Nonlinear Flight Research Articles

Aircraft Load Estimation Using Linear Parameter-Varying System-Based Hybrid Observers

The hybrid loads observer has demonstrated its precision in estimating structural loads and wind disturbances in prior applications. This level of precision is attained by combining a high-fidelity physical, nonlinear flight dynamics model with a data-driven correction model. To mitigate the typically high computational effort, the nonlinear model is substituted in this work with a linear parameter-varying (LPV) system. Therefore, the nonlinear model is approximated by scheduled Linear Time-Invariant models derived from Jacobian linearization. The robustness of this novel approach against parameter uncertainties is evaluated through simulated flight test studies using a subscale test aircraft as an example. It is demonstrated that increased model uncertainties lead to wind estimation accuracy reduction. Additionally, increased parameter uncertainties adversely affect the accuracy of structural load estimation within the model-based (physical) part of the observer. Nonetheless, this loss of accuracy can be compensated by the correction model, leading to the typical high load estimation accuracy of the hybrid loads observer. Finally, experimental data from wind-tunnel tests, utilizing a 1-degree-of-freedom representative test wing, confirms the high estimation accuracy of the LPV-based hybrid loads observer. Despite employing low-fidelity models, achieving high accuracy is feasible while maintaining the characteristic low complexity of the correction model.

Complementary Filter‐Based Incremental Nonlinear Model Following Control Design for a Tilt‐Wing UAV

ABSTRACTThis article presents an incremental nonlinear model following control (INMFC) strategy for a tilt‐wing vertical take‐off and landing (VTOL) unmanned aerial vehicle (UAV). To ensure a good and robust regulation performance, a two‐loop feedback controller, based on the incremental backstepping (IBS) methodology, is used to handle uncertainties and external disturbances robustly. In order to ensure a good mode following and to aid the tracking performance of the flight control system, the first and second‐time derivatives of the desired model response, computed by a model reference (MR) system, are either directly used as feedforward signals for the outer loop or are additionally transformed for the inner‐loop by using an incremental nonlinear dynamic inversion (INDI) grounded approach to transform the signals based on known systems kinematics. In order to uniformly handle the overactuated flight vehicle in both mission model and during the transition, an operation mode‐based weighted incremental linear control allocation approach is applied for safe operation. The performance of the suggested control approach is investigated by utilizing a high‐fidelity nonlinear flight dynamics model of the tilt‐wing system. The results presented in this paper demonstrate that the proposed control approach provides significant benefits for the robust control of the considered tilt‐wing UAV.

Reduced-order helicopter model identification from closed-loop data

This paper presents the development of an algorithm for open-loop transfer functions identification and reduced-order modelling of a dynamical system, from closed-loop data with highly correlated inputs. Suitable for aeronautical applications (particularly for intrinsically unstable vehicles such as helicopters), it allows the identification of aircraft transfer functions from the knowledge of the time histories of arbitrary external inputs and the corresponding actuated controls and responses. After a numerical verification of the proposed approach considering a simple analytical aircraft dynamical system, it is successfully applied to a realistic engineering problem consisting of identifying the transfer functions of the AW-09 helicopter that relate pilot inputs to vehicle attitude and kinematics. It is shown that helicopter responses to arbitrary pilot inputs predicted by the reduced-order model representation of the helicopter dynamics based on the rational approximation of the identified transfer functions are in good agreement with those determined through the high-fidelity nonlinear flight dynamics solver used to evaluate the closed-loop database.

Commonalities between robust hybrid incremental nonlinear dynamic inversion and proportional-integral-derivative flight control law design

Incremental Nonlinear Dynamic Inversion (INDI) has received substantial interest in the recent years as a nonlinear flight control law design methodology that features inherent robustness against bare airframe aerodynamic variations. However, systematic studies into the robust design benefits of INDI-based control over the classical divide-and-conquer philosophy have been scarce. To bridge this gap, this paper compares the setup of hybrid INDI with a standard industry benchmark that is based on two-degree-of-freedom gain-scheduled proportional-integral-derivative control. This is done on an architectural basis and in terms of achievable robust stability and performance levels with respect to a common set of design requirements. To this end, a non-smooth, multi-objective H∞-synthesis algorithm is used that incorporates mixed parametric and dynamic uncertainties in the design objective and constraints. It is shown that close similarities exist between hybrid INDI design and gain-scheduled PID control, which leads to virtually equivalent robustness and performance outcomes in both linear time-invariant and linear time-varying contexts. It is therefore concluded that the main benefit of the hybrid INDI does not lie in improved robustness properties per se, but in the opportunity to perform modular robust design in an implicit model-following context. Specifically, this implies that the areas of flying qualities, robustness, and nonlinear implementation are directly visible and accessible in the control law structure.

Wind Shear Response of Aircraft with C* and C*U Controller during Approach

This study investigates the impact of wind shear on the flight dynamics of commercial aircraft where C* and C*U control laws are employed during the approach phase. Given the high incidence of flight accidents during takeoff and landing attributed to wind shear, this research aims to enhance aviation safety by analyzing control law behavior under varying wind shear conditions. A nonlinear flight simulation model was developed, utilizing aerodynamic and engine data from a B737, to explore the aircraft’s response to different wind shear intensities. The simulation analysis was used to compare the response of the aircraft with C* and C*U controllers, respectively, under different wind shear, and to evaluate the effectiveness of its stability enhancement in wind shear. It was found that in most cases, the controller can achieve a good stabilization effect, but in some cases of wind fields, the aircraft suffered more significant oscillation.

Flight control design for a hypersonic waverider configuration: A non-linear model following control approach

DLR is currently investigating the potential of hypersonic flight systems in the context of different mission scenarios. One configuration type of higher interest for civil and military purposes is the hypersonic glide vehicle (HGV). Such HGVs operate over broad flight envelopes and pose complex flight dynamic characteristics. This article presents DLR’s generic hypersonic glide vehicle 2 (GHVG-2) and proposes an integrated non-linear flight control architecture that is based on the idea of the non-linear dynamic inversion and non-linear model following control methodologies. The proposed control scheme is designed to sufficiently and robustly handle the system dynamics of the over-actuated flight vehicle. The approach is first discussed, and the performance of the suggested control laws is later investigated via simulations of a high-fidelity non-linear flight dynamic model in the nominal case and under the presence of parametric uncertainties. The presented results demonstrate that the proposed NMFC approach provides benefits for the robust control of the regarded hypersonic system.

Quick trim modeling for tiltrotor aircraft in conversion mode

The conversion mode in tiltrotor aircraft is of paramount importance and complexity, necessitating the trim results to ensure stable tilting using the trim model. Quick trim modeling is conducted for tiltrotor aircraft in conversion mode, focusing on the aerodynamics of the rotor using modified lift line theory. Furthermore, we develop the nonlinear flight dynamics of tilt-rotor aircraft. Based on this aircraft model, a double-layer cycle iterations method is employed to establish an efficient and rapid trim model for the tiltrotor in conversion mode at any tilt angle or during any aerial maneuver. Using Boeing Model 222 as an example, trim results for conversion mode are calculated and compared with reference data to validate the effectiveness and precision of our model.

Training Sample Pattern Optimization Based on a Swarm Intelligence Algorithm for Tiltrotor Flight Dynamics Model Approximation

Neural networks have been widely used as compensational models for aircraft control designs and as surrogate models for other optimizations. In the case of tiltrotor aircraft, the total number of aircraft states and controls is much greater than that of both traditional fixed-wings and helicopters. This requires, in general, a huge amount of training data for the network to reach a satisfactory approximation precision and makes the network size rise considerably. To solve the practical problem of reducing the size of the approximating network, efforts have to be made in the efficient utilization of the limited amount of training data. This work presents the methodology of optimizing the sample pattern of the training data set by adopting the metaheuristic algorithm of the particle swarm optimizer improved by the fourth-order Runge–Kutta algorithm. A 6-degree-of-freedom nonlinear flight dynamics model of the tiltrotor aircraft is derived, along with its approximation radial basis function neural network. An example case of approximating a highly nonlinear function is studied to illustrate the principle and main parameters of the optimizer, and the approximation performance of the time-domain response of the unstable nonlinear system is revealed by the study of a Van der Pol oscillator. Then, the presented method is applied to the modeled tiltrotor aircraft for its early and late conversion modes. The optimization scheme shows great improvement in both cases, as the function approximation error is reduced significantly.

High-Speed Virtual Flight Testing Platform for Performance Evaluation of Pitch Maneuvers

To research serious nonlinear coupling problems among aerodynamics, flight mechanics, and flight control during high maneuvers, a virtual flight testing platform has been developed for a large-scale, high-speed wind tunnel, based on the real physical environment, and it can significantly mitigate risks and reduce the costs of subsequent flight tests. The platform of virtual flight testing is composed of three-degrees-of-freedom model support, measuring devices for aerodynamic and motion parameters, a virtual flight control system, and a test model. It provides the ability to realistically simulate real maneuvers, investigate the coupling characteristics of unsteady aerodynamics and nonlinear flight dynamics, evaluate flight performance, and verify the flight control law. The typical test results of a pitch maneuver with open-loop and closed-loop control are presented, including a one-degree-of-freedom pitch motion and a two-degrees-of-freedom pitch and roll motion. The serious pitch and roll-coupled motion during a pitch maneuver at a high angle of attack is revealed, and the flight control law for decoupled control is successfully verified. The comparison of the test results and the flight data of a real pitch maneuver proves the reliability and capability of virtual flight testing.

Fast Trajectory Generation with a Deep Neural Network for Hypersonic Entry Flight

Optimal entry flight of hypersonic vehicles requires achieving specific mission objectives under complex nonlinear flight dynamics constraints. The challenge lies in rapid generation of optimal or near-optimal flight trajectories with significant changes in the initial flight conditions during entry. Deep Neural Networks (DNNs) have shown the capability to capture the inherent nonlinear mapping between states and optimal actions in complex control problems. This paper focused on comprehensive investigation and evaluation of a DNN-based method for three-dimensional hypersonic entry flight trajectory generation. The network is designed using cross-validation to ensure its performance, enabling it to learn the mapping between flight states and optimal actions. Since the time-consuming training process is conducted offline, the trained neural network can generate a single optimal control command in about 0.5 milliseconds on a PC, facilitating onboard applications. With the advantages in mapping capability and calculating speed of DNNs, this method can rapidly generate control action commands based on real-time flight state information from the DNN model. Simulation results demonstrate that the proposed method maintains a high level of accuracy even in scenarios where the initial flight conditions (including altitude, velocity, and flight path angle) deviate from their nominal values, and it has certain generalization ability.

Full envelope nonlinear flight controller design for a novel electric VTOL (eVTOL) air taxi

AbstractOn-demand urban air transportation gains popularity in recent years with the introduction of the electric VTOL (eVTOL) aircraft concept. There is an emerging interest in short/medium range eVTOL air taxi considering the critical advantages of electric propulsion (i.e. low noise and carbon emission). Using several electric propulsion systems (distributed electric propulsion (DEP)) has further advantages such as improved redundancy. However, flight controller design becomes more challenging due to highly over-actuated and coupled dynamics. This study defines and resolves flight control problems of a novel DEP eVTOL air taxi. The aircraft has a fixed-wing surface to have aerodynamically efficient cruise flight, and uses only tilting electric propulsion units to achieve full envelope flight control via pure thrust vector control. The aircraft does not have conventional control surfaces such as aileron, rudder or elevator. Using pure thrust vector control has some design benefits, but the control problem becomes more challenging due to the over-actuated and highly coupled dynamics (especially in transition flight). A preliminary flight dynamics model is obtained considering the dominant effects at hover and high-speed forward flight. Hover and forward flight models are blended to simulate the transition dynamics. Two central challenges regarding the flight control are significant nonlinearities in aircraft dynamics during the transition and proper allocation of the thrust vector control specifically in limited control authority (actuator saturation). The former challenge is resolved via designing a sensor-based incremental nonlinear dynamic inversion (INDI) controller to have a single/unified controller covering the wide flight envelope. For the latter one, an optimisation-based control allocation (CA) approach is integrated into the INDI controller. CA requires special attention due to the pure thrust vector control’s highly coupled dynamics. The controller shows satisfactory performance and disturbance rejection characteristics. Moreover, the CA plays a vital role in guaranteeing stable flight in case of severe actuator saturation.

CONTROL MODEL OF A GROUP OF MANEUVERABLE UNMANNED AERIAL VEHICLES TAKING INTO ACCOUNT THEIR FLIGHT SAFETY

The article deals with the urgent scientific problem of creating an algorithmic support for an automated situational control system for group maneuverable unmanned aerial vehicles, taking into account the possibility of improving their flight safety. To realize this possibility, the authors proposed a non-linear flight model of group formation. This is the basis for the synthesis of nonlinear control laws for these aircraft. The difference of the proposed approach is taking into account the influence of changes in the speed and direction of wind flows on the laws governing the movement of aircraft in a group. Promising areas of research are considered, namely: the application of the results obtained to justify the requirements for the design characteristics of control systems and their algorithmic support in terms of not only improving their flight safety in group formations, but also ensuring the specified performance indicators for a wide range of possible flight tasks by a group of maneuverable aircraft

Research on Pilot Control Strategy and Workload for Tilt-Rotor Aircraft Conversion Procedure

This paper studies the pilot control strategy and workload of a tilt-rotor aircraft dynamic conversion procedure between helicopter mode and fixed-wing mode. A nonlinear flight dynamics model of tilt-rotor aircraft with full flight modes is established. On this basis, a nonlinear optimal control model of dynamic conversion is constructed, considering factors such as conversion corridor limitations, pilot control, flight attitude, engine rated power, and wing stall effects. To assess pilot workload, an analytical method based on wavelet transform is proposed, which examines the mapping relationship between pilot control input amplitude, constituent frequencies, and control tasks. By integrating the nonlinear optimal control model and the pilot workload evaluation method, an analysis of the pilot control strategy and workload during the conversion procedure is conducted, leading to the identification of strategies to reduce pilot workload. The results indicate that incorporating the item of pilot workload in the performance index results in a notable reduction in the magnitude of collective stick inputs and longitudinal stick inputs. Moreover, it facilitates smoother adjustments in altitude and pitch attitude. Additionally, the conversion of the engine nacelle can be achieved at a lower and constant angular velocity. In summary, the conversion and reconversion procedures are estimated to have a low workload (level 1~2), with relatively simple and easy manipulation for the pilot.

Hypersonic target interception based on short-range damage estimation

Aiming at the interception problem of hypersonic target end phase, the flight interception simulation based on semi-active radar guidance is firstly established, and a warhead based on fragment damage is designed. Secondly, research proposes an effective method of target damage and verifies the interception effect by simulation. AUTODYN was used to establish the 3D finite element model based on the nonlinear flight dynamics model, to simulate the damage process and fragmentation dispersion. In this paper, the probability of success of missile interception is estimated by using conditional probability and the distribution of fragment field combined with the miss distance in the interception process and the fragment explosive dispersion law of the steel ball, so as to ensure the destruction of the terminal hypersonic incoming weapon within the safe range.

Optimization of Airplane Landing in Crosswind Conditions for Minimum Tire Wear

Being one of the most critical phases of a flight, landing deserves specific attention, especially when the aircraft is subject to external disturbances such as wind. A notable concern associated with touchdown events, especially when crosswind is present, is tire wear. This work is aimed first at developing a nonlinear flight simulator able to handle the entire landing maneuver in non-null wind conditions, considering the airborne phase, the ground run, and the transition between them. Then, the simulator is included in an optimal process to define the landing technique associated with the minimum tire wear. The methodology is tested in a simulation environment with a realistic model of a reference aircraft, showing that a significant reduction in tire wear can be obtained by optimizing the sideslip angle at touchdown and the lateral–directional controls after the airplane touches the runway with both legs of the main landing gear. The amount of the reduction is highly variable and depends on the landing conditions, e.g., the velocity and glide path angle. It may range from some percentage points up to 45%.

Sensitivity and uncertainty analysis of the nonlinear flight dynamics system of the flexible body

Free flight of a flexible body, such as large slenderness missiles, is a complex process involving rigid-flexible coupling dynamics. The strong flexible effect and the sensitive rotational characteristics caused by large slenderness ratio provide an extreme environment for the rigid-flexible coupled system. To study the performance of nonlinear flight dynamics system of the flexible body under extreme conditions, the trajectory of javelin model with a slenderness ratio of 98.15 flying in vacuum condition is calculated, and the uncertainty and the sensitivity of the coupled system are analyzed for the first time. The Monte Carlo (MC) method and the non-intrusive polynomial chaos (NIPC) method are compared by quantifying the uncertainty in the coupled system with the random moment of inertia of principal axis (Ixx). The uncertainty in the coupled system is quantified using the second-order NIPC method. It is found that the decoupled method is sensitive to the time step due to the unsynchronization of status variables between the rotational equation and structural equation. In contrast, the coupled method is insensitive to the time step. Ixx, stiffness according to the primary modes, and the initial deformation have the largest influence on the uncertainty of the coupled system. The rotational velocity in x direction (ωx) is significantly sensitive to the random inputs. The total uncertainty region of the ωx gradually expands over time.

Flight Dynamics Modeling and Aerodynamic Parameter Identification of Four-Degree-of-Freedom Virtual Flight Test

Compared with the forced oscillation test in a conventional wind tunnel test, the wind tunnel virtual flight test can achieve partially constrained dynamic motion of the model in the wind tunnel by manipulating the control surface deflection. In this paper, a new four-degree-of-freedom (4-DOF) wind tunnel virtual flight test device is established. Compared with the 3-DOF wind tunnel virtual flight test with rotation around the center of mass, the model adds vertical motion, enabling it to simulate free flight more realistically. In this paper, the nonlinear flight dynamics model of 4-DOF wind tunnel virtual flight test is established, the differences in dynamics characteristics between it and free flight are analyzed, and the identification model of aerodynamic derivatives based on 4-DOF wind tunnel virtual flight test is derived. To ensure the safety of the test, the longitudinal altitude control law as well as the sideslip and roll angle control laws in the lateral direction are designed. Finally, a set of aerodynamic parameter identification methods based on a 4-DOF wind tunnel virtual flight test is formed. The output error method is used to identify the aerodynamic derivatives of the test model, and the accuracy of the identification results is higher than that of the 3-DOF wind tunnel virtual flight test.

Improvement of a multi-rotor UAV flight response simulation influenced by gust

Unmanned aerial vehicles (UAVs) are widely used, particularly in urban environments. However, existing studies on multi-rotor UAVs have rarely attempted simulations or experiments considering the significant intensity of gust induced by buildings. This study develops an improved real-time flight simulation for predicting the transient response of a multi-rotor UAV influenced by gust. The unsteady rotor aerodynamics which is appropriate to be implemented in the flight simulation is coupled with the nonlinear flight dynamics to predict the response of UAV due to gust accurately. Further, a straightforward gust estimation approach that is based on the nonlinear flight dynamics is proposed and validated to consider the influence of an unidentified gust. To validate and compare the proposed flight simulation, gust experiment that corresponds to urban operation is performed. The prediction obtained by the proposed flight simulation considering the gust profile was well correlated with the gust experiments. Moreover, using the flight simulation, the transient behavior and rotor aerodynamics are investigated under large gust intensities. It is found that appropriate rotor aerodynamics is crucial to predict the transient behavior of UAV by the effect of large gust intensities. Also, the transient behavior of UAV shows significantly different trend in response to the intensity of gust.

An at-scale tailless flapping wing hummingbird robot: II. Flight control in hovering and trajectory tracking

Flight control such as stable hovering and trajectory tracking of tailless flapping-wing micro aerial vehicles is a challenging task. Given the constraint on actuation capability, flight control authority is limited beyond sufficient lift generation. In addition, the highly nonlinear and inherently unstable vehicle dynamics, unsteady aerodynamics, wing motion caused body oscillations, and mechanism asymmetries and imperfections due to fabrication process, all pose challenges to flight control. In this work, we propose a systematic onboard control method to address such challenges. In particular, with a systematic comparative study, a nonlinear flight controller incorporating parameter adaptation and robust control demonstrates the preferred performances. Such a controller is designed to address time-varying system uncertainty in flapping flight. The proposed controller is validated on a 12-g at-scale tailless hummingbird robot equipped with two actuators. Maneuver experiments have been successfully performed by the proposed hummingbird robot, including stable hovering, waypoint and trajectory tracking, and stabilization under severe wing asymmetries.

Autonomous trajectory planning for multi-stage launch vehicles using mass-projection sequential penalized convex relaxation method

Autonomous trajectory planning for multi-stage launch vehicles poses great technical challenges, mainly because of the highly nonlinear flight dynamics and complex multi-phase structure. Here, this problem is solved by a novel, robust, and efficient approach within the framework of convex optimization. Focusing on the multi-phase difficulty, a mass-projection technique that substitutes the original time independent variable with the mass history is introduced to eliminate the problem’s discontinuous nature and phase-linkage event constraints, then a new sequential relaxation-and-penalization method is proposed to address the resulting problem. All non-convex terms involved in the problem are relaxed to formulate a certainly feasible semi-definite problem, the deviation between which and the true problem is penalized by blending the information from the trust region and semi-definite constraint. The combination of the mass-projection technique and the sequential relaxation-and-penalization method is found to be capable of recovering the original problem and providing the optimal solution rapidly and reliably. Three representative simulations are performed to verify the robustness and computational efficiency of the proposed approach, and comparative results show that it achieves a 100% success rate for all cases, while enabling a 69% to 98% saving of computational time compared to typical methods.