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The purpose of this paper is to design a robust angle-of-attack (AOA) tracking control system for the hypersonic reentry vehicle (HRV) based on the linear parameter varying (LPV) theory, as the aerodynamic coefficients of the hypersonic vehicle vary quickly during the reentry phase.

First, longitudinal moment trim is done along the desired flight trajectory. The linearized system at each trim point is built and the dynamic characteristics analysis is made. Then the LPV control law with parameter-dependent quadratic Lyapunov function (PDQLF-LPV) is applied to design the AOA tracking autopilot at each trim point. Frequency performance of the autopilot is assessed and the step response simulation is conducted to validate the effectiveness of the control system. Finally, actual AOA command tracking simulations based on the time-varying nonlinear model are carried out to test the correctness and robustness of the PDQLF-LPV autopilot.

Analysis results demonstrate that the PDQLF-LPV control system can track the AOA command perfectly during the whole flight envelop with dynamics parameter variation or disturbances, which indicates that it is effective to integrate the PDQLF-LPV control theory with a parameter-varying reference model for control system design of HRV.

A reference model with varying parameters is utilized to guarantee the transient performance of the autopilot, and induced L2-norm analysis is introduced to describe and guarantee the robust stability of the autopilot.

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

The aim of this study is to design a guidance method to generate a smoother and feasible gliding reentry trajectory, a highly constrained problem by formalizing the control variables profile.

A novel accelerated fractional-order particle swarm optimization (FAPSO) method is proposed for velocity updates to design the guidance method for gliding reentry flight vehicles with fixed final energy.

By using the common aero vehicle as a test case for the simulation purpose, it is found that during the initial phase of the longitudinal guidance, there are oscillations in the state parameters which cause to violate the path constraints. For the glide phase of the longitudinal guidance, the path constraints have higher values because of the increase in the atmosphere density.

The violation in the path constraints may compromise the flight vehicle safety, whereas the enforcement assures the flight safety by flying it within the reentry corridor.

An oscillation suppression scheme is proposed by using the FAPSO method during the initial phase of the reentry flight, which smooths the trajectory and enforces the path constraints partially. To enforce the path constraints strictly in the glide phase, ultimately, another scheme by using the FAPSO method is proposed. The simulation results show that the proposed algorithm is efficient to achieve better convergence and accuracy for nominal as well as dispersed conditions.

The purpose of the paper is to study the variation of optimal burnout angle at the end of the ascent phase and the optimal control deflection during the glide phase, that would maximize the downrange performance of a hypersonic boost-glide waverider, with variation in heat rate and integrated heat load limit.

The approach used is to model the boost phase so as to optimize the burnout conditions. The nonlinear, multiphase, constraint optimal control problem is solved using an hp-adaptive pseudospectral method.

The constraint heat load results for the waverider configuration reveal that the integrated heat load can be reduced by more than half with only 10 per cent penalty in the overall downrange of the hypersonic boost-glide vehicle, within a burnout speed range of 3.7 to 4.3 km/s. The angle-of-attack trim control requirements increase with stringent heat rate and integrated heat load bounds. The normal acceleration remains within limits.

The trajectory results imply lower thermal protection system weight because of reduced heat load trajectory profile and therefore lower thermal protection system cost.

The research provides further study on the trajectory design to the hypersonic boost-glide vehicles for medium range application.

The purpose of this paper is the optimal design of a reentry vehicle configuration to minimize the mission cost which is equal to minimize the heat absorbed (thermal protection system mass) and structural mass and to maximize the drag coefficient (trajectory errors and minimum final velocity).

There are two optimization approaches for solving this problem: multiobjective optimization (lead to Pareto optimal solutions); and single‐objective optimization (lead to one optimal solution). Single‐objective genetic algorithms (GA) and multiobjective Genetic Algorithms (MOGA) are employed for optimization. In second approach, if there are n objectives (n+1) GA run is needed to find nearest point (optimum point), which leads to increase the time processing. Thus, a modified GA called single run GA (SRGA) is presented as third approach to avoid increasing design time. It means if there are n objectives, just one GA run is enough.

Two multi module function – Ackley and bump function – are selected for examination the third approach. Results of MOGA, GA and SRGA are presented which show SRGA approach can find the nearest point in much shorter time with acceptable accuracy.

GA, MOGA and SRGA approaches are applied to multidisciplinary design optimization of a reentry vehicle configuration and results show the efficiency of SRGA in complex design optimization problem.

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

The purpose of this paper is to present a non‐equilibrium viscous shock layer (VSL) solution procedure that considerably improves computational efficiency, especially for long slender bodies.

The VSL equations are solved in a shock oriented coordinate system. The method of solution is spatial marching, implicit, finite‐difference technique, which includes coupling of the normal momentum and continuity equations. In the nose region, the shock shape is specified from an algebraic expression and corrected through global passes through that region. The shock shape is computed as part of the solution beyond the nose region and requires only a single global pass. For this study, a seven‐species (O₂, N₂, O, N, NO, NO⁺, e⁻) air model is used.

The present approach eliminates the need for initial shock shape, which was required by previous method of solution. This method generates its own shock shape as a part of solution and the input shock shape obtained from a different solution is not required. Therefore, in comparison with the other VSL methods, the present approach dramatically reduces the CPU time of calculations. Moreover, by using the shock oriented coordinate systems the junction point problem in sphere‐cone configurations is solved.

This method is an excellent tool for parametric study and preliminary design of hypersonic vehicles.

The present method provides a computational capability which reduces the CPU time, and expands the range of application for the prediction of hypersonic heating rates.

The purpose of this paper is to design a disturbance observer-based finite-time global sliding mode control scheme for the attitude tracking control problem of the reentry vehicle with parameter uncertainties and disturbances.

Feedback linearization is first introduced to transform vehicle model into three independent second order uncertain subsystems. Then a finite-time controller (FTC) is proposed for the nominal system on the basis of the homogeneity theory. Thereafter the integral sliding mode method is introduced for the vehicle with disturbances. The finite time convergence is achieved and global robustness is also assured by the combination of finite time control method and integral sliding mode strategy. Furthermore, to improve the attitude angle tracking accuracy a novel finite time disturbance observer (DO) is constructed.

Simulation is made for the reentry vehicle with disturbances involved. And the results show the finite-time convergence, tracking accuracy and robustness of the proposed strategy.

The proposed control strategy has three advantages. First of all it can achieve finite time convergence and avoid singularity. Moreover, it can also realize global robustness. Finally, a new kind of DO is introduced to improve the tracking accuracy.

The purpose of this paper is to design a global robust and continuous control scheme for the attitude tracking control problem of the reentry vehicle with parameter uncertainties and disturbances.

First, feedback linearization is applied to the model of reentry vehicle, resulting in three independent uncertain subsystems. Then a new second-order time-varying sliding function is proposed, based on which a continuous second-order time-varying sliding mode control (SOTVSMC) law is proposed for each subsystem. The global robustness and convergence performance of the closed-loop reentry vehicle control system under the proposed control law are proved.

Simulation is made for a reentry vehicle through the assumption that there is external disturbance to aerodynamic moment and the aerodynamic parameters as well as the atmospheric density are perturbed. The results verify the validity and robustness of the proposed strategy.

The SOTVSMC attitude controller based on feedback linearization is proposed for the reentry vehicle. The advantages of the proposed SOTVSMC are twofold. First, the global second order sliding mode is established, which implies that the closed-loop system is global robust against matched parameter uncertainties and disturbances in reentry. Second, the chattering problem is significantly alleviated.