Flight Path Angle Research Articles

Performance Assessment of Discrete-Event Drag Modulation for Mars Entry with Real-Time Guidance

Entry flight performance is assessed for single-stage discrete-event drag-modulation trajectory control on Mars with two different real-time guidance algorithms: a heuristic velocity trigger and numerical predictor–corrector. Three degree-of-freedom simulation and Monte Carlo techniques are used to determine flight performance across a range of mission and vehicle design parameters. Trends are identified in flight performance across different initial conditions, ballistic-coefficient ratios, and target ranges. Results indicate that both guidance algorithms can provide landing accuracy better than 10 km across likely vehicle properties and entry conditions. The heuristic velocity trigger performs nearly as well as the numerical predictor–corrector for low-ballistic-coefficient ratios and entry flight-path angles steeper than approximately . The numerical predictor–corrector provides consistent flight performance across all feasible mission and vehicle parameters with accuracy better than approximately 5 km. Overall, single-stage discrete-event drag-modulation trajectory control is a feasible option for accurate landings for ballistic coefficients below approximately and landed altitudes above 0 km.

Realization of trajectory precise tracking for hypersonic flight vehicles with prescribed performances

This work attempts to achieve precise tracking control for the longitudinal dynamics of hypersonic flight vehicles (HFVs) without adopting universal approximators (e.g., fuzzy logic systems, neural networks, etc.). To this purpose, the system nonlinearities are well constrained to be bounded within some compact sets and are tackled by means of adaptation technique. Apart from achieving precise tracking, some prescribed performances (e.g., convergence rate, maximum steady tracking error, etc.) of the tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch rate are also preserved. The proposed method is complexity-reduced and structurally simple in the sense that the time derivatives of the virtual control laws are no longer required and that the number of adaptation parameters have been reduced to only five due to the absence of universal approximators. Barbalat lemma is combined with Lyapunov theory to prove the closed-loop stability, while guaranteeing that the tracking errors eventually converge to zero through choosing appropriate design parameters. The effectiveness of the proposed control scheme is demonstrated by comparative numerical simulations.

An analytical computation of aircraft’s longitudinal trimmed conditions considering its fuel mass flow rate

The aim of this article is to give simple expressions of aircraft’s longitudinal trimmed conditions taking into account the instantaneous fuel mass flow rate, i.e. the variation of total mass. The computation of aircraft trim points is not a new problem. Nevertheless, current analytical computations are classically performed with a constant total weight of the aircraft, hence assuming that the rate of decrease of the weight due to the fuel mass flow rate has insignificant effects on the results. Thus, the goal of this study has been to assess the effect of weight variation on aircraft trimmed condition and to compute correctly “extended trimmed conditions” defined as the equilibrated conditions in flight considering the weight decrease of the aircraft. It has been demonstrated that the weight variation must have an ad-hoc form to lead to extended trimmed conditions. Moreover, extended trimmed conditions do not correspond to a perfect level flight as it is the case at constant weight, but must present a slightly positive flight path angle leading to a regular increase in altitude. And the corrected longitudinal commands including throttle and elevator positions at a given airspeed and altitude have been computed for extended trimmed conditions and compared to the basic case at constant weight. Finally, all the analytical expressions given in this article have been verified through a numerical simulation performed in the case of a twin-engine aircraft representative of the Airbus wide-body family.

Integrated Morphing Strategy and Trajectory Optimization of a Morphing Waverider and Its Online Implementation Based on the Neural Network

In previous studies, a variable-sweep-wing morphing waverider was proposed and its aerodynamic performance and dynamic model were provided. This morphing waverider can change sweep angle according to different flight scenario in order to achieve an optimal flight performance. For the traditional fixed-geometry waverider, the main objective of the trajectory planning problem is to find an optimal trajectory consisting of time-dependent variables including the angle of attack, the velocity, the altitude, the flight path angle and so on. As for this morphing waverider, an optimal morphing wing changing strategy is also required to be calculated together with an optimal trajectory. At first, to alleviate computational cost and improve trajectory-planning efficiency, aerodynamic coefficients of the morphing waverider are approximated and modeled as polynomial functions of multiple variables including the Mach number, the angle of attack and the sweep angle. Thereafter, an offline integrated optimization problem of both wing morphing strategy and trajectory based on the Gauss pseudo-spectral method is investigated, which can fulfill actual task requirements and variable constraints. Compared with four specific fixed-wing waverider configurations, this morphing waverider has a larger downrange distance and a lower angle of attack. However, the real flight trajectory of the morphing waverider may deviate from the nominal condition due to multiple uncertainties and this morphing waverider is required to have an intelligent online optimization ability. Therefore, an online optimization method based on the neural network is proposed for both wing morphing strategy and trajectory optimization. Finally, the overall performance of this method is examined by comparisons and Monte Carlo runs.

Flight Evaluation of Helicopter Curved Point-in-Space Approach Procedures

Helicopter point-in-space instrument procedures are key to enabling simultaneous noninterfering procedures and enhancing all-weather access in dense airspace and remote locations. This paper describes the flight evaluation of navigation and human performance in helicopter curved point-in-space procedures as part of Single European Sky Air Traffic Management Research. An experimental procedure was designed at Donauwörth heliport including radius-to-fix legs with descent gradients and airspeed variations in the terminal segments, followed by a steep, straight-in final approach segment. Two strategies were evaluated for vertical descent profiles: fixed flight path angle, and fixed vertical speed. Three test pilots were instructed to execute the entire approach until the missed approach point in simulated instrument meteorological conditions using advanced autopilot modes and head-down flight and navigation displays. Navigation performance was measured using cross-track and vertical-track deviations. Pilot workload and situational awareness were measured using the task load index and the situational awareness rating technique, respectively. The results showed that flight paths were maintained within the required navigation performance limits despite strong crosswinds, and the final approach glidepath was successfully captured in all cases. All pilots reported low workload, adequate spare capacity, and high situational awareness in all cases. Furthermore, the fixed flight path angle descent was found to induce lower workload and required fewer crew actions compared with the fixed vertical speed descent. Owing to the small sample size, conclusions with statistical significance cannot be established.

Adaptive Entry Guidance for Hypersonic Gliding Vehicles Using Analytic Feedback Control

This paper presents an adaptive, simple, and effective guidance approach for hypersonic entry vehicles with high lift-to-drag (L/D) ratios (e.g., hypersonic gliding vehicles). The core of the constrained guidance approach is a closed-form, easily obtained, and computationally efficient feedback control law that yields the analytic bank command based on the well-known quasi-equilibrium glide condition (QEGC). The magnitude of the bank angle command consists of two parts, i.e., the baseline part and the augmented part, which are calculated analytically and successively. The baseline command is derived from the analytic relation between the range-to-go and the velocity to guarantee the range requirement. Then, the bank angle is augmented with the predictive altitude-rate feedback compensations that are represented by an analytic set of flight path angle needed for the terminal constraints. The inequality path constraints in the velocity-altitude space are translated into the velocity-dependent bounds for the magnitude of the bank angle based on the QEGC. The sign of the bank command is also analytically determined using an automated bank-reversal logic based on the dynamic adjustment criteria. Finally, a feasible three-degree-of-freedom (3DOF) entry flight trajectory is simultaneously generated by integrating with the real-time updated command. Because no iterations and no or few off-line parameter adjustments are required using almost all analytic processing, the algorithm provides remarkable simplicity, rapidity, and adaptability. A considerable range of entry flights using the vehicle data of the CAV-H is tested. Simulation results demonstrate the effectiveness and performance of the presented approach.

Disturbance observer-based backstepping control for hypersonic flight vehicles without use of measured flight path angle

In this paper a nonlinear control method is proposed for the tracking control of hypersonic flight vehicles. The designed control laws do not utilize the measured flight path angle due to its inferior accuracy in practical engineering. For this, an estimated flight path angle is designed via the measurements of the altitude and velocity. A tracking differentiator is designed for constructing nonlinear disturbance observer which is used to estimate the model uncertainties including the parameter indeterminacies and external disturbances in the channels of velocity and pitch rate. A robust high-order differentiator is introduced to avoid the employment of the measured flight path angle and estimate the lumped disturbance in dynamics of flight path angle. Meanwhile, the possible saturation of the control inputs is considered and compensated by the auxiliary states. The boundness of closed-loop signals is proved through the Lyapunov theory. Comparative simulations are carried out and the results demonstrate the effectiveness of the proposed method.

Feasibility study on applying continuous descent operations in congested airspace with speed control functionality: Fixed flight-path angle descent

Continuous descent operations (CDO) are an efficient descent operation for passenger/cargo aircraft and implemented at various airports worldwide. However, it is difficult for air traffic controller (ATCo) to predict the CDO trajectory and control the CDO aircraft, therefore limiting the applicable window only during the low traffic periods. To maximize potential benefits by introducing the CDO, it is required to implement the CDO into congested airspace and time window. This study introduces an augmentation to CDO application in the congested airspace, called fixed flight-path angle (Fixed-FPA) descent. The fixed-FPA descent was originally proposed and investigated only for small passenger jet aircraft; thereafter the fixed-FPA descent was introduced to large passenger jet aircraft. This proposed procedure consists of several altitude restrictions along the arrival route. By following the altitude restrictions, the aircraft flies with a specified flight-path angle. Additionally, specifying the flight-path angle facilitates the prediction of the CDO trajectory by ATCo. Moreover, by setting a shallower flight-path angle compared with the conventional CDO, the fixed-FPA descent is capable of speed control. The preceding studies conducted only the preliminary feasibility study of the fixed-FPA descent on large jet aircraft. In this study, a series of full-flight simulator experiments and Monte Carlo simulations were conducted to assess the operational feasibility and demonstrate the capabilities of fixed-FPA descent. Experimental results demonstrated that the fixed-FPA descent meets the requirements for integrating the CDO into congested airspace, such that the vertical path of the CDO can be predicted by the ATCo, and the speed of the CDO aircraft is controllable. Additionally, the simulation results revealed that the fixed-FPA descent has better fuel efficiency than the conventional when the descending aircraft is required to delay its arrival time.

A Novel Hybrid Robust Control Design Method for F-16 Aircraft Longitudinal Dynamics

This paper presents a hybrid robust control design method for a third-order lower-triangular model of nonlinear dynamic systems in the presence of disturbance. In this paper, a novel control design is presented systematically to synthesize a robust nonlinear feedback controller, called backstepping sliding mode control (BSMC), for the proposed system by a combined approach of backstepping design and sliding mode control. In this approach, a family of the “sliding surface” is introduced in state transformations. Then, a smooth switching function of the sliding surface is introduced and enforced to include in virtual feedbacks and a real control law from the control selection phrases of the backstepping design loop. The achieved control method proves a well-tracking command with asymptotic stability, provides a robustness in the presence of uncertainties, and eliminates completely a chattering phenomenon. The application of flight-path angle control corresponding to the longitudinal dynamics of a high-performance F-16 aircraft simulation model is implemented. Under some assumptions, full nonlinear longitudinal dynamics is reformed into a lower-triangular system for a direct application to formulate a control law. A closed-loop system is achieved for in-flight simulation with different flight profiles for a comparison of the existing methods. Also, an external disturbance on different loading/unloading conditions in flight is applied to verify and validate robustness of the proposed control method.

A segmented and weighted adaptive predictor-corrector guidance method for the ascent phase of hypersonic vehicle

In this study, considering the various terminal constraints, and strong coupling between different flight states, a novel segmented and weighted adaptive predictor-corrector guidance method is proposed for the ascent phase of hypersonic aircraft. Firstly, by means of the analysis of whole ascent phase, it can be found that the magnitudes of different states vary greatly during the ascent phase. In order to reduce the impact of the difference, a dimensionless policy is adopted for the dynamic equations. And then, based on the all-coefficient adaptive control theory, the time-varying dynamic factors which will be used in the guidance law are calculated. Analyzing the dynamic factors and the whole flight characteristics of ascent phase, it can be concluded that the change of attack angle has great and monotonous influence on the terminal flight path angle and altitude, and the flight path angle at the later period of ascent phase has little impact on the guidance channel of altitude. Consequently, the whole flight phase is divided into the first flight subphase whose guidance object is eliminating the terminal altitude and velocity errors with the weighted guidance law, and the second flight subphase when the terminal flight path angle and velocity errors are used to correct the guidance command. What's more, the selection principle of guidance parameters is analyzed, and it is very important for the terminal guidance accuracy of various states. Finally, the effectiveness and robustness of the proposed guidance law are demonstrated by the Monte-Carlo simulations. The comparison simulation also shows that the effectiveness of the dimensionless scheme and weighted policy which can both improve the guidance accuracy.

Barrier Lyapunov Functions-Based Adaptive Fault Tolerant Control for Flexible Hypersonic Flight Vehicles With Full State Constraints

One of the key problems for space vehicles is how to deal with the contradiction between the control constraints and the disturbances from multiple resources. This paper focuses on the adaptive full state constrained controller design problem for the flexible air-breathing hypersonic vehicles with multisource uncertainties. In simultaneous presence of the aerodynamical uncertainties, the modeling errors, the external disturbances, and the contingent actuator failures, an adaptive fault-tolerant control scheme is put forward in the context of dynamic surface control. Then, the barrier Lyapunov functions are utilized to guarantee that the constraints on the velocity, the flight path angle, the altitude, and the pitch rate are never violated. In virtue of the bound estimation approach, the multisource disturbances are effectively dealt with. Finally, a number of illustrative examples are provided to demonstrate the effectiveness of the proposed methodology.

Analytical Earth-Aerocapture Guidance with Near-Optimal Performance

An aerocapture maneuver employs a single atmospheric pass to reduce orbital energy and establish a closed orbit. Modulating the spacecraft’s vertical lift component (via bank control) during atmospheric flight in an optimal fashion will minimize the post-exit propulsive burn required to establish a target orbit. This paper presents a new analytical predictor–corrector guidance algorithm for the Earth-aerocapture problem. Bank control is open loop (lift-up) during the descent phase and closed loop (lift-down) during the ascent phase in order to emulate the bang–bang bank structure of optimal aerocapture. The guidance is developed using analytical functions representing the flight-path angle and the composite effects of atmospheric density, lift and drag coefficients, and vehicle mass along the ascent trajectory. These functions result in a closed-form equation for exit velocity and a method for predicting the switching condition from lift-up to lift-down control. Monte Carlo simulations demonstrate the robustness, accuracy, and near-optimal performance of this new analytical guidance method.

Discrete-Event Drag-Modulated Guidance Performance for Venus Aerocapture

Drag modulation provides a straightforward approach to aerocapture trajectory control. In this paper, two guidance algorithms are assessed for Venus aerocapture: a predictive-trigger and a numerical predictor–corrector. A hybrid root finder is developed for both single- and multistage jettison. Architecture performance is assessed using Monte Carlo methods. Two apoapsis altitude targets, 2000 and 10,000 km, are considered alongside two entry flight-path angles, and . The hybrid root finder improved targeting accuracy and robustness compared with a standard bisection technique. Each of the guidance algorithms performed better for shallower entry angles. The benefit of multi-event jettison architectures is analyzed in this study. A second jettison event is shown to significantly improve apoapsis targeting accuracy, whereas a third jettison event further improves this accuracy, but to a lesser degree, demonstrating multistage jettison’s potential to improve aerocapture robustness.

A novel reduced-order guidance and control scheme for hypersonic gliding vehicles

A novel analytical model between roll, pitch rates and components of acceleration of the hypersonic vehicle is established, and a reduced-order gliding guidance and control (G&C) design approach for the hypersonic vehicle is proposed in this paper. The six-degree-of-freedom (6DOF) dynamical and kinematic equations of the hypersonic vehicle in the gliding phase are described. An analytical model suitable for the bank to turn (BTT) control strategy is derived by connecting body rates with components of acceleration in the ballistic coordinate system. A novel reduced-order guidance and control design model with respect to quasi-equilibrium gliding flight is deduced and converted into the strict feedback form. The three channel body rates are treated as pseudo-inputs for tracking errors of flight path angle and heading angle of the hypersonic vehicle. Then, the commanded control surface fin deflections of the hypersonic vehicle are obtained by controlling tracking errors of the flight path angle, heading angle, and the body rates by adopting the block dynamic surface control method. In this paper, the aerodynamic coefficient interpolation process for obtaining the commanded angle of attack and bank angle based on expectant guidance overload is avoided. Meanwhile, the control loop of tracking Euler angles for getting the desired body rates is also elided. Finally, effectiveness and robustness of the novel G&C design method are verified and investigated. Moreover, the feasibility of entering quasi-equilibrium gliding phase only depending on the aerodynamic control mechanism is discussed.

UAV's Precise Trajectory Tracking Control Based on Nonlinear Dynamic Inverse and Quaternions

The precise tracking 3D trajectory that changes dramatically within the boundary of flight performance is the essential capability of the UAV applied to air combat, which requires that flight control law design be adapted to nonlinear characteristics of flight dynamics and solve the singularities problem during the flight. Continuous trajectory control on the basis of nonlinear dynamic inversion (NDI) is studied. The singularities problem is caused by continuous trajectory expressed by flight velocity and flight-path angles. A sudden change of flight-path axis system happens when aircraft flies along a continuous trajectory which results in singularities. A method for amending flight-path axis system is presented to solve the sudden change problem of flight-path axis system. Finally, the combination of the maneuver generator based on quaternions and amending flight-path axis system realize the precise trajectory tracking control without singularities and obtain excellent tracking characteristics.

Uncertainty Analysis for Return Trajectory of Vertical Takeoff and Vertical Landing Reusable Launch Vehicle

The uncertainties during the return trajectory of vertical takeoff and vertical landing reusable launch vehicle weaken the ability of precision landing and make the return process more challenging. This paper is devoted to quantifying the probability uncertainty of return trajectory with uncertain parameters. The uncertainty model of return multi-flight-phase under the uncertainties of initial flight path angle, axial aerodynamic coefficient, and atmospheric density is established using the generalized polynomial chaos expansion method. By parameterizing random uncertainties and introducing random parameters into the uncertainty model, the uncertainty analysis problem of return trajectory is transformed into stochastic trajectory approximation problem. The coefficients of the polynomial basis function are solved by the stochastic collocation method. Then state solutions, statistical properties, and global sensitivity with Sobol index are established based on coefficients. The simulation results show the efficiency and accuracy of this method compared with the Monte Carlo method, the evolution process of main output parameters under random parameters, and relative importance for random parameters. Through the uncertainty analysis of the return trajectory, the robustness of return trajectory can be quantified, which is contributed to improving the safety, reliability, and robustness of recovery and landing mission.

Generalized Polynomial Guidance for Terminal Velocity Control of Tactical Ballistic Missiles

This paper proposes generalized polynomial guidance for controlling the terminal velocity vector (speed and flight path angle), which could be critical for the effectiveness of the warhead of tactical ballistic missiles. A polynomial reference trajectory satisfying the initial and terminal altitudes and flight path angles is introduced with a guidance parameter that can be chosen to change the terminal speed. A single differential equation of the speed along the reference trajectory is then derived and an iterative search method for determining the guidance parameter to satisfy the prescribed terminal speed is proposed. Numerical simulation study with various impact angle and terminal speed constraints is conducted to demonstrate the performance of the proposed guidance method for terminal velocity control. Robustness of the proposed method to drag variations is also investigated to check the feasibility of generalized polynomial guidance for a practical purpose.

Integrated Guidance and Control Using Model Predictive Control with Flight Path Angle Prediction against Pull-Up Maneuvering Target.

Integrated guidance and control using model predictive control against a maneuvering target is proposed. Equations of motion for terminal homing are developed with the consideration of short-period dynamics as well as actuator dynamics of a missile. The convex optimization problem is solved considering inequality constraints that consist of acceleration and look angle limits. A discrete-time extended Kalman filter is used to estimate the position of the target with a look angle as a measurement. This is utilized to form a flight-path angle of the target, and polynomial fitting is applied for prediction. Numerical simulation including a Monte Carlo simulation is performed to verify the performance of the proposed algorithm.

Midcourse Guidance Strategy for Multistage Interceptors with Coasting Phase

This paper proposes a new approach on the impact angle control guidance problem for the multistage interceptor with nonmaneuvering phases, called coasting phase, and high acceleration buildup during the boosting phase. First, the required coasting time is determined to reach the target within the given time span considering operation time of the kill vehicle. Then, the required flight path angle profiles and corresponding guidance commands during the boosting phase are derived, in order to achieve the desirable impact angle and to minimize guidance errors at the end of the flight. To do so, the position and velocity changes of each phase are analytically calculated, and then the relationship between the time derivative of the flight path angle during the boosting phase and guidance errors accumulated throughout the flight is established. Some practical error compensation algorithms for the proposed guidance strategy are also presented. The significance of this paper lies in that it is the new analytic approach on how to determine flight path profiles of a multistage interceptor to achieve a terminal impact angle constraint considering both booting and coasting. The proposed guidance strategy is evaluated and proven to be effective through a case study with nonlinear simulations.

Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.