https://www.fossen.biz/home/papers/JohansenFossen%20Automatica%202013.pdf

Control allocation—A survey

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.

Control-Oriented Modeling 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.

Nonlinear Longitudinal Dynamical Model of an Air-Breathing Hypersonic Vehicle

The performanceand computational requirements ofoptimization methodsfor control allocation areevaluated Two control allocation problems are formulated: a direct allocation method that preserves the directionality of the moment and a mixed optimization method that minimizes the error between the desired and the achieved momentsaswellasthecontroleffortTheconstrainedoptimizationproblemsaretransformedinto linearprograms so that they can be solved using well-tried linear programming techniques such as the simplex algorithm A variety of techniques that can be applied for the solution of the control allocation problem in order to accelerate computations are discussed Performance and computational requirements are evaluated using aircraft models with different numbers of actuators and with different properties In addition to the two optimization methods, three algorithms with low computational requirements are also implemented for comparison: a redistributed pseudoinverse technique, a quadratic programming algorithm, and a e xed-point method The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods The performance gains of optimization methods, measured in terms of the error between the desired and achieved moments, are found to be small on the average but sometimes signie cantAvariety ofissuesthataffecttheimplementation ofthevariousalgorithmsin ae ight-controlsystem are discussed

Evaluation of optimization methods for control allocation

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.

Nonlinear Robust Adaptive Control of Flexible Air-Breathing Hypersonic Vehicles

For high Mach number flows, M ≥ 4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional inviscid flow, a perpendicular column of fluid stays intact as it passes over a solid surface. Thus, the pressure at the surface can be calculated assuming the surface were a piston moving into a column of fluid. In this work, first-order piston theory is used to calculate the forces, moments, and stability derivatives for longitudinal motion of a hypersonic vehicle. Piston theory predicts a relationship between the local pressure on a surface and the normal component of fluid velocity produced by the surface’s motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow, oblique shock, or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. Prandtl-Meyer flow and oblique shock theory are utilized to provide flow properties over the surfaces of the vehicle. These flow properties are used to determine the steady forces and moments and are also included in the unsteady flow calculations. Thus, this work utilizes a combination of Prandtl-Meyer flow, oblique shock, and piston theory to calculate forces and moments. The unsteady effects include perturbations in the linear velocities and angular rates, due to rigid body motion. A flexible vehicle model is developed to take into account the aeroelastic behavior of the vehicle. The vehicle forebody and aftbody are modelled as cantilever beams fixed at the center-of-gravity. Piston theory is used to account for the changes in the forces and moments due to the flexing of the vehicle. Piston theory yields an analytical model for the longitudinal motion of the vehicle, thus allowing design trade studies to be performed while still providing insight into the physics of the problem.

A Flexible Hypersonic Vehicle Model Developed with Piston Theory

: 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.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA444973&Location=U2&doc=GetTRDoc.pdf

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

: This paper describes the design of a nonlinear control law for an air-breathing hypersonic vehicle. The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics. To overcome the analytical intractability of this model, a nominal control-oriented model is constructed for the purpose of feedback control design. Analysis performed on the nominal model reveals the presence of unstable zero dynamics with respect to the output to be controlled, namely altitude and velocity. By neglecting certain weaker couplings and resorting to dynamic extension at the input side, a simplified nominal model with full vector relative degree with respect to the regulated output is obtained. Standard dynamic inversion can then be applied to the simplified nominal model, and this results in approximate linearization of the nominal model. Finally, a robust outer loop control is designed using LQR with integral augmentation in a model reference scheme. Simulation results are provided to demonstrate that the approximate feedback linearization approach achieves excellent tracking performance on the truth model for two choices of the system output. Finally, a brief case study is presented to qualitatively demonstrate the robustness of the design to parameter variations.

Approximate Feedback Linearization of an Air-Breathing Hypersonic Vehicle (PREPRINT)

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.

/pdf/robust-nonlinear-sequential-loop-closure-control-design-for-1wy87o5dor.pdf

Michael A. Bolender

Papers

A Flexible Hypersonic Vehicle Model Developed with Piston Theory

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

Approximate Feedback Linearization of an Air-Breathing Hypersonic Vehicle (PREPRINT)

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

Effects of Unsteady and Viscous Aerodynamics on the Dynamics of a Flexible Air-breathing Hypersonic Vehicle