Nonlinear Aerodynamic Model Research Articles

Finite-time nonsingular terminal sliding mode control-based fuzzy smooth-switching coordinate strategy for AHV-VGI

This paper presents a fuzzy smooth-switching coordinate strategy for air-breathing hypersonic vehicle with variable geometry scramjet inlet (AHV-VGI), which can improve the aerodynamic performance of hypersonic vehicle by moving the movable lip to capture more airflow. The longitudinal model of AHV-VGI is firstly formulated, followed by a strict feedback form model. Wherein, the multiple nonlinear aerodynamic models are established with different elongation distance of translating cowl. Secondly, a finite-time nonsingular terminal sliding mode control (NTSMC) method is introduced to develop velocity and altitude subsystem controllers for each model. After that, an interval type-2 fuzzy logic system technique is employed to guarantee the smoothness during switching process between the adjacent NTSMC controllers. Furthermore, the Lyapunov function combined with adaptive laws are constructed to prove the finite-time stability of the closed-looped switching system. Finally, simulation results are provided to validate the effectiveness of these theoretical results.

Post-stall flight dynamics of commercial transport aircraft configuration: A nonlinear bifurcation analysis and validation

Loss-of-control has become the largest fatal accident category for worldwide commercial jet accidents, and any initiative aimed at preventing such events requires an understanding of the fundamental aircraft behavior, especially the flight dynamics at post-stall region at which loss-of-control usually occurred. A series of low-speed static and dynamic wind tunnel tests of the Common Research Model over a large angle of attack/sideslip envelope was conducted and a non-linear aerodynamic model was developed. The bifurcation analysis, complemented by time-history simulation was used to understand the post-stall flight dynamics and the numerical analysis results were preliminary validated by wind tunnel virtual flight test. Several representative post-stall behaviors for the transport aircraft have been identified, including departure, periodic oscillation, post-stall gyration and steep spiral, etc. Furthermore, the predicted periodic oscillation in pitch motion has been perfectly duplicated in wind tunnel virtual flight test. The approach used in this work shows a promising way to uncover the flight dynamics of transport aircraft at extreme and loss-of-control flight conditions, as well as to apply to nonlinear unsteady aerodynamics modeling and validation, flight accident investigation, advanced flight control law design or studying initiative for loss-of-control prevention or mitigation.

Identification of nonlinear aerodynamic damping from stochastic crosswind response of tall buildings using unscented Kalman filter technique

This study presents a new approach for identification of aerodynamic damping of tall buildings from stochastic crosswind response time history using unscented Kalman filter (UKF) technique. The system damping ratio is expressed as a polynomial function of building displacement or velocity, which is equivalent to a polynomial function of amplitude of harmonic motion. The structural system with nonlinear system damping under stochastic excitation is modeled as a single degree of freedom system with a white noise input. The augmented state variables of the system, which also include unknown system frequency, damping and stochastic excitation parameters, are estimated simultaneously with the UKF technique from the response measurement data. The aerodynamic damping is then extracted from the system damping by subtracting the structural damping. Firstly, the stochastic response time histories of a tall building model at various wind speeds with a known nonlinear aerodynamic model are simulated and the performance of the UKF technique and the influence of selections of various parameters involved are investigated. Secondly, the aerodynamic damping of a square-shaped tall building is identified based on aeroelastic building model wind tunnel test data. The response statistics are then computed using the identified damping and compared with the measurement data to verify the accuracy of identification.

Simulating aeroelastic response of a self-sustained oscillating rigid airfoil using a boundary oscillation method

The present study presents a new nonlinear unsteady aerodynamic model to investigate the aeroelastic behavior of a self-sustained oscillating rigid airfoil. Here the unsteady Euler equations are considered simulating inviscid compressible transonic flow over an oscillating airfoil. In regard to providing boundedness criteria, a high-order technique based on a normalized variable diagram scheme has been presented. Since using dynamic mesh for simulating flow over a dynamic airfoil is too complex and requires many computational efforts, the current paper proposes a nonorthogonal and static mesh with oscillation of flow boundary. The results are compared with both well-validated numerical methods and experimental data. A time-marching method is employed to determine system responses. The predicted flutter boundary for NACA0012 airfoil at different free-stream Mach numbers is in fair agreement with direct flutter tools of the Hopf bifurcation points. Finally, the influences of the center of mass and elastic axis position on the system aeroelastic behavior are examined.

Nonlinear flutter control of a long-span closed-box girder bridge with vertical stabilizers subjected to various turbulence flows

This study investigated the influence of different heights of upward vertical central stabilizers (UVCS) in flutter performance of long-span suspension bridges through developing nonlinear three-dimensional Finite Element (FE) bridge model using large-deformation beam elements with 14 degrees of freedom (DOFs). Using Runyang Yangtze River Bridge as a case study, the developed FE model firstly incorporates a nonlinear aerodynamic force model of the 2D closed-box girder with various UVCS, and the model predicted critical flutter wind velocities of the bridges were validated using wind tunnel testing results. A series of parametric studies were then carried out to study the aerodynamic performance of the bridge under different vertical intensities of incoming turbulence flow (Iw) by developing multi-variable non-stationary stochastic wind fields. The numerical results show that the installation of UVCS could not only modify from first-order to second-order symmetrical vertical oscillation configuration, but also change the coupled oscillation from the stable condition to the unstable limit cycle of flutter divergence. Furthermore, UVCS mainly governs the vertical DOF partication in the coupled bending-torsional oscillation of the bridge, while the increase of the height of UVCS results in a higher critical flutter wind velocity but a lower torsional frequency, particularly for the 1.1 m UVCS when Iw is over 2.84%.

Trajectory Estimation of Hypersonic Glide Vehicle Based on Analysis of Aerodynamic Performance

Due to high speed and high maneuverability of hypersonic glide vehicles (HGVs), the state estimation of such targets has always been a research hotspot. In order to improve accuracy of the trajectory estimation, a nonlinear aerodynamic parameter model for target estimation based on aerodynamic performance analysis is proposed. Firstly, the dynamic characteristics of the hypersonic glide vehicle during the hypersonic gliding stage was analyzed. Then, aiming at HTV-2-liked vehicle, the engineering calculation method was used to form the reference aerodynamic model for the target estimation. Secondly, a deviation model described by first-order Markov process was introduced to compensate the uncertainties of the unknown maneuver information from the target. Finally, extended Kalman filter was utilized to estimate the state of the target. The simulation results show that the proposed model is able to improve the accuracy of acceleration estimation for the HTV-2-liked hypersonic gliding vehicles.

Hybrid PD-Fuzzy and PD Controllers for Trajectory Tracking of a Quadrotor Unmanned Aerial Vehicle: Autopilot Designs and Real-Time Flight Tests

This paper presents a hybrid nonlinear control system, comprising of a conventional proportional-differential (PD) controller and a PD-type fuzzy logic autopilot for the trajectory tracking of a quadcopter drone. Given the inherent nature of traditional control, which is model-based, and the essence of fuzzy logic control, which is knowledge-based, the proposed hybrid controllers can provide a more robust solution in the face of uncertainties. Both controllers operate in a parallel incremental form to improve the transient performance and the robustness of the closed-loop control system. Through extensive computer simulations supported by real-time flight tests, this paper highlights the efficacy of the proposed hybrid control system in the presence of some parameter variations, nonlinear aerodynamic models, and some external disturbances (e.g., wind gusts). The Dryden and 1–cos turbulence models are employed to represent the effects of wind gusts under realistic flight environments. The stability analysis of the closed-loop control system is conducted using Lyapunov’s indirect method.

Nonlinear Structural, Nonlinear Aerodynamic Model for Static Aeroelastic Problems

The paper presents the derivation of a modal nonlinear structural model and its coupling with a nonlinear aerodynamic model for static aeroelastic analysis of highly deformable configurations. The structural analysis, intended for geometrically nonlinear structures, computes the deformations of a beamlike structure by dividing it into a few segments. Large deformations are treated as the sum of large, rigid-body displacements of the segment plus small, elastic deformation within the segment. The latter are computed using a modal approach, where the natural modes of each segment are calculated with augmented large fictitious masses to improve the coupling between segments. The use of a modal method in a large-deformation case introduces difficulties in the application of compatibility equations, which are explained and addressed in the paper. The nonlinear aerodynamic model is an equivalent strip theory, in which each section is assigned a database of aerodynamic coefficients. Both the aerodynamic and structural models are suitable for beam-like wing structures and are highly computationally efficient. The numerical examples include three loading cases that validate the implementation of the methodology and demonstrate its use for static aeroelastic applications.

Nonlinear Responses of a Slender Wing With a Store

The aeroelastic characteristics of the slender wing with store have been studied for several years. However, the nonlinear aeroelastic behaviors of the wing-store system have not been understood thoroughly. In this paper, the nonlinear aeroelastic model of a slender wing with a store is constructed. In the model, the geometric structural nonlinearity of the wing, and the kinematic nonlinearities of the wing and the store are considered. Two unsteady aerodynamic models are both employed to determine the aerodynamic loads. One is the linear unsteady aerodynamic model based on Wagner function, and the other is the nonlinear ONERA aerodynamic model. Simulation results are given to show that for the cases of employing the linear unsteady aerodynamic model based on Wagner function, the bifurcation diagrams are very complex and change with the variations of store position. For the cases of using the nonlinear ONERA model, the bifurcation diagrams are very simple and insensitive to the variations of the store position. Additionally, with the decrease of store spanwise coordinate, the system bending oscillation equilibrium position is reduced to zero, and the maximum absolute value of the bending response peak is also decreased. With the increase of the horizontal distance between the wing elastic center and the store mass center, the system response peak is decreased. Moreover, it is found that for the systems with the linear unsteady aerodynamic model based on Wagner function, the obtained response peak is larger and the nonlinear critical velocity is smaller than those with the ONERA model.

Nonlinear behaviors of the flutter occurrences for a twin-box girder bridge with passive countermeasures

The flutter control effectiveness of passive aerodynamic countermeasures for long-span bridges is much dependent on the configuration of these countermeasures. The present study investigated the nonlinear flutter behaviors of a twin-box girder bridge with application of four common types of countermeasures, i.e. upward vertical central stabilizers (UVCS), downward vertical central stabilizers (DVCS), external guide vanes (EGV) and internal guide vanes (IGV). Particularly, the displacement bifurcation, power spectrums, oscillation configurations and failure modes of the bridge with these four countermeasures were systematically studied using a nonlinear aerodynamic force model (NAFM). The model predications were validated using wind tunnel testing data. It shows that the oscillation configuration of the bridge without countermeasures is an anti-symmetrical bending-torsional coupled motion with a hard-flutter phenomenon. Furthermore, the installation of 0.4 h/H UVCS or DVCS could lead to a relatively higher critical flutter wind velocity through prolonging the limit cycle oscillation of soft flutter, especially for 0.4 h/H UVCS. In addition, the flutter performance of the bridge with EGV dominated by the torsional DOF in soft flutter was superior to that with IGV dominated by the vertical DOF in soft flutter.

Nonlinear Model Identification Methodology for Small, Fixed-Wing, Unmanned Aircraft

This paper describes system identification of a nonlinear flight dynamic model for a small, low-cost, fixed-wing unmanned aircraft with a limited instrumentation system. Unique challenges include greater sensitivity to atmospheric disturbances and degraded data quality. Methods are presented to improve the fidelity of the identified model, including use of the vortex lattice method to supplement flight-test data and the synthesis of data from distinct flight-test maneuvers. The parameter estimation strategy is based on the time-domain formulation of the output-error method using the nonlinear flight dynamic equations for a rigid aircraft with a nonlinear aerodynamic model. Methods are presented that increase the accuracy of parameter estimates compared with standard procedures based solely on flight-test data. The paper describes a detailed application of these procedures to a particular small, fixed-wing aircraft so that they can readily be adapted to other aircraft at a similar scale.

Parameters estimation methodology for the nonlinear rolling motion of finned cylindrical body

Identification of nonlinear roll dynamics of finned cylindrical bodies is a critical step when assessing free motion stability and trajectories of aerially dispensed munitions or decoys. In this paper the authors present a parameter estimation process that focuses on identifying nonlinear aerodynamic models that characterize the roll dynamics of a cylindrical body with wrap around fins using data from a series of dynamic wind tunnel tests. This is a three step approach that combines ordinary least squares, stepwise regression and the augmented output-error method, and it is initially tested using simulation data corrupted by white Gaussian noise and then applied to the wind tunnel data. Roll and roll rate dynamics were captured through a series of high angle of attack free-to-roll tests carried out at an airspeed of 35m/s corresponding to a Reynolds number of 800,000. The results and discussion in this paper demonstrate how simulation can be used to develop and mature a system identification routine followed by its assessment through wind tunnel test data. It is shown that high order nonlinear models with up to 14 terms can be parameterized to provide high levels of agreement with roll and roll rate dynamics observed in the dynamic wind tunnel tests.

Reduced-Order Modeling for Nonlinear Aeroelasticity with Varying Mach Numbers

AbstractThis paper proposes a nonlinear aerodynamic reduced-order model robust to different Mach numbers based on a recursive neural network. To model the nonlinear features with varying flow param...

Modeling and switching control of air-breathing hypersonic vehicle with variable geometry inlet

In this paper, a multi-model switching control is developed for air-breathing hypersonic vehicle with variable geometry inlet(AHV-VGI). A variable geometry inlet with the translating cowl is adopted to capture the enough air mass flow for the scramjet engine, which can ensure a more powerful thrust. However, the using of VGI causes the unknown changes of the aerodynamics and thrust, making the model of AHV more complex. Therefore, we firstly analyze the thrust characteristic with the translating cowl and present the conception of optimal elongation distance of translating cowl(EDTC). Consequently, multiple different nonlinear aerodynamic models are constructed by curve fitting for each position of the translating cowl. Then, a switching mechanism dependent on EDTC is proposed and the adaptive RBF neural controllers are designed for velocity subsystem and altitude system of every model. Furthermore, the common Lyapunov functional is constructed to prove the stability of the multi-model switching process. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control approach for AHV-VGI.

An alternative simulation approach for the ONERA aerodynamic model and its application in the nonlinear aeroelastic analysis of slender wings with pylon-store system

The ONERA aerodynamic model is a nonlinear aerodynamic model which includes the effects of dynamic stall. With the strip theory, the ONERA model is usually used in the aeroelastic analysis of slender wings. To the classical approach for the ONERA model, the circulatory and nonlinear parts are all described by using aerodynamic elements and the simulation cost may be very high. In this paper, an alternative simulation approach is proposed to simplify the calculations for the ONERA model, in which the circulatory part of the ONERA model is solved analytically by using Duhamel integral method. In this way, the corresponding aerodynamic loads can be directly expressed in the modal space of the wing motion through only introducing two additional variables. For a slender wing model, the new simulation approach is used to analyze its nonlinear aeroelastic responses. In the simulation, the number of the state variables for the system using the proposed approach is reduced modestly comparing with that using the classical approach. In addition, for a slender wing with a pylon-store system which includes a free-play gap, both the proposed approach and the classical approach with the same number of aerodynamic elements are used to analyze the nonlinear dynamic behaviors of the system. Simulation results are given to show that the pylon-store system with a free-play gap can lead the occurrence of sub-critical Hopf bifurcation for a slender wing. Additionally, some nonlinear dynamic phenomena about the wing-pylon-store system are observed by using the new approach. But these phenomena cannot be predicted by employing the classical approach with the same number of aerodynamic elements used in the new approach. The peak of the post-critical responses obtained from the classical approach are larger than those obtained from the new approach in most range of free-stream velocity. The nonlinear flutter velocity predicted by using the classical approach is lower than that predicted by using the new approach.

Wind-induced nonlinear behaviors of twin-box girder bridges with various aerodynamic shapes

Wind-induced nonlinear oscillations of twin-box girder bridges are very sensitive to the aerodynamic shape of the deck (i.e., slot width ratio (SWR) and wind fairing shape) due to the complicated flow characteristics around the bridge deck. This paper presents a fully integrated finite element (FE) model in time domain, involving a nonlinear aerodynamic force model and a bridge FE model, to allow the investigation of nonlinear oscillation behaviors of long-span twin-box girder bridges with various SWRs and wind fairing shapes. The parameters in integrated FE model were firstly identified by using CFD simulation, and then, the proposed model was validated by conducting wind tunnel testing using sectional models and full-bridge aeroelastic models. It demonstrates that the developed integrated model has the capability of simulating the nonlinear flutter behaviors of twin-box girder bridges with various aerodynamic shapes. Furthermore, the prediction results show that the wind fairing shape has significant impact on the degree of freedom participation in coupled oscillation and failure modes, as well as flutter performance of the bridges. In addition, there is an increase in amplitudes of the limit cycle oscillations with the increase in the SWR of the twin-box girder bridges, and the relationships between the bending-torsional coupled oscillation, failure modes, and SWR of the bridges with anti-symmetric wind fairings are opposite to those with symmetric wind fairings.

Study on the High-Speed and Close of the UVA Cooperative Formation Controller Design

Aiming at the high-speed flight of the UAVs cooperative formation, when a single UAV has occurred, need to exit the formation flight and be close or super close to form of the formation quickly. A fast close cooperative formation controller design method is proposed to make up for low the fighting robustness, and be shortcomings of timeliness poorly and analyze the dynamic characteristic of UAV formation flight. Taking the external factors known into consideration, setting up for the longitude maneuver of nonlinear thrust vector and unsteady aerodynamic model, according to the formation velocity, flat tail rudder angle and thrust vector and pitch angle velocity for corresponding input commend signals for the controller to research the dynamic characteristic of UAV formation flight. Meanwhile, the formation flight distance error is the convergence to a fixed value, and the stability of the cooperative formation flight is good. The simulation of results show that the controller can effectively improve the speed of the close or super close to formation, and maintain the stability of the formation flight, which provides a method of the close or super close formation flight controller design.

Numerical study on the aerodynamic coupling effects of spinning and coning motions for a finned vehicle

A numerical method was used to compute the flow over a four-finned vehicle under supersonic conditions to study the aerodynamic characteristics of a spinning finned vehicle in a coning motion. For each flow condition, the side force and side moment of a combined spinning and coning motion were computed at roll angles of 0°–90°. The results of the non-rolling, coning, and spinning motions were superposed by using a nonlinear aerodynamic model, and the superposed side force and side moment were compared with those of the combined motion. The results indicated significant aerodynamic coupling effects with the combined motion at low Mach numbers and high coning and spin rates. Flow analysis showed that the coupling effects were mainly produced by the shockwaves and expansion waves around fins.

A ground-based test facility for airborne magnetic gradient tensor instruments simulating calibration flights

Progress is slow in terms of the research and evaluation of calibration algorithms for full tensor magnetic gradient instruments using airborne tests. The main reason is that, based on knowledge gained by actual calibration flights, problems exist regarding high risk, high costs, and long development cycles. In this paper, we describe a ground-based simulation facility for calibration flights which combines the nonlinear aerodynamic model with a magnetic interference model. Environmental magnetic fields can be calculated and produced by tri-axial coils, which are measured by the magnetic tensor gradiometer in calibration flights. Influence from systematic errors and magnetic interference can be extracted from the simulated calibration flight provided by the facility. Compared to system evaluation in airborne operation, this method has the benefit of zero risk, low costs, and short duration of evaluation cycles. In view of ground-based multi-degree of freedom motion platforms, it has the advantages of simple manufacture, good dynamic characteristics, and adaptability to different aircraft types.

Nonlinear Rolling Motion of Triform Finned Missiles

A theoretical investigation of the rolling motion of triform configurations at high angles of attack is presented. A nonlinear aerodynamic flow model, derived from strip and slender body theories, is used to predict the aerodynamic roll coefficients of triform tailed missiles at high angles of attack. The flow model predictions are compared to the estimates of a panel-based code and a computational fluid dynamics code at two Mach numbers.