Stability Derivatives Research Articles

Aerodynamic Modeling of a Flying Wing Featuring Ludwig Prandtl’s Bell Spanload

This paper presents the aerodynamic modeling of a flying wing featuring Ludwig Prandtl’s bell spanload. The aerodynamic models are developed using a medium fidelity vortex-lattice method and using a Reynolds-Averaged Navier–Stokes computational fluid dynamics solution across a wide range of in-flow angle conditions. A methodology is developed to directly compare the spanwise force distributions from each method. Excellent agreement is seen in the prediction of spanwise inertial aerodynamic forces from each method, as well as in stability and control derivatives dominated by lift and moment contributions. The phenomenon of proverse yaw, caused by the twist distribution necessary to produce the bell spanload, is seen in the high and low-order analysis, with similar off-axis control power predicted.

Unstable tilt-rotor maximum likelihood wavelet-based identification from flight test data

PurposeThe purpose of this paper is to present the methodology that was used to perform system identification of a dynamically unstable tilt-rotor from flight test data. The method incorporated wavelet transform into the maximum likelihood principle formulation, emphasizing both time and frequency responses. Using wavelets allowed to additionally filter noise in the data, and this increased the estimation quality. This approach did not require measurement and process noise modeling in contrast to the Kalman filter usage for parameter estimation.Design/methodology/approachIn the study, lateral-directional stability and control derivatives of an unstable tiltrotor in hover were estimated. This was performed by applying the maximum likelihood output error method. The estimated model response was decomposed using the Mallat pyramid and matched to wavelet coefficients obtained directly from measurements. In addition, a coherence-based weighting function was used to put more emphasis on the most reliable data. For comparison, the same set of data was used to identify a model with the same structure using the maximum likelihood principle with an incorporated Kalman filter.FindingsIt was found that maximum likelihood principle and wavelet transform allowed for estimating aerodynamic coefficients of a dynamically unstable aircraft. The estimation was performed with high accuracy.Practical implicationsThe designed method can be used for system identification of unstable aircraft and when additional noise is present (e.g. when noise due to turbulence was observable during the flight test or higher noise levels were present in the sensors data).Originality/valueThe paper presents verification of a wavelet-based maximum likelihood principle output error method using flight test data.

Analysis of longitudinal dynamic stability of tandem wing aircraft

PurposeTandem wing aircrafts belong to an unconventional configurations group, and this type of design is characterised by a strong aerodynamic coupling, which results in lower induced drag. The purpose of this paper is to determine whether a certain trend in the wingspan impact on aircraft dynamic stability can be identified. The secondary goal was to compare the response to control of flaps placed on a front and rear wing.Design/methodology/approachThe aerodynamic data and control derivatives were obtained from the computational fluid dynamics computations performed by the MGAERO software. The equations of aircraft longitudinal motion in a state space form were used. The equations were built based on the aerodynamic coefficients, stability and control derivatives. The analysis of the dynamic stability was done in the MATLAB by solving the eigenvalue problem. The response to control was computed by the step response method using MATLAB.FindingsThe results of this study showed that because of a strong aerodynamic coupling, a nonlinear relation between the wing size and aircraft dynamic stability proprieties was observed. In the case of the flap deflection, stronger oscillation was observed for the front flap.Originality/valueResults of dynamic stability of aircraft in the tandem wing configuration can be found in the literature, but those studies show outcomes of a single configuration, while this paper presents a comprehensive investigation into the impact of wingspan on aircraft dynamic stability. The results reveal that because of a strong aerodynamic coupling, the relation between the span factor and dynamic stability is nonlinear. Also, it has been demonstrated that the configuration of two wings with the same span is not the optimal one from the aerodynamic point of view.

An efficient and robust Lagrange multiplier approach with a penalty term for phase-field models

In this paper, we propose and analyze a variant of Lagrange multiplier approach with a penalty term for phase-field models. More precisely, we develop two types of linear second-order decoupled and unconditionally energy stable time-stepping schemes for phase-field models based on the Crank-Nicolson (CN) and the second order backward differentiation formulations (BDF2), where the scalar multiplier variable is evaluated by solving a nonlinear algebraic equation. Comparing with the Lagrange multiplier method (Cheng et al. (2020) [6]) for phase-field models, a scalar penalty term is first introduced to improve the time-step size constraint for the convergence of Newton's iterative algorithm for the nonlinear algebraic equation, which allows us to obtain robust and efficient numerical schemes for phase-field models. Moreover, we only use first order time-stepping scheme to approximate the scalar multiplier variable, which will not affect the second order accuracy of the unknown phase function with some special Lagrange multiplier functions. Meanwhile, it plays an essential role in the derivation of energy stability of the proposed BDF2-based scheme on the nonuniform temporal mesh. In addition, the energy stability of the CN scheme is rigorously established. Furthermore, we deduce that the proposed BDF2 scheme is energy stable with the adjacent time-step ratios no more than 4.8645. Finally, a series of numerical tests are presented to numerically validate the efficiency and stability of our proposed Lagrange multiplier approach.

A linear adaptive second‐order backward differentiation formulation scheme for the phase field crystal equation

AbstractIn this article, we present and analyze a linear fully discrete second order scheme with variable time steps for the phase field crystal equation. More precisely, we construct a linear adaptive time stepping scheme based on the second order backward differentiation formulation (BDF2) and use the Fourier spectral method for the spatial discretization. The scalar auxiliary variable approach is employed to deal with the nonlinear term, in which we only adopt a first order method to approximate the auxiliary variable. This treatment is extremely important in the derivation of the unconditional energy stability of the proposed adaptive BDF2 scheme. However, we find for the first time that this strategy will not affect the second order accuracy of the unknown phase function by setting the positive constant large enough such that The energy stability of the adaptive BDF2 scheme is established with a mild constraint on the adjacent time step radio . Furthermore, a rigorous error estimate of the second order accuracy of is derived for the proposed scheme on the nonuniform mesh by using the uniform bound of the numerical solutions. Finally, some numerical experiments are carried out to validate the theoretical results and the efficiency of the proposed scheme combined with the time adaptive strategy.

Evaluation of derivative in damping in the Newtonian limit for non-planar wedge

The current work derives the analytical expression for damping derivative of a non planar wedge when γ tends to one and Mach number tends to infinity. Ghosh’s developed strip theory is utilized to derive the expression of damping derivative. With regard to a variety of geometrical and flow characteristics, the current theory can forecast the damping derivatives of a non planar wedge. Prior to performing exhaustive calculations and trial research, it is vital to know about these damping derivatives in order to freeze and arrive at the geometrical and kinematic similarity parameters. The ongoing technique, which is exceptionally useful during the plan stage, predicts the damping subordinates in pitch for a flat wedge effortlessly. In the Newtonian limit, the equations derived for stability derivatives become precise. The pivot position is found to influence the damping derivative directly.Additionally, it has been noted that at high angles of attack, the centre of pressure shifts significantly from the leading edge to the trailing edge. Consequently, according to the viewpoint of stability, this behavior may be utilized to stabilize the aeronautical vehicle. Therefore, in this case, the expression for the damping derivative is non-linear, the findings have been affected accordingly. However, the behaviour is linear up to a fifteen degree angle of attack before the pattern becomes non-linear.

Comparison of Linear Flexible Aircraft Model Structures on Large Flexible Tiltrotor Aircraft

Structural modes for large aircraft occur at low frequencies and must be accounted for in the flight dynamics modeling and control system design process. An analysis is performed on various linear representations of flexible aircraft with an application to the lateral/directional flexible dynamic response of the notional Large Civil Tiltrotor (LCTR2) in hover. The goal of the work is to compare the treatment of the coupling between the rigid-body and structural states within various model structures and to develop conversions between the various model forms. The analysis shows that mean-axis and other simplified analytical representations of flexible aircraft, originally developed for fixed-wing aircraft, are also able to correctly capture the dynamic response of a tiltrotor. First, a linear model is obtained from a multibody simulation using numerical perturbation methods. This is compared with a mean-axis model, where structural dynamics are appended onto rigid-body dynamics, as would be obtained if the rigid-body aircraft response were the starting point in an analytical development of the structural coupling. Comparisons are also given with a model that would be obtained from system identification using flight-test data. Key stability and control derivatives are compared to highlight similarities and differences between the various models. The results from the analysis show the multibody model treats the structural coupling in a significantly different way than an analytical model buildup. For example, the structural coupling to roll rate response varies up to two orders of magnitude between the models, yet the overall response is identical. This work shows analysis of the structural/rigid-body coupling developed for analytical models is also valid for models developed from a multibody analysis. Lastly, structural flexibility will be shown to alter the characteristics of the lateral hovering cubic of the LCTR2 by increasing damping of an unstable oscillatory mode.

Parametric model identification of delta wing UAVs using filter error method augmented with particle swarm optimisation

AbstractFrom arsenal delivery to rescue missions, unmanned aerial vehicles (UAVs) are playing a crucial role in various fields, which brings the need for continuous evolution of system identification techniques to develop sophisticated mathematical models for effective flight control. In this paper, a novel parameter estimation technique based on filter error method (FEM) augmented with particle swarm optimisation (PSO) is developed and implemented to estimate the longitudinal and lateral-directional aerodynamic, stability and control derivatives of fixed-wing UAVs. The FEM used in the estimation technique is based on the steady-state extended Kalman filter, where the maximum likelihood cost function is minimised separately using a randomised solution search algorithm, PSO and the proposed method is termed FEM-PSO. A sufficient number of compatible flight data sets were generated using two cropped delta wing UAVs, namely CDFP and CDRW, which are used to analyse the applicability of the proposed estimation method. A comparison has been made between the parameter estimates obtained using the proposed method and the computationally intensive conventional FEM. It is observed that most of the FEM-PSO estimates are consistent with wind tunnel and conventional FEM estimates. It is also noticed that estimates of crucial aerodynamic derivatives ${C_{{L_\alpha }}},\;{C_{{m_\alpha }}},\;{C_{{Y_\beta }}},\;{C_{{l_\beta }}}$ and ${C_{{n_\beta }}}$ obtained using FEM-PSO are having relative offsets of 2.5%, 1.5%, 6.5%, 3.4% and 7.6% w.r.t. wind tunnel values for CDFP, and 1.4%, 1.9%, 0.1%, 9.6% and 7.5% w.r.t. wind tunnel values for CDRW. Despite having slightly higher Cramer-Rao Lower Bounds of estimated aerodynamic derivatives using the FEM-PSO method, the simulated responses have a relative error of less than 0.10% w.r.t. measured flight data. A proof-of-match exercise is also conducted to ascertain the efficacy of the estimates obtained using the proposed method. The degree of effectiveness of the FEM-PSO method is comparable with conventional FEM.

Experimental Assessment of Aero-Propulsive Effects on a Large Turboprop Aircraft with Rear-Engine Installation

This paper deals with the estimation of propulsive effects for a three-lifting surface turboprop aircraft concept, with rear engine installation at the horizontal tail tips, conceived to carry up to 130 passengers. This work is focused on how the propulsive system affects the horizontal tailplane aerodynamics and, consequently, the aircraft’s static stability characteristics using wind tunnel tests. Both direct and indirect propulsive effects have been estimated. The former produces moments whose values depend on the distance from the aircraft’s centre of gravity to the thrust lines and propeller disks. The latter entails a change in the angle of attack and an increment of dynamic pressure on the tailplane. Several tests were also performed on the body-empennage configuration to investigate the propulsive effects on the aircraft’s static stability without the appearance of any aerodynamic interference phenomena, especially from the canard. The output of the experimental campaign reveals a beneficial effect of the propulsive effects on the aircraft’s longitudinal stability, with an increase in the stability margin of about 2.5% and a reduction in the directional stability derivative of about 4%, attributed to the different induced drag contributions of the two horizontal tail semi-planes. Moreover, the rolling moment coefficient experiences a greater variation due to the propulsion depending on the propeller rotation direction. The outcomes of this paper allow the enhancement of the technical readiness level for the considered aircraft, giving clear indications about the feasibility of the aircraft configuration.

Computation of Stiffness and Damping Derivatives of an Ogive in a Limiting Case of Mach Number and Specific Heat Ratio

This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity. In such conditions, these stability derivatives depend on the Ogive’s shape and not the Mach number. Generally, the Mach number independence principle becomes effective from M = 10 and above. The Ogive nose is obtained through a circular arc on the cone surface. Accordingly, the following arc slopes are considered λ = 5, 10, 15, −5, −10, and −15. It is found that the stability derivatives decrease due to the growth in λ from 5 to 15 and vice versa. For λ = 5 and 10, the damping derivative declines with an increase in λ from 5 to 10. Yet, for the damping derivatives, the minimum location remains at a pivot position, h = 0.75 for large values of λ. Hence, when λ = −15, the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.

Wind Estimation Based on Estimation of Lateral-Directional Stability Derivatives of Aircraft

Wind Estimation Based on Estimation of Lateral-Directional Stability Derivatives of Aircraft

Effect of ice accretion on aerodynamic characteristics of pipeline suspension bridges

Pipeline suspension bridges may confront the issue of ice accretion in areas prone to glaze ice or rime. Ice accretion is known to influence the wind-induced responses of various structures, while the effects on the wind-induced responses of pipeline suspension bridges received little attention. To this end, this paper investigated the effect of ice accretion on the aerodynamic characteristics of pipeline suspension bridges from a series of wind tunnel tests. The influences of the shape of cross-section, ice shape, ice class, and Reynolds number on mean aerodynamic force coefficients were examined through static wind tunnel tests. The galloping stability was further examined based on the quasi-steady galloping theory according to the mean aerodynamic force coefficients. Furthermore, the effects of ice class and ice shape on the aeroelastic stability and flutter derivatives of a pipeline suspension bridge were investigated through dynamic wind tunnel tests. The results comprehensively reveal how ice accretion affects the aerodynamic characteristics of the bridge. Ice accretion on the girder can increase the static aerodynamic force, probability of galloping, and leads to vortex-induced vibration. Research results can provide a basis for aerostatic and buffeting analyses and a reference for the wind-resistant design of similar bridges in cold regions.

Nonlinear system control analysis and optimization using advanced Pigeon-Inspired optimization algorithm

The Pigeon-Inspired optimization (PIO) algorithm is a novel intelligent optimization algorithm inspired by birds’ behavior as their travel. This; behavior modeled to be used for solving many optimization problems in different fields. However; it always suffers from unstable behavior when used with nonlinear; time-varying systems. In; this paper, this algorithm is adapted to calculate the optimum controller gains for roll and pitch channels in a guided tactical missile. The; vehicle model is presented in a nonlinear; form and then shown in a linearized form for the sake of an autopilot design. The PIO; algorithm is supported and accompanied by an adaptive algorithm to determine the initial states and constraints for the PIO algorithm to enhance the behavior of the optimization algorithm to speed up the convergence rate to reach an optimum and feasible solution. Also; an estimation function is incorporated to estimate model parameters variation such as dynamic pressure, stability derivatives, and mass properties. Meanwhile; a comparative analysis is carried out with original PIO and particle swarm optimization algorithms, utilizing a non-linear; model with the presence of noise source and disturbance to ensure the ability of the algorithm to make the autopilot robust and stable against several sources of uncertainties.

Adjoint-based limit cycle oscillation instability sensitivity and suppression

Dynamical systems often exhibit limit cycle oscillations (LCOs), self-sustaining oscillations of limited amplitude. LCOs can be supercritical or subcritical. The supercritical response is benign, while the subcritical response can be bi-stable and exhibit a hysteretic response. Subcritical responses can be avoided in design optimization by enforcing LCO stability. However, many high-fidelity system models are computationally expensive to evaluate. Thus, there is a need for an efficient computational approach that can model instability and handle hundreds or thousands of design variables. To address this need, we propose a simple metric to determine the LCO stability using a fitted bifurcation diagram slope. We develop an adjoint-based formula to efficiently compute the stability derivative with respect to many design variables. To evaluate the stability derivative, we only need to compute the time-spectral adjoint equation three times, regardless of the number of design variables. The proposed adjoint method is verified with finite differences, achieving a five-digit agreement between the two approaches. We consider a stability-constrained LCO parameter optimization problem using an analytic model to demonstrate that the optimizer can suppress the instability. We also consider a more realistic LCO speed and stability-constrained airfoil problem that minimizes the normalized mass and stiffness. The proposed method could be extended to optimization problems with a partial differential equation (PDE)-based model, opening the door to other applications where high-fidelity models are needed.

Adaptive Control of Wire-Borne Underactuated Brachiating Robots Using Control Lyapunov and Barrier Functions

Executing safe brachiation maneuvers with a cable-suspended underactuated robot is a challenging problem due to the complications induced by the cable dynamics. We present and experimentally implement an online adaptive controller for a wire-borne brachiating robot swinging on a vibrating cable. An adaptive function approximation approach is proposed to estimate the unknown dynamics of the flexible cable as an external force applied to the robot. Robust control Lyapunov and barrier functions are designed and incorporated into quadratic programs to synthesize a unified adaptive control framework, which formally guarantees the stability and safety of the brachiating robot in the presence of dynamic uncertainties, actuator constraints, and obstacles in the environment. The stability analysis and derivation of the adaptation law are carried out through a Lyapunov analysis. We demonstrate and validate the proposed control framework using extensive hardware experiments with an underactuated brachiating robot operating on a flexible cable. Simulation results, hardware experiments, and comparisons with a baseline controller show that the proposed quadratic programming-based controller achieves reliable tracking performance and disturbance estimation in the presence of model uncertainties, actuator limits, and safety constraints.

Steady-State Aerodynamic Modeling Architecture Overview

An aerodynamic model is a mathematical representation of the behavior of a vehicle in free flight, and the architecture defines the set of variables and equations used to construct the aerodynamic forces and moments. Aeromodels are widely used to represent aerodynamic performance during the design, development, and validation of air vehicles. Architecture selection drives source data requirements and therefore has ramifications for simulation accuracy, program cost, and schedule. This paper describes four approaches appropriate for simple cruciform airframes and provides selection rationale for each. These architectures employ table lookups and the principle of superposition to combine basic stability and control effectiveness components. Body axis mixed architecture provides an efficient method for modeling winged vehicles with limited maneuver requirements. Maneuver mixed-panel architecture enables efficient data collection for a wide range of airframe configurations, providing high accuracy around trim points. Single-panel architecture allows a large domain of flight conditions to be modeled with first-order accuracy using a relatively small data set. Lastly, polar architecture is ideal to reduce the number of independent variable dimensions for spinning projectiles. The architectures described are for the core of the aerodynamic model: steady-state aerodynamic behavior without detailed drag buildup, uncertainty, stability derivatives, transient effects, or application-specific elements.

Flight testing verification of lateral-directional dynamic stability of gliding birds due to wing dihedral

PurposeUnlike conventional aircraft, birds can glide without a vertical tail. The purpose of this paper is to analyse the influence of dihedral angle spanwise distribution on lateral-directional dynamic stability by the simulation, calculation in the development of the bird-inspired aircraft and the flight testing.Design/methodology/approachThe gliding magnificent frigatebird (Fregata magnificens) was selected as the study object. The geometric and mass model of the study object were developed. Stability derivatives and moments of inertia were obtained. The lateral-directional stability was assessed under different spanwise distributions of dihedral angle. A bird-inspired aircraft was developed, and a flight test was carried out to verify the analysed results.FindingsThe results show that spanwise distribution changing of dihedral angle has influence on the lateral-directional mode stability. All of the analysed configurations have convergent Dutch roll mode and rolling mode. The key role of dihedral angle changing is to achieve a convergent spiral mode. Flight test results show that the bird-inspired aircraft has a well-convergent Dutch roll mode.Practical implicationsThe theory that birds can achieve its lateral-directional stability by changing its dihedral angle spanwise distribution may explain the stability mechanism of gliding birds.Originality/valueThis paper helps to improve the understanding of bird gliding stability mechanism and provides bio-inspired solutions in aircraft designing.

System Identification of a Subscale Distributed Electric Propulsion Aircraft

Flight testing of a 21%-scale Cirrus SR22T aircraft with a distributed electric propulsion system was performed with the goal of identifying the influence of distributed propulsion units on the aircraft flight dynamics. Stability and control derivatives for this configuration were identified for a linear aircraft model, including throttle-based control influences of a semispan-distributed array of propulsors. Unknown model parameters were identified from flight test data under unsteady excitation of control effectors using frequency-domain system-identification methods, and the resultant model was validated against independently acquired sets of flight data. The identified throttle-based control derivatives were characteristic of anticipated local thrust contributions from each propulsor and associated proportional yawing moments. Additional throttle-based control influences were also observed, through modulation in the aircraft lift, pitch, and roll characteristics. Furthermore, significant spanwise nonuniformity was observed in the aircraft lift sensitivity to throttle changes, which was linked to three-dimensional influences of the wing aerodynamics. These observations demonstrate the inherent degree of interconnectivity between aerodynamics, propulsion, and control subsystems characteristic of aircraft with distributed electric propulsion systems.

An investigation into directional characteristics of the rocket plane in a tailless configuration

This paper embraces result of wind tunnel tests of a rocket plane designed to space tourism application. The rocket plane is designed in a tailless configuration with a leading edge extension (LEX) and side plates on the wing’s tip which work as all moving tail. Usually for such a concept of control, movable surfaces are position in a horizontal direction while in the considered concept there is no classical rudder, and the movable surfaces are mounted with a significant dihedral angle. The research was carried out in the subsonic closed circuit wind tunnel with an open test section. Moreover, MGAERO and PANUKL package were used for numerical computations. The first research question is to investigate how the configuration of the side plate affects the directional stability of the rocket plane. The second aim is to study the efficiency of the side plates deflected like an all moving tail for both low and high angles of attack. As a result of this investigation, the directional stability derivatives and the control derivatives were obtained. Finally, the experimental results were compared with numerical outcomes to establish does software with no full flow model can be applicable for design an aircraft with all moving tail in case of low of angles of attack.

Stability Evaluation of a Fixed-Wing Unmanned Aerial Vehicle with Morphing Wingtip

Aeronautical applications of morphing technologies are continued to increase their popularity and wide spread application during last years. The technology takes place in not only military, but also civil applications that aims providing superior performances to manned or unmanned aircraft than conventional configurations. However, multidisciplinary approach is required for an aerial vehicle to have ultimate outcome from such an application due to existence of interdisciplinary interactions. Therefore, this research aims to investigate effects of morphing wingtip application on longitudinal and lateral-directional stabilities of a fixed-wing unmanned aerial vehicle, which have remarkable effect on autonomous control performance considerations. In this article, morphing wingtip refers to folding the wing from a determined spanwise location with a dihedral angle. With the aim of the study, wingtips of an unmanned aerial vehicle were folded with 15, 30 and 45 degrees of dihedral angles to be compared with original non-dihedral design. Longitudinal and lateral-directional characteristics of new variations were evaluated in terms of stability derivatives by means of linearized equations of motion that were also presented in state-space representation. Aerodynamic impacts of each variation were assessed by means of computational results obtained from analyses with three-dimensional panel method. Furthermore, taking inertial changes into consideration, concluding remarks on both longitudinal and lateral-directional stability derivatives were presented for each configuration.