’s X-40A, and the total in-flight simulator research aircraft was employed to flight test the algorithms during approach and landing. The inner loop employs a modelfollowing/dynamic-inversion approach with optimal control allocation to account for control-surface failures. Further, the reference-model bandwidth is reduced if the control authority in any one axis is depleted as a result of control effector saturation. A backstepping approach is utilized for the guidance law, with proportional feedback gains that adapt to changes in the reference model bandwidth. The trajectory-reshaping algorithm is known as the optimum-path-to-go methodology. Here, a trajectory database is precomputed off line to cover all variations under consideration. An efficient representation of this database is then interrogated in flight to rapidly find the “best” reshaped trajectory, based on the current state of the vehicle’s control capabilities. The main goal of the flight-test program was to demonstrate the benefits of integrating trajectory reshaping with the essential elements of control reconfiguration and guidance adaptation. The results indicate that for more severe, multiple control failures, control reconfiguration, guidance adaptation, and trajectory reshaping are all needed to recover the mission.

Adaptive Terminal Guidance for Hypervelocity Impact in Specified Direction

The problem of guiding a hypersonic gliding vehicle in the terminal phase to a target location is considered. In addition to the constraints on its final position coordinates, the vehicle must also impact the target from a specified direction with very high precision. The proposed 3-dimensional guidance laws take simple proportional forms. The analysis establishes that with appropriately selected guidance parameters the 3-dimensional guided trajectory will satisfy these impact requirements. We provide the conditions for the initial on-line selection of the guidance law parameters for the given impact direction requirement. The vehicle dynamics are explicitly taken into account in the realization of guidance commands. To ensure high accuracy in the impact angle conditions in an operational environment, we develop closed-loop nonlinear adaptation laws for the guidance parameters. We present the complete guidance logic and associated analysis. Simulation results are provided to demonstrate the effectiveness and accuracy of the proposed terminal guidance approach. I. Introduction Recent interests in developing on-demand global-reach payload delivery capability have brought to the forefront a number of underlying technological challenges. Such operations will involve responsive launch, autonomous entry flight, and precision terminal maneuvers. In certain scenarios the mission requirements call for the payload to impact the target location from a specific direction with supersonic speed. One example is to impact the target in a direction perpendicular to the tangent plane of the terrain at the target. The terminal guidance system will be responsible for directing the vehicle to the target and achieving the desired impact direction. The impact precision requirements under the scenarios considered are very high and stringent. For instance, the required Circular Error Probable (CEP) of the impact distance is just 3-meter. 1 The errors of the impact angles are desired to be within 0.5 deg. The very high speeds throughout the terminal phase only make it considerably more difficult to achieve these levels of precision. Yet cost considerations dictate that the terminal guidance algorithm should be relatively simple and computationally tractable for real-time operations. While a number of guidance methods can guide the vehicle to the target, not many address the unique need for impact from a specific direction. One method that can is the so-called “dive-line” guidance approach in Ref. 2. In this method one or more lines intersecting the Earth are established. The final dive-line intersects the target, and its direction can be set to the desired direction. The vehicle’s velocity vector is

An Aerothermal Flexible Mode Analysis of a Hypersonic Vehicle

Abstract : This paper describes a method for the determination of the flexible modes of an air-breathing hypersonic vehicle. The method outlined here takes into account changes in vehicle mass and structural temperature over the duration of the vehicles trajectory. A simple sizing program is outlined to estimate the vehicle volume, mass, and planform requirements for a dual-cycle (rocket and scramjet) powered vehicle. It is shown that the varying mass effects dominate the frequencies and mode-shapes over the structural heating effects. We then discuss the effects of the structural modes on the transmission zeros.

Reference Command Tracking for a Linearized Model of an Air-Breathing Hypersonic Vehicle

The focus of this paper is on control design and simulation for an air-breathing hypersonic vehicle. The challenges for control design in this class of vehicles lie in the inherent coupling between the propulsion system, and the airframe dynamics, and the presence of strong exibilit y eects. Working from a highly nonlinear, dynamically-coupled simulation model, control designs are presented for velocity, angle-of-attack, and altitude command input tracking for a linearized version of a generic air-breathing hypersonic vehicle model linearized about a specic trim condition. Control inputs for this study include elevator deection, total temperature change across the combustor, and the diuser area ratio. Two control design methods are presented, both using linear quadratic techniques with integral augmentation, and are implemented in tracking control studies. The rst approach focuses on setpoint tracking control, whereas in the second, a regulator design approach is taken. The eectiv eness of each control design is demonstrated in simulation on the full nonlinear model of the generic vehicle.