Aircraft Dynamics Research Articles

Flight Dynamics and Control of an eVTOL Concept Aircraft with a Propeller-Driven Rotor

The objective of this investigation is threefold. First, to assess the flight dynamics of an electric vertical take-off and landing (eVTOL) concept aircraft with a propeller-driven rotor. Second, to develop an automatic flight control system (AFCS) for this concept aircraft. Third, to verify the potential safety benefits of the concept aircraft by analyzing the autorotation performance following a total loss of power. The paper begins with an overview of the design of the aircraft and description of the simulation model, including a detailed discussion on the inflow model of the propellers that drive the main rotor. Next, the flight dynamics are assessed at hover and in forward flight. An AFCS based on dynamic inversion is developed to provide stability and desired response characteristics about the roll, pitch, yaw, and heave axes for speeds ranging from hover to 80 kt. Additionally, an RPM governor is implemented to hold the main rotor angular speed constant at its nominal value. Finally, simulations that make use of the AFCS are performed to analyze the autorotation performance following total loss of power.

Computational study of single and clustered parachutes in the wake of an aircraft

This work continues a long-term study toward bridging the gap between flight dynamics simulation of ring-slot extraction parachutes in the wake of an aircraft and high-fidelity computational fluid dynamics. Extraction-parachute system designs primarily rely on the empirical or semi-empirical methods generated from flight tests. Traditional wind tunnel experiments of this environment provide limited data due to difficulty in capturing scale and realistic aircraft engine effects. A computational fluid dynamics study of rigid-model single and clustered ring slot parachutes in the wake of a C-17 aircraft permits an alternate determination of parachute performance characteristics, including stability, to inform reduced order models. The presented simulations include force and moment data for the single- and triple- extraction parachute clusters. These data complement experimental and flight test data. The outcome of this study will help reduce the cost of drop testing and enable larger parameter studies to enhance system design and safety.

Method for determining of aircraft landing performance by the simulation modeling

The paper considers the method for determining of aircraft landing performance, the basic of which is landing roll depending on the type and tire inflation pressure, runway surface condition, aircraft weight, availability of brake parachutes. The given results are received by the simulation modeling of aircraft spatial movement on a landing mode. The model of aircraft dynamics includes modules of aircraft movement kinematic parameters calculation, engine thrust, landing gear ground reaction, retarding force in wheel brakes and brake parachutes. Adequacy and reliability of the designed model of aircraft movement is confirmed by comparison of values of movement kinematic parameters obtained as a result of simulation modeling, and the parameters received from a real flight of the maneuverable aircraft. The designed simulation model allows us to analyze change of aircraft movement kinematic parameters, defining its flight mode. By the results of the conducted study, it has been defined that halving of normal operational pressure in MLG wheels decreases aircraft landing roll by over forty per cent. Installation of КТ-163D wheels instead of КТ-251А reduces landing roll by approximately a factor of one and a half times, use of brake parachutes reduces aircraft landing roll almost twice at landing on an icy runway. The introduced method is recommended to be used while studying aircraft landing performance during its design or modernization. It is also suggested to integrate the designed method for determining landing performance as a part of on-board information and control system with the view of immediate aircraft landing performance determination in real-time operation in specific flight conditions.

Frequency Domain Analysis of F-16 Aircraft in a Variety of Flight Conditions

Examining the flight quality of an aircraft to ensure the stability of the aircraft, increase maneuverability, and make the aircraft easier to control by the pilot necessitates an examination of the natural stability of the system. Within the scope of the paper, the frequency domain response of the F-16 aircraft dynamics is analyzed using Simulink models considering two different flight regimes because the frequency-domain methods have many distinct and important advantages over time-domain methods. Aerodynamic, propulsive, and atmospheric databases are used to create the nonlinear model. The trim analysis for cruise flights is carried out to obtain trim parameters. The aircraft is numerically linearized using the small perturbation theory. The linearized dynamics for each trim condition are used to create transfer functions for each input. The linear model is subsequently examined in the frequency domain to obtain information about the dynamic behavior of the aircraft, and flight quality analysis was examined by considering the lateral and longitudinal modes of the aircraft by international standards. It has been clearly understood the stability augmentation system design has critical importance for the modes with unstable or long steady-state duration.

Frequency Domain Analysis of F-16 Aircraft in a Variety of Flight Conditions

Examining the flight quality of an aircraft to ensure the stability of the aircraft, increase maneuverability, and make the aircraft easier to control by the pilot necessitates an examination of the natural stability of the system. Within the scope of the paper, the frequency domain response of the F-16 aircraft dynamics is analyzed using Simulink models considering two different flight regimes because the frequency-domain methods have many distinct and important advantages over time-domain methods. Aerodynamic, propulsive, and atmospheric databases are used to create the nonlinear model. The trim analysis for cruise flights is carried out to obtain trim parameters. The aircraft is numerically linearized using the small perturbation theory. The linearized dynamics for each trim condition are used to create transfer functions for each input. The linear model is subsequently examined in the frequency domain to obtain information about the dynamic behavior of the aircraft, and flight quality analysis was examined by considering the lateral and longitudinal modes of the aircraft by international standards. It has been clearly understood the stability augmentation system design has critical importance for the modes with unstable or long steady-state duration.

Estimation of Atmospheric Gusts Using Integrated On-Board Systems of a Jet Transport Airplane—Flight Simulations

Currently, quite accurate measurements of atmospheric gusts are carried out by airport systems only in the vicinity of the runways. There is a still open issue of availability of information about real wind gusts at cruising altitudes and during approach at a considerable distance from the airfield. Standard on-board systems of a jet transport airplane provide some information which is desirable to have knowledge of how flight parameters reflect real gust parameters and their impact on the aircraft dynamics. The paper proposes an algorithm for headwind gust magnitude estimation in relation to aircraft response. The analysed estimation algorithms assume the use of data available from the existing on-board systems only without the employment of any extra sensors or ground and satellite systems. In this way, many problems caused by different structures, configurations, and ways of installation of additional sensors and structural changes are rejected. The algorithms use the classical method for estimation of wind parameters as well as a linear longitudinal model of aircraft dynamics, taking into account the influence of wind gusts. Data fusion was realised with the use of three filtration methods. Results were evaluated to select the most accurate method of the estimation. Test data were obtained from advanced flight simulation. The experimental scenario considered a flight of a passenger twin-engine jet airplane through a layer of programmed gusts. The results of the flight simulations allowed us to determine the accuracy of the proposed gust estimation algorithms in reference to the ideal wind-speed data analysis obtained directly from the simulation environment (with the accuracy of the simulation process). The use of the proposed gust estimation algorithms may provide more accurate signal for integrated on-board systems, especially for wind shear detection and sped-up response time of flight control systems, protecting aircrafts against the adverse impact of encountered wind shear or gusts, e.g., auto-thrust or auto-throttle systems. The dedicated algorithm presented in the paper may increase the safety level of take-off and approach phases in gusty conditions and also during significant changes in wind speed at cruising altitudes in the case of crossing the area of jet stream occurrence.

PROBLEMS OF EVOLUTION OF RIGID BODY MOTION SIMILAR TO LAGRANGE TOP

The problem of evolution of the rigid body rotations about a fixed point continues to attract the attention of researches. In many cases, the motion in the Lagrange case can be regarded as a generating motion of the rigid body. In this case the body is assumed to have a fixed point and to be in the gravitational field, with the center of mass of the body and the fixed point both lying on the dynamic symmetry axes of the body. A restoring torque, analogues to the moment of the gravity forces, is created by the aerodynamic forces acting on the body in the gas flow. Therefore, the motions, close to the Lagrange case, have been investigated in a number of works on the aircraft dynamics, where various perturbation torques were taken into account in addition to the restoring torque. Many works have studied the rotational motion of a heavy rigid body about a fixed point under the action of perturbation and restoring torques. The correction of the studied models is carried out by taking into account external and internal perturbation factors of various physical nature as well as relevant assumptions according to unperturbed motion. The results of reviewed works may be of interest to specialists in the field of rigid body dynamics, gyroscopy, and applications of asymptotic methods. The authors of this papers present a new approach for the investigation of perturbed motions of Lagrange top for perturbations which assumes averaging with respect to the phase of the nutation angle. Nonlinear equations of motions are simplified and solved explicitly, so that the description of motion is obtained. Asymptotic approach permits to obtain some qualitative results and to describe evolution of rigid body motion using simplified averaged equations. Thus it is possible to avoid numerical integration. The authors present a unified approach to the dynamics of angular motions of rigid bodies subject to perturbation torques of different physical nature. These papers contains both the basic foundations of the rigid body dynamics and the application of the asymptotic method of averaging. The approach based on the averaging procedure is applicable to rigid bodies closed to Lagrange gyroscope. The presented brief survey does not purport to be complete and can be expanded. However, it is clear from this survey that there is an literature on the dynamics of rigid body moving about a fixed point under the influence of perturbation torques of various physical nature. The research in this area is in connection with the problems of motion of flying vehicles, gyroscopes, and other objects of modern technology

Research on deployment process of gravitational airdrop UAV

Due to the space limitation of the launching platform, the wings of the space-based gravity delivery UAV need to be folded before launching. In the process of wing folding and launching, the dynamics model of UAV will show the characteristics of multiple rigid bodies and multiple degrees of freedom, and the aerodynamic characteristics of UAV are also quite different from that of cruise stage, so the traditional aircraft dynamics modeling method is no longer applicable. In this paper, the multibody dynamics model of gravitational airdrop UAV is first built based on the Lagrange equation, and then according to the aerodynamic change on unmanned aerial vehicle in deploying process, the angle between the wing and the fuselage is introduced as a new variable, the UAV launch phase nonlinear aerodynamic model is established, and through comparison with software calculation results the reliability of the aerodynamic model is verified. Based on the aerodynamic model and dynamics model, the dynamic response of UAV deployment process is simulated, and the influence of UAV deployment process on UAV subsequent pulling stage under the same control instructions is compared, and the dynamics and kinematics characteristics of gravity launch are studied and explored. Finally, the simulation results are compared with the experimental data, indicating that the multi-body dynamic model established in this paper can accurately describe the dynamic response of UAV in the launching stage and the subsequent modification stage, which can provide reference for the technical personnel engaged in the design, test and use of related models.

System identification method based on interpretable machine learning for unknown aircraft dynamics

Data-driven discovery of dynamics via machine learning has become the frontier work of modeling and control, and also provides great help for expanding the application range of model-based control methods. However, many machine learning methods need huge training data, and the generalization ability outside the training area is limited. These factors impede the development of machine learning in fields such as aerospace. To solve this problem, a new interpretable learning algorithm for aircraft systems is studied, which can consider the influence of control input and be implemented online to respond quickly to the system changes. Simulation results show that compared with the conventional neural network method, the proposed algorithm has higher performance, fewer data demands, and higher computational efficiency. Finally, the model identified online by the proposed algorithm is used in the model-based controller to further verify the effectiveness of this algorithm.

Development and validation of the multicopter modelling code: a physics-based tool for multicopter analysis

PurposeThis study aims to present details of the development and validation of the multicopter modelling code (MMC), a tool for the analysis of small-scale multicopters based on flight physics.Design/methodology/approachThe development effort involved the study of aircraft dynamics and translating the equations of motion into MATLAB code. The authors also developed several auxiliary functions, so that the tool could trim the aircraft about a steady state, linearize the dynamic equations to produce a model that could be used for control systems design and carry out flight simulation.FindingsMMC proved to be of good accuracy, producing results similar to those of other software such as AcuSolve, Overflow and the Rensselaer Multicopter Analysis Code (RMAC), which served as the motivation for this study.Originality/valueThe tool presented here provides an alternative to the aforementioned software, which are not freely available, programmed in MATLAB, a language well known to engineers and scientists.

Identifying transient and persistent errors in aircraft cruise trajectory prediction using Bayesian state estimation

Recorded aircraft trajectory data may vary significantly from predictions based on physics-informed models. This discrepancy may be attributed to inadequacies in the trajectory prediction models, including errors in modeling aircraft dynamics, and omission of inputs such as weather data, equipment malfunctions, and pilot errors. In this work, we represent model errors as additional external inputs to the trajectory prediction model, evaluate them using Bayesian state estimation, and update the trajectory prediction model to address these errors. In doing so, we distinguish between two types of model errors – transient and persistent errors – of which only persistent errors are considered for correction. In this study, we estimate the model error for the completed portion of ongoing flights, separate out the persistent error and account for it in the system model, which allows for an improved prediction of aircraft trajectory for the remaining flight duration. We perform verification and validation of the proposed methodology using both synthetically generated data as well as historically recorded data corresponding to flights affected by adverse weather conditions and engine failure.

An application of interval type-2 fuzzy model based control system for generic aircraft

This paper presents a design application of Interval Type-2 (IT2) Takagi–Sugeno (T–S)​ Fuzzy Model Based (FMB) control system for generic aircraft. The IT2 T–S FMB flight control system consists of an IT2 T–S fuzzy model and a fuzzy controller connected in a closed-loop. The IT2 T–S​ fuzzy model is obtained by linearizing the nonlinear aircraft dynamics about various representative points (equilibrium points) of the flight envelope with some fuzzy rules. The aircraft flight envelope parameters, i.e., operating altitude and aircraft speed are characterized as premise parameters and elements of stability and control derivative matrix are identified as consequent parameters of fuzzy model. Longitudinal dynamics of X-29A research aircraft is selected for design of IT2 T–S FMB control system. To achieve the optimum design flexibility, an imperfectly matched premise and membership function dependent (MFD) stability analysis is considered. In MFD stability conditions, the information of flight envelope parameters is included to capture the nonlinearity pertaining to variation in flight conditions. The closed-loop response of IT2 T–S FMB controller is presented at trim equilibrium points by taking four initial angle of attack flight conditions. The performance analysis of designed controller is also presented and discussed in comparison with Fuzzy LQR and LQR based optimal controllers. The simulation results reveal that proposed IT2 T–S FMB controller not only stabilizes the aircraft dynamics but also provides improved transient performance as compared with Fuzzy LQR and LQR based optimal controllers. This demonstrates the utility of IT2 T–S FMB control system for aircraft/ UAV’s related application.

Effects of landing gear layout on the safe rollout envelope of equipped–skid aircraft

Rollout is an inevitable phase of realizing horizontal landing for an equipped–skid aircraft; therefore, one should pay attention to the safety of the entire rollout process. The research presented herein analyzes the effects of the landing gear layout on the safe rollout envelope, which is the set of all states where the aircraft can remain in the desired state region during the entire rollout phase. First, the nonlinear reachability analysis and its internal relation with a safe envelope are briefly described. To improve the calculation efficiency of approximating the safe envelope, a mixed implicit explicit (MIE) scheme is introduced. Subsequently, a simple yet accurate model of nonlinear aircraft dynamics is established and the dangerous state region during the rollout phase is defined. Finally, based on the numerical results, the effects of the layout type on the safe envelope are discussed. In addition, a reasonable safety evaluation index is proposed to quantitatively analyze the effects of position parameters on the rollout safety. The results indicate that with the application of the variable friction skid, the safe envelope of the wheel–skid aircraft is larger than that of the all–skid aircraft. Compared with the original position parameters, the optimized values increase the rollout safety of the wheel–skid aircraft by 4.18%.

Importance sampling for probabilistic prognosis of sector-wide flight separation safety

This study develops a probabilistic simulation methodology for the en-route safety assessment of multiple aircraft flying within an airspace sector. This assessment is affected by multiple sources of uncertainty, such as external inputs such as wind gust, internal factors such as aircraft component failure, and model errors (e.g., in the aircraft dynamics model) and variability in observed trajectories. The concern is to evaluate whether any pair of aircraft fail to maintain a minimum required lateral separation, and the safety assessment problem involves the prognosis of separation violations between all possible aircraft pairs within the sector, over a duration of interest. Some of the uncertainty sources are modeled as random variables and others as random processes. We combine two deterministic trajectory prediction models – the kinematics-based Generalized National Airspace Trajectory-Prediction System (GNATS), and the dynamics-based Base of Aircraft Data (BADA) – to formulate a probabilistic aircraft dynamic model which also includes model errors as additional external inputs. A computationally efficient importance sampling-based scheme is developed for this safety assessment problem involving a large number of aircraft. This approach is demonstrated using historical flight data, for aircraft operating in the Houston air traffic sector.

Fundamental Framework to Plan 4D Robust Descent Trajectories for Uncertainties in Weather Prediction

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings.

Finite horizon analysis of autolanded aircraft in final approach under crosswind

The paper presents a worst-case touchdown performance analysis of auto-landed aircraft under complex wind disturbance. It takes advantage of the fact that the approaching aircraft effectively follows a predefined trajectory provided by the instrument landing system. Thus, the aircraft dynamics’ linearization along the approach trajectory results in a finite horizon linear time-varying (LTV) representation. This naturally allows to include altitude triggered control law changes and changes in the flight dynamics, e.g., due to ground effect, in the analysis. To cover a broad range of environmental and aircraft parameter combinations in the worst-case analysis, a time-varying trajectory uncertainty description is introduced. The uncertainty’s input/output behavior is covered by integral quadratic constraints. Thus, recent advances on the worst-case gain analysis of finite horizon LTV systems can be used. The corresponding analysis condition is based on a parameterized Riccati differential equation’s solvability, which leads to a readily solvable nonlinear optimization problem. Applying the robust LTV framework, worst-cases for common touchdown criteria, such as vertical touchdown velocity, are calculated. These worst-cases cover the influence of complex wind fields and a large aircraft and environmental parameter set. The results are evaluated against corresponding Monte Carlo simulation on the original high fidelity, industry-sized nonlinear aircraft model.

Aeroelastic evaluation of a flexible high aspect ratio wing UAV: Numerical simulation and experimental flight validation

Aeroelastic phenomena occur when aerodynamic and structural loads interact in an unstable manner. This is a major concern in the design of modern high aspect ratio wing (HARW) aircraft, as these structures are more prone to deflection during flight and thus affecting the flight performance. Studying these effects in full scale aircraft is prohibitively costly and risky. Scaled flight test demonstrators with flexible wings offer a low cost and risk solution to evaluate the aeroelastic response of HARW aircraft. In this work, the sizing, design and testing of an in-house developed flexible-wing unmanned air vehicle (UAV) is presented. First, the rigid-wing aircraft platform and its performance characteristics are presented, followed by the wing modifications to make it flexible. The wing flexibility was designed such that coupling of flight-dynamic modes and elastic modes is observed in-flight. A full numerical characterization of the aircraft was first performed, including structural, aerodynamic and aeroelastic computational models. Next, ground vibration and static loading tests were performed to validate the structural models. Flight tests were conducted to obtain data on aircraft dynamics, and strain measurements along the wing spar. An indirect shape reconstruction method based on strains was employed to extract wing displacements from measured strain data. Flight test data was then compared against simulated aeroelastic results. It was observed that for the HARW flexible wing aircraft, a degree of coalescence between the aircraft short period mode and first out-of-plane bending mode of the wing was present. By using different excitation functions applied to the control surfaces, this coalescence was recorded during flight tests and good agreement with the simulated results was observed. The results obtained are an important step in the study of fluid-control-structure interaction issues in HARW aircraft.

On Structural Parameter Optimization Method for Quad Tilt-Wing UAV Based on Indirect Size Estimation of Domain of Attraction

To deal with the flexibility in the electric aircraft design, this study develops a structural parameter optimization method. The quad tilt-wing aircraft exhibits rotary-wing flight and fixed-wing flight modes by tilting its wings. This study focuses on the domain of attraction, which is a class of state vectors that converge to a static equilibrium point after infinite time. The method indirectly estimates the size of domain of attraction of an aircraft by calculating the radius of a sphere that is encompassed by the domain. In addition, after investigating the relationship between change in structural parameters and the size of the domain of attraction, the structural parameters that maximize the size of the domain are surveyed. The effectiveness of the proposed method is demonstrated for the optimization of the quad tilt-wing aircraft. The quad tilt-wing aircraft exhibits rotary-wing flight and fixed-wing flight modes by tilting its wings. As the characteristics of the dynamics of the quad tilt-wing aircraft demonstrate a significant nonlinear change depending on the tilt angle of the wing, we propose a method to optimize the structural parameters for an easy control of the aircraft. Simulation results show that the optimization scheme identifies the parameters that enable the aircraft to perform agile control to address a disturbance moment. Further, although the same controller is used in the original and optimized aircraft, the optimized aircraft can handle a disturbance in a shorter time when compared with the original aircraft.

Photorealistic simulation platform for autonomous landing of fixed-wing aircraft

To investigate the vision-based autonomous landing of fixed-wing aircraft, we propose a photorealistic simulation platform that leverages ROS, Unreal Engine, and Pixhawk 4. This platform adopts a software-in-the-loop model consisting of rendering, control, communication, and sensor modules. To achieve realistic rendering control, the seawater hydrodynamics and fixed-wing aircraft dynamics are modeled. Based on the platform, we create simulation scenarios under different weather and disturbance conditions for autonomous landing of the aircraft carrier. The platform solves the problem that datasets of related scenes are difficult to collect and experiments are difficult to carry out. To verify the developability of the platform, we design and implement a runway line feature point extraction method (vision-based pose estimation algorithm), and evaluate the performance of the method under various conditions. Experiments show that our software-in-the-loop platform enables vision-based algorithm verification and supports simulation research for the autonomous landing of fixed-wing aircraft.

Adaptive Flight Control in the Presence of Limits on Magnitude and Rate

Input constraints as well as parametric uncertainties must be accounted for in the design of safe control systems. This paper presents an adaptive controller for multiple-input-multiple-output (MIMO) plants with input magnitude and rate saturation in the presence of parametric uncertainties. A filter is introduced in the control path to accommodate the presence of rate limits. An output feedback adaptive controller is designed to stabilize the closed loop system even in the presence of this filter. The overall control architecture includes adaptive laws that are modified to account for the magnitude and rate limits. Analytical guarantees of stable adaptation, bounded trajectories, and satisfactory tracking are provided. Three flight control simulations with nonlinear models of the aircraft dynamics are provided to demonstrate the efficacy of the proposed adaptive controller for open loop stable and unstable systems in the presence of uncertainties in the dynamics as well as input magnitude and rate saturation.