Michael A. Bolender

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.

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.

Control Allocation for Over-actuated Systems

Much emphasis has been placed on over-actuated systems for air vehicles. Over-actuating an air vehicle provides a certain amount of redundancy for the flight control system, thus potentially allowing for recovery from off-nominal conditions. Due to this redundancy, control allocation algorithms are typically utilized to compute a unique solution to the over-actuated problem. Control allocators compute the commands that are applied to the actuators so that a certain set of forces or moments are generated by the control effectors. Usually, control allocation problems are formulated as optimization problems so that all of the available degrees of freedom can be utilized and, when sufficient control power exists, secondary objectives can be achieved. In this work, a survey of control allocation techniques is given

Robust nonlinear sequential loop closure control design for an air-breathing hypersonic vehicle model

This paper describes the design of a nonlinear robust/adaptive controller for an air-breathing hypersonic vehicle model. Due to its complexity, a high fidelity model of the vehicle dynamics derived from first principles is used only in simulations, while a simplified model is adopted for control design. This control-oriented model retains most of the features of the high fidelity model, including non-minimum phase characteristic of the flight-path angle dynamics and strong couplings between the engine and flight dynamics, whereas flexibility effects are regarded as a dynamic perturbation. A nonlinear sequential loop-closure approach is adopted to design a dynamic state-feedback controller that provides stable tracking of velocity and altitude reference trajectories and allows to impose a desired trim value for the angle of attack. Simulation results show that the proposed methodology achieves excellent tracking performances in spite of parameter uncertainties.

Anti-Windup Control for an Air-Breathing Hypersonic Vehicle Model

Abstract : An anti-windup controller modification is implemented in control system design for a model of the longitudinal dynamics of an air-breathing hypersonic vehicle. Anti-windup control allows the input constraints to be considered explicitly in the design of linear controllers to track a reference trajectory for the vehicle velocity, altitude, and angle of attack. The presence of anti-windup alleviates the need of keeping large penalties on the magnitude of the control input to avoid the occurrence of saturation. This, in turn, allows tighter tuning of the controller gains to obtain faster and more accurate trajectory tracking. The paper employs recent developments in anti-windup design to deal with the presence of exponentially unstable dynamics, which are typically encountered in air-breathing vehicle models. Simulation results on a fully nonlinear model are presented to validate the controller design.