Gust Input Research Articles

Improved Gust Tolerance of a Cyclocopter UAV Using Onboard Flow Sensing

This paper describes the gust rejection study of a twin-cyclocopter micro air vehicle with two cyclorotors and an anti-torque nose rotor. A gust rejection controller relying on velocity feedback and onboard flow sensing was implemented in a closed-loop feedback system. Tethered experiments were conducted with the vehicle mounted on a 6-DOF stand in front of a synthetic gust generation device capable of providing up to 4 m/s step gust input. Planar gusts along the longitudinal and lateral axis of the cyclocopter and crosswinds were systematically studied. Both pitch control (varying nose rotor rpm) and thrust vectoring control strategies were evaluated to counteract perturbation along the longitudinal axis, while the cyclocopter used differential rotational speed of the cyclorotors for lateral gusts. Results showed that thrust vectoring was more effective than pitch control in reducing displacement from gust. Pitch control using the position feedback controller resulted in a maximum gust tolerance of 2.8 m/s with a duration of 3 s. while thrust vector control using the combined flow feedback and position feedback controller was able to withstand 4 m/s step gust input with 1 s duration with only 0.01 m displacement. In addition, flow feedback was more effective than position feedback in minimizing position error. The cyclocopter was also able to mitigate step gusts of 2.8 m/s in magnitude and 3 s duration with crosswind components at 30 deg from the longitudinal axis. The difference in performance can be attributed to the cyclocopter's unique thrust vectoring capability.

Hover Handling Qualities of Fixed-Pitch, Variable-RPM Quadcopters of Increasing Size

Fixed-pitch, variable-RPM quadcopters of increasing size are simulated in hover. Three aircraft sizes are considered, with rotor diameters of 4, 6, and 8 ft(1.2, 1.8, and 2.4 m) and gross weights of 300, 680, and 1200 lb (136, 308, and 544 kg) respectively. Control design is performed for each aircraft using CONDUITR, first using standard ADS-33E-PRF handling qualities specifications. Froude scaling is then applied to the specifications in order to design more comparable, aggressive controllers for the two smaller aircraft. Piloted commands and gust inputs are simulated in the time domain in order to estimate the necessary motor current margins needed for adequate maneuverability local to hover. Of the maneuvers considered, a yaw rate step requires the highest current margin for the smallest aircraft, while the longitudinal velocity step requires the highest current margin for the others, regardless of the Froude scaling of the handling qualities metrics. Using the maximum current values from these simulations, the motor weight fraction is 8.3–10.6% for the 300-lb vehicle, 11.6–13.0% for the 680-lb vehicle, and 15.8% for the 1200 lb. Motor weight requirements can be reduced on the larger two aircraft by flying with the pitch and roll axes exclusively in the attitude command, attitude hold mode, rather than translational rate command. In this case, step commands in yaw rate are limiting for the 680-lb vehicle (10.7–11.8% motor weight fraction) and heave commands are limiting for the 1200-lb vehicle (13.6% motor weight fraction). Estimated motor weight requirements are also reduced by decreasing the rotor inertia and introducing additional filtering into the aircraft commands.

Sparse Gaussian process regression for multi-step ahead forecasting of wind gusts combining numerical weather predictions and on-site measurements

Accurate forecasts of wind gusts are crucially important for wind power generation, severe weather warnings, and the regulation of vehicle speed. To improve the short-term and long-term forecasting accuracy, the sparse Gaussian process regression (GPR) model that reduces the complexity of full GPR is employed for wind gust forecasting by combining numerical weather prediction (NWP) data and on-site measurements. Historical measurements of wind gusts and the European Centre for Medium-Range Weather Forecasts (ECMWF) data are used as inputs of sparse GPR models. In particular, the historical wind gust input allows the sparse GPR model to adapt to the local change of wind speed at specific locations. A moving window strategy is introduced to perform multi-step forecasting and reduce the size of training data. The feasibility of the proposed method is illustrated by measurements collected from the outdoor competition venues in the 2022 Winter Olympics. The presented approach is then compared with the ECMWF, GPR, random forest, ECMWF-Sparse GPR, and ECMWF-MLR models. The results indicate that the proposed method exhibits the best forecasting performance than other models, and it improves the forecasting accuracy in both short-term and long-term time scales.

Design optimization of a wind turbine blade under non-linear transient loads using analytic gradients

This work presents and compares two formulations for the co-design optimization of a wind turbine blade under non-linear transient loads: the Nested Analysis and Design (NAND) and the Simultaneous Analysis and Design (SAND) approaches. Analytic sensitivies are used in order to ensure the convergence of the optimization within reasonable computational resources. The two formulations are compared on a mass minimization problem with dynamic constraints, solved with the interior-point method in IPOPT, for a gust input and a turbulent input. Results shows that the NAND and SAND approaches converge towards the same optimum with similar performances. The SAND approach benefits from a simpler design sensitivity analysis and a sparse jacobian of the constraints.

Testing of Folding Wingtip for Gust Load Alleviation of Flexible High-Aspect-Ratio Wing

Folding wingtips have begun to feature on recent aircraft designs, as a solution for compliance with existing airport gate width regulations while enabling high-aspect-ratio wings for lower induced drag and better overall fuel efficiency. Recent studies have suggested that by allowing folding of the wingtip during flight, additional gust load alleviation can be achieved. This paper describes the first experimental study of the folding wingtip concept, when applied to a highly flexible, high-aspect-ratio wing. Using a low-speed wind tunnel with a vertical gust generator, the experiment examined the load alleviation performance through a range of one-minus-cosine gust inputs and found up to 11% reduction in peak wing-root bending moment. In addition, a movable secondary aerodynamic surface was fitted to the folding wingtip, which demonstrated that such a device was able to control the orientation of the folding wingtip effectively in steady aerodynamic conditions, as well as achieving further reduction in peak wing-root bending moment during gust encounters through active control.

Nonlinear dynamics and gust response of a two-dimensional wing

In this paper, aeroelastic equations for a two-dimensional wing encountering a wind gust are presented and solved numerically. The indicial aerodynamic theory based on Wagner’s function is adopted to obtain aerodynamic forces and moments acting on the wing in the time domain. The dynamics of the wing is approximated via two degrees-of-freedom, i.e. pitch and plunge. The structural stiffness is modeled by a linear translational and a nonlinear torsional spring. Two different types of stiffness nonlinearities are examined: (i) flat spot or dead zone to model free-play, and (ii) hysteresis. For given system parameters, bifurcation diagrams are presented, and time-history, power-spectral density, phase-plane and Poincaré diagrams are shown at different flow velocities. We show that the dynamics of the system with the free-play nonlinearity may be very complex with the possibility of the occurrence of chaos through period-doubling bifurcations. In contrast, the dynamics with the hysteresis nonlinearity is found to be rather simple, where a Hopf bifurcation is the only bifurcation observed. The response of the nonlinear system to sharp-edged and 1-cosine gust profiles are also obtained at different flow velocities and compared to the time response of the system with no gust input. It was found that the gust input may cause the nonlinear system to get attracted to a periodic orbit in the subcritical flow regime. In addition, basin of attraction is obtained for various amplitudes of the sharp-edged gust. It is discussed that as the gust becomes stronger, the likelihood of the occurrence of limit-cycle oscillation increases while the stable points become less dispersed inside the stability map and form a finite region confined to large values of initial conditions.

ドローンの空力特性のモデル化と突風応答改善

Improvement of gust responses is required for the safe operation of the drone. The drone dynamics was modeled based on the nonlinear equation of motion expressed on the body-fixed axis using the aerodynamic forces and moments developed theoretically. The aerodynamics forces and moments were constructed from the blade element theory and momentum theory, which contain the specifications of the drone explicitly. The developed model was applied to the response analysis of the gust input. The sensitivities of the drone specifications to the gust responses were revealed, and the design guidelines were stated. Additionally, disturbance observer was designed and validated by the numerical simulations. It will be applied to the gust alleviation control of the drone.

Strategy for robust gust response alleviation of an aircraft model

The aeroelastic response to time-dependent gusts or turbulence should be considered in airplane design. A robust generalized predictive control law for gust response alleviation is designed and simulated on an aircraft model by using the real wind tunnel response and approximated gust input. Based on the open-loop response of an aircraft model at different test conditions, a nominal Auto Regressive (AR) model with parameter uncertainty is identified. Singular Value Decomposition is designed to reduce the dimension of the uncertainty matrix. Afterwards, with the identified online aeroelastic model and its uncertainty, a robust generalized predictive control (GPC) is applied to alleviate the wing tip acceleration at all test conditions, including varying flow velocities and varying gust frequencies. Finally, the alleviation effect of gust response at different test conditions is estimated based on the comparison of simulated closed-loop acceleration with an experimental open-loop one. The comparison indicates that after robust gust response alleviation control, the wing tip acceleration response can be reduced by up to 70% under all test conditions. Remarkably, the control law is robust to the parameter uncertainties and input uncertainties, which is applicable to the gust alleviation wind tunnel test.

GPC-Based Gust Response Alleviation for Aircraft Model Adapting to Various Flow Velocities in the Wind Tunnel

A unified autoregressive (AR) model is identified, based on the wind tunnel test data of open-loop gust response for an aircraft model. The identified AR model can be adapted to various flow velocities in the wind tunnel test. Due to the lack of discrete gust input measurement, a second-order polynomial function is used to approximate the gust input amplitude by flow velocity. Afterwards, with the identified online aeroelastic model, the modified generalized predictive control (GPC) theory is applied to alleviate wing tip acceleration induced by sinusoidal gust. Finally, the alleviation effects of gust response at different flow velocities are estimated based on the comparison of simulated closed-loop acceleration with experimental open-loop one. The comparison indicates that, after gust response alleviation, the wing tip acceleration can be reduced up to 20% at the tested velocities ranging from 12 m/s to 24 m/s. Demonstratively, the unified control law can be adapted to varying wind tunnel velocities and gust frequencies. It does not need to be altered at different test conditions, which will save the idle time.

On the use of geometry design variables in the MDO analysis of wing structures with aeroelastic constraints on stability and response

A Multidisciplinary-Design-Optimization (MDO) approach for the initial design of wing structures based on the integrated modeling of structures, aerodynamics, flight dynamics, and aeroelasticity, has been developed. The procedure is based on the use of a standard numerical optimizer which employs structural, aeroelastic, and aerodynamic analyzers (a finite-element analyzer for structures, panel method analyzer for aerodynamics, and a longitudinal trim analyzer for flight mechanics) in the MDO process. The space discretizations of the numerical models – namely, the structural and aerodynamic meshes – are dynamically updated as function of wing-structure geometry variables during the optimization process. The geometric-updating procedure has been validated using available analytical solutions for a structural optimization problem. The obtained MDO solutions are essentially based on a first-principle formulation but, in the meanwhile, they do not result to be computationally expansive. Moreover, in order to make the implemented MDO algorithm more computationally efficient and effective, an analytical method based on Matched-Filter Theory (MFT) has been used to evaluate the worst aeroelastic-response case due to a gust input having an assigned energy level with the purpose of obtaining a final design also optimizing the gust-response performance. The optimization capabilities of using geometry design variables vs the standard structural design variables in the MDO process have been highlighted. Moreover, the use of a composite objective function, combining structure and aerodynamic issues, has been shown further capabilities of the presented MDO procedure. Finally, some results are also presented for a benchmark regional aircraft wing to show the potentiality of the approach.

Gust response modeling and alleviation scheme design for an elastic aircraft

Time-domain approaches are presented for analysis of the dynamic response of aeroservoelastic systems to atmospheric gust excitations. The continuous and discrete gust inputs are defined in the time domain. The time-domain approach to continuous gust response uses a state-space formulation that requires the frequency-dependent aerodynamic coefficients to be approximated with the rational function of a Laplace variable. A hybrid method which combines the Fourier transform and time-domain approaches is used to calculate discrete gust response. The purpose of this approach is to obtain a time-domain state-space model without using rational function approximation of the gust columns. Three control schemes are designed for gust alleviation on an elastic aircraft, and three control surfaces are used: aileron, elevator and spoiler. The signals from the rate of pitch angle gyroscope or angle of attack sensor are sent to the elevator while the signals from accelerometers at the wing tip and center of gravity of the aircraft are sent to the aileron and spoiler, respectively. All the control laws are based on classical control theory. The results show that acceleration at the center of gravity of the aircraft and bending-moment at the wing-root section are mainly excited by rigid modes of the aircraft and the accelerations at the wing-tip are mainly excited by elastic modes of the aircraft. All the three control schemes can be used to alleviate the wing-root moments and the accelerations. The gust response can be alleviated using control scheme 3, in which the spoiler is used as a control surface, but the effects are not as good as those of control schemes 1 and 2.

Aircraft gust load estimation due to atmospheric turbulence under different flight conditions

AbstractBased on power spectral technique and Lyapunov approach, methodology to determine the vertical gust load on aircraft encountering atmospheric turbulence under different flight conditions is presented in this paper. Modified longitudinal short period aircraft equations of motion to reflect gust inputs are solved. Family of five linear dynamics models of increasing gust excitation complexity are developed to describe the normal load factor throughout an aircraft due to vertical gust. These models (except Model 2) give a rapid estimation of normal load factor in case complete data are not readily available. Numerical model constructed for a Boeing 747 jet transport is solved to illustrate the results. These results show that Model 5 exhibits higher frequency contents when compared with other models under different flight conditions. The normal load factor of aircraft is estimated at different probabilities of not exceeding the corresponding load factor value based on statistical technique. The Models 1, 3, 4 and 5 predict the load factor with maximum 5% error when compared with Model 2 which considered all gust penetration effects. Finally, the results show a good agreement with the published work in load factor determination, at different probabilities of not exceeding this value when encountering a turbulent vertical gust.

Sensitivities and Approximations for Aeroservoelastic Shape Optimization with Gust Response Constraints

Analytic sensitivities with respect to configuration shape design variables are derived for state-space models of aeroservoelastic systems excited by gust inputs. Minimum-State rational function approximations are used to transform aerodynamic load expressions from the frequency domain to the time domain, and sensitivities of such approximations are extended from terms associated with structural motions to terms associated with the downwash due to gusts. Sensitivity-based approximations of the resulting gust response behavior, including Taylor-Series based direct approximations of the RMS of the response, or Lyapunov equation solutions using Taylor-Series based approximate system matrices are compared. The paper contributes to the development of design-oriented analysis techniques for multidisciplinary design optimization of flight vehicles.

Numerical Simulation and Reduced-Order Modeling of Airfoil Gust Response

I. Abstract Computational Fluid Dynamics (CFD) based simulations, along with parametric and non-parametric Reduced-Order Models (ROM) for gust responses are presented. A CFD code is enhanced to simulate responses of an airfoil to arbitrary shaped gust inputs. Time-domain Auto-Regressive-Moving-Average (ARMA) models are identified based on CFD responses to random gust excitations, using system-identification methods. Responses to discrete gusts of various shapes, amplitudes and gradient lengths are computed via the ROMs and compared to responses simulated directly by the CFD code. The ROMs predict the lift and pitching moment histories accurately throughout the subsonic and transonic regimes. They offer significant savings in computational resources compared to the full CFD simulation, since only one CFD run is required for ROM identification, from which responses to arbitrary shaped gusts can be rapidly estimated. The combination of ROMs and full CFD simulations offers a computationally efficient tool set of various-fidelity time-domain models for gust responses. The ROMs can be used for rapid tuned-gust analyses, and the critical cases can be simulated with a full CFD run, providing pressure distribution for airframe structural design.

Dynamic Response of Aeroservoelastic Systems to Gust Excitation

Frequency-domain and time-domain approaches to dynamic response analysis of aeroservoelastic systems to atmospheric gust excitations are presented. The discrete and continuous gust inputs are defined in either time-domain or stochastic terms. The various options are formulated in a way that accommodates linear control systems of the most general form. The frequency-domain approach is based on the interpolation of generalized aerodynamic force coefficient matrices and the application of Fourier transforms for time-domain solutions. The time-domain approach uses state-space formulation that requires the frequency-dependent aerodynamic coefficients to be approximated by rational functions of the Laplace variable. Once constructed, the state-space equations of motion are more suitable for time simulations and for the interaction with control design algorithms. However, there is some accuracy loss because of the rational approximation. The spiral nature in the complex plane of the gust-related aerodynamic terms is discussed, and means are provided for dealing with the associated numerical difficulties. A hybrid formulation that does not require the rational approximation of the gust coefficients is also presented for optional use in discrete gust response analysis. The various methods were utilized in the ZAERO software and applied to a generic transport aircraft model.

Prediction of Time-Correlated Gust Loads Using an Incremental Stochastic Search

A new algorithm for e nding gust inputs that maximize aircraft response loads subject to a constraint that is dee ned by an existing requirement is described. Such gust inputs have two main applications: the study of time-correlated loads in stress analysis, and the estimation of design loads in design and certie cation analysis. The algorithm is applicable to nonlinear systems subject to commonly satise ed restrictions. The performance of the algorithm is demonstrated on linear and nonlinear cone gurations of a realistic model of a commercial wide-body aircraft, and the results are compared with those generated via two existing search methods.

Effect of wind shear on airspeed during airplane landing approach

Equations are presented for calculating the gust velocity along the landing flight path of an airplane due to the presence of wind shear. Based on this gust input data, airplane equations of motion are solved to determine the minimum airspeed developed during trimmed flight along the landing flight path. Using the developed gust equations, it is shown that the use of a tilted vortex pair provides an improved agreement with measured wind shear velocities. Here, a longitudinal velocity ratio is defined along with a selected vortex core radius. The nonlinear gust velocities are then approximated by a broken line linear ramp gust to use as input gust data for the airplane equations of motion. From this, the minimum airspeed is found along with the flight-path position.

Multivariable flight control for an attack helicopter

This paper discusses advanced flight control for the Apache YAH-64 helicopter. The control laws have been flight tested and were extensively evaluated with fixed-base piloted simulation as part of the Advanced Rotorcraft Technology Integration Flight Experiment. The control system employs as sensors normal and lateral acclerometers and three body rate gyros; for control, it uses collective, tail rotor, and lateral and longitudinal cyclic controls. The control laws were developed to provide decoupling, gust attenuation, desensitization, and stability augmentation in the face of aircraft modeling uncertainty. A multivariable proportional-plus-integral element is the basic ingredient of the control. Various analyses are presented, including frequency and time responses and stability robustness properties using singular-value and structured singular-value techniques. Responses of the controlled helicopter to pilot and gust inputs are examined using time histories.

Study of Rotor Gust Response by Means of the Local Momentum Theory

The vertical gust response of the helicopter rotor in cruising flight is studied analytically by means of the local momentum theory (LMT) and experimentally in a wind tunnel utilizing a gust generator. By introducing the unsteady aerodynamic effects into the LMT and by considering the elastic deformation of the rotor blade, the vibratory characteristics of flapping blades and of the rotor forces can be obtained. Since the LMT makes it possible to calculate the instantaneous load distribution along the rotor blade in desired azimuthal or timewise intervals, the effects of gradual penetration of the rotor into the gust can be studied and the Fourier analysis or power spectrum analysis of the rotor response applied to any kind of gust input. Some results obtained analytically are verified by the experimental tests performed in the wind tunnel which generates step, sinusoidal and random vertical gusts by the motion of a series of cascaded vanes upstream of the rotor.

Aircraft elastic mode control

I 1914, a patent was granted for a Stabilizing Device for Flying Machines, which would counteract the disturbance (gust) and prevent it from having an injurious effect on the stability of the machine. Since then over thirty other U.S. patents related to gust load alleviation have been issued. During the same time period, advances in aerodynamic, structural, propulsion, and control systems technology have resulted in two orders of magnitude increase in speed and altitude regimes of aircraft flight. This performance increase has not been matched by improved aircraft gust response characteristics. Since atmospheric turbulence cannot be avoided entirely, airplanes have been constructed to withstand gust loads. The aircraft dynamic response resulting from gust inputs is usually considered only for determining the estimated additional structural strength needed for survival. At the present time about one structural failure in 10 flying hours is expected and accepted. As yet, the benefits to be gained from gust alleviation control systems have not been realized since such systems have not been applied to a production airplane. A spectacular illustration of the effects of gusts on aircraft occurred on January 10, 1964. A B-52H flying at low altitude encountered a patch of severe turbulence. During the first 5.7 sec, its rigid-body and elastic mode dynamic responses built up until, under a combination of rigid-body and elastic mode excursions, the tail loads exceeded ultimate design values. This B-52 lost 85% of its vertical tail because of the gusts with an estimated peak velocity of 120 fps. Under these circumstances its yaw damper was saturated, resulting in virtually an unaugmented rigid-body dynamic response. The gusts did not fail the tail, but they excited responses that did. Amazinglyj the pilot was able to land this airplane. The effects of turbulence on large flexible aircraft have led to concern in four major areas: ride qualities (crew and passenger comfort as a function of vibration level), structural fatigue life, peak structural loads, and handling qualities. There is also the additional concern of aircraft upsets which on occasion has resulted in disastrous vehicle-pilot-control system interaction.' With the advent of highly flexible airplanes, such as the B-52, XB-70, C-5A, and SST, there is a need for more than rigid-body gust alleviation. Turbulence feeds as much or more energy into the lower-frequency normal elastic modes of these type airplanes as it does into the rigidbody dynamics. Thus, there is a demonstrated need for elastic mode control systems which can suppress the level of normal accelerations at selected locations on the structure. This paper will attempt to survey the research and development which has been done on such systems. It is limited to results in the open literature; although, significant work has been done and documented in several classified reports. Rigid-body gust alleviation research over the years has been extensive and varied, notwithstanding the fact that no system has been incorporated into a production airplane. In 1938, Reiie Hirsch worked out a system which was test flown much later in 1954. In 1950, Douglas Aircraft Company was flying a C-47 equipped with gust alleviation flaps. In 1954, Cornell Aeronautical Laboratory flew a lateral-directional system in a PT-26. NACA performed a significant series of demonstration flights in a C-45 starting in 1952.In England, a Lancaster bomber was flown with a flap gust