Flight Path Angle Research Articles

Assessment of a small UAV speed polar graph by conducting flight tests

Purpose The purpose of this paper is to present an approach to a polar graph measurement by a flight testing technique and to propose a baseline research method for future tests of UAV polar graphs. The method presented can be used to demonstrate a conceptual and preliminary design process using a scaled, unmanned configuration. This shows how results of experimental flight tests using a scaled flying airframe may be described and analysed before manufacturing the full scale aircraft. Design/methodology/approach During the research, the flight tests were conducted for two aerodynamic configurations of a small UAV. This allowed the investigation of the influence of winglets and classic vertical stabilizers on the platform stability, performance and therefore polar graphs of a small unmanned aircraft. Findings A methodology of flight tests for the assessment of a small UAV’s polar graph has been proposed, performed and assessed. Two aerodynamic configurations were tested, and it was found that directional stability had a large influence on the UAV’s performance. A correlation between the speed and inclination of the altitude graph was found – i.e. the higher the flight speed, the steeper the altitude graph (higher descent speed, steeper flight path angle). This could be considered as a basic verification that the recorded data have a physical sense. Practical implications The polar graph and therefore glide ratio of the aircraft is a major factor for determining its performance and power required for flight. Using the right flight test procedure can speed-up the process of measuring glide ratio, making it easier, faster, robust, more effective and accurate in future research of novel, especially unorthodox configurations. This paper also can be useful for the proper selection of requirements and preliminary design parameters for making the design process more economically effective. Originality/value This paper presents a very efficient method of assessing the design parameters of UAVs, especially the polar graph, in an early stage of the design process. Aircraft designers and producers have been widely performing flight testing for years. However, these procedures and practical customs are usually not wide spread and very often are treated as the company’s “know how”. Results presented in this paper are original, relatively easily be repeated and checked. They may be used either by professionals, highly motivated individuals and representatives of small companies or also by ambitious amateurs.

Integrated Guidance and Control of Multiple Interceptor Missiles Based on Improved Distributed Cooperative Control Strategy

In this study, an improved cooperative integrated guidance and control (IGC) design method is proposed based on distributed networks to address the guidance and control problem of multiple interceptor missiles. An IGC model for a leading interceptor is constructed based on the relative kinematic relations between missiles and a target and the kinematic equations of the missiles in a pitch channel. The unknown disturbances of the model are estimated using a finite-time disturbance observer (FTDO). Then, the control algorithm for the leading interceptor is designed according to the disturbance estimation and nonsingular fast dynamic surface sliding mode control (SMC). To enhance the rate of convergence of the cooperative control commands for the interceptors, an improved cooperative control strategy is proposed based on the leader-follower distributed network. Consequently, the two velocity components of the interceptor in the pitch channel can be obtained, which are subsequently converted to the total velocity and flight path angle commands of the interceptor using kinematic relations. The control algorithm for the following interceptor is similarly designed using an FTDO and dynamic surface SMC. The effectiveness of the improved distributed cooperative control strategy for multiple interceptors is validated through simulations.

Shape Optimization of Reentry Vehicles to Minimize Heat Loading

The objective of the current study is to design an optimum reentry vehicle shape that minimizes heat loading subject to constraints on the maximum values of surface heat flux and temperature. A new heat loading formulation is developed for objective function evaluations. Axisymmetric Navier–Stokes and finite-rate chemical reaction equations are solved to evaluate the objective and constraint functions. The Menter SST turbulence model is employed for turbulence closure. A gradient-based method is used for optimization. The sensitivities of the objective and constraint functions are evaluated using the finite-difference method. In shape optimization, the geometry change or the geometry itself is parameterized using different numbers of nonuniform rational basis spline (NURBS) or Bezier curves. Designs are performed at different trajectory points of the IRV-2 vehicle. The effects of flight path angle and reentry velocity on the heat transfer and trajectory characteristics of the original and designed geometries are quantified.

Analysis of control programs and climb paths of the hypersonic first stage of an aerospace system

Control programs and flight paths of the hypersonic first stage of an aerospace system in climb with acceleration to hypersonic velocity are analyzed. Two approaches to determining the control programs and flight paths are identified: the "traditional" approach and the "optimization" one. The "traditional" approach implies specifying a typical mission profile with max-q and peak heat flux. In the case of the "optimization" approach the problem of propellant mass minimum is stated and solved using the method of Pontryagins maximum principle. It concerns the mass of propellant consumed in hypersonic acceleration for various terminal flight path angles. Optimal control programs and optimal flight paths are determined. Those meeting the max-q and peak heat flux requirements are selected. The results of modeling the motion of a hypersonic booster with typical and optimal angle-of-attack schedules corresponding to the "traditional" and "optimization" approaches are presented and discussed. It is established that less propellant is consumed in the case of optimal control, which is accounted for by more efficient use of the hypersonic booster's aerodynamic performance due to direct control of the angle of attack.

Integrated guidance and control of interceptors with impact angle constraint against a high-speed maneuvering target

An integrated guidance and control method is investigated for interceptors with impact angle constraint against a high-speed maneuvering target. Firstly, a new control-oriented model with impact angle constraint of the integrated guidance and control system is built in the pitch plane by combining the engagement kinematics and missile dynamics model between the interceptor and target. Secondly, the flight path angle of the target is estimated by extended Kalman filter in order to transform the terminal impact angle constraint into the terminal line-of-sight angle constraint. Thirdly, a nonlinear adaptive sliding mode control law of the integrated guidance and control system is designed in order to directly obtain the rudder deflection command, which eliminates time delay caused by the traditional backstepping control method. Then the Lyapunov stability theory is used to prove the stability of the whole closed-loop integrated guidance and control system. Finally, the simulation results confirm that the integrated guidance and control method proposed in this paper can effectively improve the interception performance of the interceptor to a high-speed maneuvering target.

Mission Analysis for the EM-1 CubeSats EQUULEUS and OMOTENASHI

OMOTENASHE and EQUULEUS are two 6-U CubeSats by JAXA and The University of Tokyo to be launched in 2019 onboard of NASA's Exploration Mission 1. This paper presents the nominal trajectories and an overview of the mission analysis work and approaches. EQUULEUS trajectory exploits the Earth -Sun -Moon dynamics to capture the spacecraft into a libration orbit around the Earth -Moon L2 point, using only -10 m/s of deterministic Av. Mission analysis cost and complexity, however, are driven by the statistical maneuvers because of the expected limited performances in orbit determination (because of limited ground station availability) and execution errors. OMOTENASHE mission analysis requires multiple iterations where the robustness to errors is evaluated over the design space. It is found that the spacecraft should approach the Moon with a shallow flight path angle of about -5°, avoid crater rims and mountains, and start the free fall at about 130 m height. For both missions, the initial week of operations, including Avl execution, is critical, and ground station support is being negotiated by the teams with JAXA and with international partners.

Analytical solutions for longitudinal-plane motion of hypersonic skip-glide trajectory

The analytical solutions for longitudinal-plane motion of hypersonic skip-glide trajectory are proposed by perturbation theory. First, the analytical solution of downrange distance is approximated by the outer solutions of a two-timescale singular perturbation system where the solution error is less than 2%. Then, the zeroth-order solutions and first-order corrections of altitude and flight-path angle are developed using regular perturbation techniques which could decompose the coupled and nonlinear system into a sequence of linear problems to solve in order. Because the first-order system for altitude and flight-path angle is a linear time-varying system that cannot be solved by traditional method such as Laplace transform, two methods are put forward to simplify the system: spectral decomposition method (SDM) and linear transformation method (LTM). SDM assumes the system to be time invariant and then uses spectral decomposition to solve it. LTM introduces a small compensation into the system such that the system can be decoupled into two independent first-order differential equations by linear transformation. Then, by combining the advantages of the two kinds of solutions, more accurate integrated analytical solutions are proposed. The simulation results show that the analytical solutions are in good agreement with the numerical solutions. In addition, the computation time of the analytical solutions is about two orders of magnitude less than that of the numerical solutions.

Finite-Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming

Referring to the optimal tracking guidance of aircraft, the conventional time based kinematics model is transformed into a downrange based model by independent variable replacement. The deviations of in-flight altitude and flight path angle are penalized and corrected to achieve high precision tracking of reference trajectory. The tracking problem is solved as a linear quadratic regulator applying small perturbation theory, and the approximate dynamic programming method is used to cope with the solving of finite-horizon optimization. An actor-critic structure is established to approximate the optimal tracking controller and minimum cost function. The least squares method and Adam optimization algorithm are adopted to learn the parameters of critic network and actor network, respectively. A boosting trajectory with maximum final velocity is generated by Gauss pseudospectral method for the validation of guidance strategy. The results show that the trained feedback control parameters can effectively resist random wind disturbance, correct the initial altitude and flight path angle deviations, and achieve the goal of following a given trajectory.

Fast, robust and near-optimal approximation of GTO trajectories and payload capacities of multistage rockets

A method for automatically generating approximate trajectories for multistage rockets, launching into a geostationary transfer orbit, is presented. It can either be used to generate an initial guess or to determine the payload capacity of a given launcher. Only the apogee is directly optimized. When the maximum payload of the launcher is used, the perigee will gravitate towards its target value. The method is applicable to configurations consisting of three stages or two stages plus boosters. The trajectory is divided into three steps, one for each stage plus one for all boosters. Five control parameters are used: The first is the constant pitch rate, used during the pitch over maneuver. The other four define the angle of attack rate functions. A declining exponential function is used for $$\dot{\alpha }_2(t)$$ , whereas $$\dot{\alpha }_3(t)$$ is chosen so that $$\alpha _3(t)$$ becomes an inverted parabola. The trajectory algorithm consists of an outer and an inner loop. The outer loop varies the pitch rate to attain the correct apogee. It calls the inner loop, which adjusts the two parameters that define $$\dot{\alpha }_2(t)$$ so that the flight path angle rate at the end of the second step becomes zero. Tests were performed for a model of Ariane 40. Its payload capacity was determined in less than $${30}\hbox { s}$$ and the result matched the one produced by a conventional approach. Moreover, a Monte Carlo simulation, based on the Ariane 40 model, was performed for both applications. The success rate was 94% for the first and 93% for the second case.

Three-Dimensional Impact Time and Angle Control Guidance Based on MPSP

A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised using the model predictive static programming (MPSP) method, and the control saturation constraint is incorporated in the MPSP algorithm. The first-order-lag acceleration of the missile is taken as the state variable to realize the convergence of the terminal acceleration to zero. Moreover, a collision avoidance strategy for three-dimensional missile cooperative flight is proposed. The simulation results show that the guidance law can make the missiles hit the target accurately at the same time with the ideal impact angles and can realize the control saturation constraints of the missiles. This can increase the attack effects and is significant for collaborative attacks.

A New Collision Control Guidance Law Based on Speed Control for Kill Vehicles

In this paper, a new guidance law for intercepting ballistic missiles at high altitude is proposed. The proposed guidance method, called collision control guidance, unlike the conventional guidance method which controls the collision triangle by adjusting the flight-path angle, achieves a collision triangle by controlling the interceptor speed. In the proposed method, a new impact point (or collision triangle) is first determined that automatically nullifies a given initial heading angle error without changing the flight-path angle. Speed control is followed until a particular time in order to reach the new impact point. In this paper, the control effectiveness and the fuel consumption of the proposed method are analyzed to provide better insight into the proposed method. It turns out that compared to existing methods the proposed method can save fuel when intercepting a high-speed target. Numerical simulations confirm the performance of the proposed method.

Optimal perturbation guidance with constraints on terminal flight-path angle and angle of attack

This paper presents the design of a singular-perturbation-based optimal guidance with constraints on terminal flight-path angle and angle of attack. By modeling the flight-control system dynamics as a first-order system, the angle of attack is introduced into the performance index as a state variable. To solve the resulting high-order optimal guidance problem analytically, the posed optimal guidance problem is divided into two sub-problems by utilizing the singular perturbation method according to two time scales: range, altitude, and flight-path angle are the slow time-scale variables while the angle of attack is the fast time-scale variable. The outer solutions are the optimal control of the slow-scale subsystem. Thereafter, by applying the stretching transformation, the fast-scale subsystem establishes the relationships between the outer solutions and acceleration command. Then, the optimal command can be obtained by solving the fast-scale subsystem also using the optimal control theory. The proposed guidance can achieve a near-zero terminal acceleration as well as a small miss distance. The superior performance of the guidance is demonstrated by adequate trajectory simulations.

Optimal Periodic Control of Hypersonic Cruise Vehicle: Trajectory Features

Optimal periodic control is an effective technique to reduce aerodynamic heating and fuel consumption of hypersonic cruise vehicles. Herein, this optimal control problem has been solved by nonlinear programming and passed the posteriori check of optimality. The results indicate that the lift coefficient and velocity in dynamical model could be recognized as constants. Accordingly, the original 3D system consists of velocity, flight path angle, and altitude, which could be decoupled into a 2D subsystem and a 1D one. The 2D subsystem could describe the correlation between the flight path angle and altitude. And the period length is mainly dependent on the maximum altitude difference. The 1D subsystem has been proved to be feasible to describe the variation of kinetic energy or velocity. On basis of the subsystems, the heating and fuel performances of periodic cruise have been studied. The heating performance is mainly dependent on the maximum altitude difference, and the fuel consumption is mainly dependent on the drag coefficient. The features concluded in this paper can support rapid trajectory planning or suboptimal feedback design of hypersonic cruise vehicles.

Marginal tracking algorithm for hypersonic reentry gliding vehicle

Here, the trajectory of hypersonic reentry gliding vehicle is tracked in the East-North-Up (ENU) coordinate system (CS) using a novel marginal tracking algorithm. Firstly, the trajectories are compared and analysed through numerical simulation. The authors try to establish the manoeuvring models based on flight path angle and heading angle. However, they are all invisible in the ENU CS. Fortunately, inclination angle and azimuth angle can be utilised to replace them. Secondly, the trajectory is projected onto the longitudinal and horizontal observation planes and is tracked synchronously in them. The three-dimensional tracking is achieved through measurement data preprocessing, marginal filtering, and state merging. Finally, the parameters of manoeuvring models in two observation planes are set. Simulation shows that the algorithm has a good robustness and high tracking precision.

Dynamic Sliding-Mode Control Scheme for Hypersonic Vehicles Considering Nonminimum Phase Characteristics and Performance Recovery

This paper presents a performance recoverable control scheme for air-breathing hypersonic vehicles (HSVs) with nonminimum phase characteristics. As elevator and throttle are the only two control inputs available for longitudinal trajectory tracking of HSVs, there are two representative problems emerged. One is the nonminimum phase behavior in pitch dynamics of HSVs due to elevator-to-lift coupling, which prevents the application of standard inversion-based control techniques. The other is the engine performance recovery control with the disabled propulsion system, when flight states of HSVs exceed the safe working boundary, causing engine flameout. In view of the above, a comprehensive control scheme is proposed to realize performance recoverable and high-precision trajectory tracking of nonminimum phase HSVs. First, a dynamic integral sliding-mode (DISM) control method based on the Byrnes-Isidori (B-I) normalized form is proposed, achieving asymptotic tracking of velocity and flight path angle (FPA) while stabilizing internal dynamics. The control method transforms the FPA tracking problem into a stabilization problem of an augmented system consisting of internal dynamics and dynamic compensator, making closed-loop pole adjustable, and thus improves the tracking performance. Second, on this basis, a performance recoverable control scheme is proposed to achieve the automatic performance recovery of HSVs when the engine flameout occurs due to the stall of the HSVs. It achieves temporary acceleration by adjusting the trajectory, thus obtaining the conditions for engine restart. The simulations of the nominal condition and engine flameout condition are presented, respectively, to verify the proposed control scheme. From the simulation results, the proposed control scheme is shown to have superior tracking accuracy with internal dynamics stable, and the robustness is fully verified by the Monte Carlo simulations. Especially, speed autonomous recovery and engine restart are achieved during the engine flameout, which demonstrates the effectiveness of the proposed performance recovery control scheme.

Missile Initial Engagement Determination and Terminal Phase Guidance

Abstract This paper discusses an approach for determining the initial engagement point and steering missile during its terminal phase such that it can hit a ground target from predefined direction. The guidance algorithm generates maneuver reference, in terms of normal acceleration, that is fed to the flight control system. The algorithm is based on Proportional Navigation (PN) approach, with scheduled navigation gains. The navigation gains are scheduled as a function of Line of Sight (LOS) and desired flight path angles at engagement stage, hence it may be exploited for determining the initial engagement point. For a desired navigation gain value, the LOS is also related to the maximum value of normal acceleration reference, hence it can be used for limiting the maneuver that must be executed by the missile. The guidance system then is integrated with the flight maneuver controller. The flight control system regulates the normal acceleration, so that the missile will follow the desired trajectory and hit the target. The algorithm then is implemented and tested on a hypothetical cruise missile model. The simulation results show that the guidance approach can generate good maneuver reference, and that the performance of the normal acceleration tracking controller will significantly affects the accuracy of the system.

Rapid Altitude Tracking for Air-Breathing Hypersonic Vehicle With Limited Angle of Attack

This paper focuses on the altitude tracking issue for air-breathing hypersonic vehicles. It proposes a rapid altitude tracking method with synthetical consideration on the angle of attack constraint, which is crucial to keep the scramjet away from the inlet unstart. For the inner-loop, the novel compensator is considered in the conjunction of the backstepping approach to design a flight path angle tracking controller. The compensator helps the controller to limit the angle of attack with the uncertainties. For the out-loop of the control system, the altitude controller involves the combination of Bang-Bang control and the sliding mode technique to generate the command which accommodates the constraint on the angle of attack. The atmosphere density model is taken into account, which makes the proposed method more adaptable to the altitude variation. The effectiveness of the proposed control method is evaluated in the simulations.

Adaptive Polynomial Guidance With Impact Angle Constraint Under Varying Velocity

Considering the velocity of the missile cannot remain constant in most applications due to the effect of aerodynamic drag and thrust, a feasible adaptive impact angle control guidance law under varying velocity is proposed. The design of the guidance command is transformed into the design of the flight path angle, which is proposed as a general polynomial function of time-to-go with unknown coefficient. In addition, the unknown coefficient can be acquired from the boundary condition of the position. To cope with unpredictable disturbances, the adaptive scheme to initialize and recalculate the control parameter at each time step is also adopted. First, the guidance law is proposed with constant velocity. Then the law is extended to a more practical situation by considering varying velocity, and the estimation of time-to-go under varying velocity is proposed. Different simulations are carried out to verify the performance of the proposed guidance law.

Interval Type-2 FNN-Based Quantized Tracking Control for Hypersonic Flight Vehicles With Prescribed Performance

This paper presents a tracking control scheme with quantization mechanism for hypersonic flight vehicles (HFVs) with prescribed performance using an interval type-2 fuzzy neural network (IT2FNN). A parameterized tracking error model of the HFV is derived with some considered uncertainties, which are approximated by an IT2FNN. The tracking control of the velocity and altitude of the HFV is designed by using a prescribed performance control technique. It allows that transient characteristics of the tracking errors can be improved and adjusted by some prescribed performance functions. According to an adaptive backstepping control design procedure, novel continuous control laws of the fuel equivalency ratio, canard deflection, and elevator deflection are designed with logarithmic quantization mechanism, for the sake of avoiding inadvertently increasing the effective gains of continuous controllers as well as reducing loads of the communication from controller unit to actuator unit. Besides, the limited tracking errors of the flight path angle and angle-of-attack can be achieved by applying the designed controllers. Finally, the presented tracking controllers with quantization mechanism are validated by comparative simulations.

Optimal Maneuver Trajectory for Hypersonic Missiles in Dive Phase Using Inverted Flight

To determine the optimal trajectory for the dive phase of a hypersonic missile, a maneuver strategy using inverted flight is presented. The combat scene that the hypersonic missile attacks the fixed target on the ground is considered in this paper. Particularly, a maneuvering form named inverted flight is first applied to the hypersonic missiles. Afterward, an optimal trajectory is designed by minimizing the attack time with a preset terminal flight path angle, where the constraints of the angle of attack, dynamic pressure, heating transfer rate, and normal overload are taken into account. In order to solve the designed trajectory optimization problem, an improved hp-adaptive pseudospectral method with mesh size reduction is presented. The simulation results show that the proposed algorithm can significantly reduce the mesh scale with satisfactory accuracy and the trajectory obtained by the proposed algorithm is in accordance with the actual flight law. Furthermore, contrast simulation demonstrates that the inverted flight has better trajectory performance than normal flight.