Lateral-directional Dynamics Research Articles

A Simple, Correct Pedagogical Presentation of Airplane Longitudinal Dynamics

Various shortcomings and inaccuracies in the existing approach and presentation of airplane flight dynamics in pedagogy have been identified. An improved pedagogical presentation is offered which is clean - uses the two timescales in longitudinal dynamics to derive short period and phugoid mode parameters, simple - starts with the longitudinal dynamics equations rather than the complete six degree of freedom formulation, and correct - uses a physically correct model of the dynamic (rate) derivatives and employs the concept of a static residual in deriving the slower (phugoid) mode approximations. The redundant and confusing concepts of dimensional derivatives and static stability are junked. A companion paper presents a similar approach to the lateral-directional dynamics.

Revised Analytical Criteria for Aircraft Lateral - Directional Instabilities

Following the recently revised presentation of the theory of small-perturbation flight dynamics by the authors, the present paper considers the newly corrected aircraft lateral-directional equations with trim angle of attack as a parameter. The dynamics is modeled by a set of second-order equations written in matrix form which makes it convenient to derive conditions for onset of instability. The static instability criterion is directly obtained and is seen to match entirely the condition for spiral mode instability. An approximate criterion for dynamic instability is obtained by considering the undamped lateral-directional dynamics, which happens to be a Hamiltonian system. The onset of dynamic instability corresponds to the occurrence of a Hamiltonian Hopf bifurcation which can be explicitly evaluated. This yields a new criterion for dynamic instability which is simpler and easier to use than the Routh discriminant. Also, the new criterion has the Cnβ, dyn parameter as a leading term which explains why this parameter may be used as an indicator for wing rock onset.

A Simple, Correct Pedagogical Presentation of Airplane Lateral-Directional Dynamic

This paper offers a clean and correct pedagogical presentation of the theory of airplane lateral-directional dynamics. In this work, the definition of the dynamic (rate) derivatives has been corrected, distinct timescales corresponding to the standard lateral-directional modes have been identified, and a multiple timescale procedure including static residuals has been followed to derive new literal approximations to the modes. The lateral-directional small-per-turbation equations have themselves been written without having to first derive the complete 6-degree of freedom equations of airplane motion. New, physically meaningful results for the Dutch roll and spiral mode parameters are obtained and discussed. This work complements the revised presentation of airplane longitudinal dynamics in a companion paper.

Prescribed‐time cooperative output regulation of heterogeneous multi‐agent systems

AbstractCooperative output regulation problem has been studied on the basis of an observer which is capable of estimating the state of the leader system in a distributed fashion. However, in the literature, the convergence rate is at best exponential with infinite settling time. To improve the transient performance of the closed‐loop system, a prescribed‐time distributed control law is synthesized to solve the cooperative output regulation problem for a class of linear multi‐agent systems with external disturbances. Different from existing works, we first design a distributed observer to estimate the state of the dynamic leader in the fixed time which is independent of the initial conditions. The design of such an observer extends the results from a homogeneous multi‐agent system to a heterogeneous one. And then a time‐varying distributed control law is designed on the basis of the parametric Lyapunov function technique. The efficiency of our design has been validated in the control of the lateral directional dynamics of aircraft systems.

Stability Augmentation in Lateral Directional Dynamics: A Multivariable Approach

This paper delves into the concept of stability augmentation in lateral-directional dynamics, focusing on a multivariable approach. In aircraft control systems, ensuring lateral-directional stability is crucial for safe and efficient flight. The primary objective is to examine the feedback control system's role in enhancing stability and how it interacts with the aircraft's inherent dynamics. We begin by exploring the basic augmentation system for lateraldirectional dynamics, which includes the feedback of body-axis roll rate to ailerons and yaw rate to the rudder, commonly referred to as the yaw damper. One of the key challenges addressed in this paper is the need to overcome the interference caused by the yaw damper when coordinating turns. This interference results from the constant nonzero yaw rate present during coordinated turns. To address this issue, the concept of "transient rate feedback" is introduced, which uses a washout filter to differentiate the feedback signal and minimize its effect during steady-state conditions. The paper presents mathematical models and transfer functions that describe the behavior of the lateral-directional augmentation system. It discusses the impact of different parameters, such as the time constants of actuators and washout filters, on the system's performance. The design of the feedback loops for roll and yaw control is elaborated upon, emphasizing the trade-offs between roll response, dutch roll damping, and roll-yaw coupling. Simulation results are used to evaluate the effectiveness of the stability augmentation system in improving the aircraft's roll response and dutch roll damping under varying flight conditions. The paper concludes with insights into the challenges and benefits of multivariable control system design for lateral-directional stability augmentation in aircraf

Robust sliding mode augmenting integral backstepping for lateral-directional control of a highly maneuverable aircraft

In this paper, a robust hybrid backstepping and sliding mode control is designed for lateral-directional control of a highly maneuverable aircraft. A systematic approach is implemented in tracking the reference trajectory of a high-fidelity aircraft model, which inculcates non-linear coupled dynamics. A smooth switching function to eliminate the chattering phenomenon is used in the sliding surface and integrated into the backstepping architecture, which guarantees asymptotic stability of the state trajectories. Separate controllers are designed for longitudinal dynamics to address the system in the strict-feedback form, which is an essence of the backstepping methodology. For backstepping control, angular rates are utilized as virtual control inputs in the subsystems considered. Stability analysis is carried out meticulously in the sense of Lyapunov, which guarantees closed-loop system stability. The performance of the considered controllers in the paper is evaluated with the minimum gains by infusing random uncertainties in the aerodynamic model and inertial parameters. Various real-time flight scenarios pertaining to lateral-directional dynamics with and without side-wind are simulated and discussed.

Simplified analytical models for hypersonic lateral-directional stability

The balance of lateral and directional static stability plays an important role in the lateral-directional dynamics and vehicle design. The theory of geometric influence on the lateral and directional static stability is mature for conventional aircrafts. However, the distinct configuration characteristics and flow physics for hypersonic vehicles may lead to different design theory, which is absent now. In order to solve this problem, simplified analytical models of lateral-directional static derivatives are proposed based on the simplified geometry model. It's found that the lateral and directional stability both increase as the deflection angle, dihedral angle, or angle of attack increases, whereas the influence of sweep angle can be neglected. The difference lies in that the lateral stability is proportional to dihedral angle while the directional stability is proportional to the square of dihedral angle. The reasonable accuracy is validated in comparison with the inviscid numerical solutions. Furthermore, the influence mechanism of viscous effects on the lateral and directional stability is investigated in detail based on the numerical results. It's found that the strong viscous interaction can improve the lateral stability evidently, and both the strong viscous interaction and the shear stress can lead to the increase of the directional stability. In addition, the lateral stability is slightly reduced by the chemical nonequilibrium effects.

Self-triggered sliding mode control for Digital Fly-by-Wire aircraft system

The present work copes with the sliding mode control problem for the lateral-directional dynamics of Digital Fly-by-Wire aircraft, which is modeled as Markovian jump systems due to sudden change of the internal parameter. The triggered condition is developed, combining with the designed triggered sliding mode controller, to ensure the reachability of the sliding domain around the specified sliding surface. And then, the sufficient condition is derived to achieve the uniform boundedness of the system state when remaining in the sliding domain. Furthermore, based on the proposed triggered condition, a mode-independent self-triggered scheme is designed to determine the triggering instants, according to which the next triggering instant can be computed in advance by utilizing the state information at current triggering instant. Finally, the simulation results are given to validate the proposed method.

Stability Characteristics of Wing Span and Sweep Morphing for Small Unmanned Air Vehicle: A Mathematical Analysis

Morphing aircraft are the flight vehicles that can reconfigure their shape during the flight in order to achieve superior flight performance. However, this promising technology poses cross-disciplinary challenges that encourage widespread design possibilities. This research aims to investigate the flight dynamic characteristics of various morphed wing configurations that can be incorporated in small-scale UAVs. The objective of this study was to analyze the effects of in-flight wing sweep and wingspan morphing on aerodynamic and flight stability characteristics. Longitudinal, lateral, and directional characteristics were evaluated using linearized equations of motion. An open-source code based on Vortex Lattice Method (VLM) assuming quasi-steady flow was used for this purpose. Trim points were identified for a range of angles of attack in prestall regime. The aerodynamic coefficients and flight stability derivatives were compared for the aforementioned morphing schemes with a fixed-wing counterpart. The results indicated that wingspan morphing is better than wing sweep morphing to harness better aerodynamic advantages with favorable flight stability characteristics. However, extension in wingspan beyond certain limits jeopardizes the advantages. Dynamically, wingspan and sweep morphing schemes behave in an exactly opposite way for longitudinal modes, whereas lateral-directional dynamics act in the same fashion for both morphing schemes. The current study provided a baseline to explore the advanced flight dynamic aspects of employed wing morphing schemes.

System Identification for a Small, Rudderless, Fixed-Wing Unmanned Aircraft

This paper presents a system identification procedure for a class of small, rudderless, fixed-wing unmanned aircraft. The procedure is demonstrated on an aircraft that is equipped with only two aerodynamic control surfaces (called elevons) and one electric motor. A physics-based, first-principles approach is used to obtain the initial model parameters. The initial model is used to design flight tests wherein the longitudinal and the lateral-directional dynamics are separately excited. The aircraft is rudderless and this introduces a key challenge in the model identification. Specifically, the lateral-directional model has more free parameters than can be identified using the elevon excitations alone. This paper resorts to two novel steps to navigate this roadblock. First, this paper uses black-box methods to identify sensitive modes whose damping ratios and natural frequencies change significantly compared with their initial values. Second, gray-box methods are used to update the stability and control derivatives related to these sensitive modes, while retaining the remaining derivatives at their respective initial values. Additional flight tests are conducted to validate the updated model parameters.

Mode decoupling robust eigenstructure assignment applied to the lateral-directional dynamics of the F-16 aircraft

In this paper, a robust controller is designed which is based on the eigenstructure assignment technique. With this technique, the physical modes of the system are decoupled by the appropriate shaping of the eigenvectors. While keeping the desired eigenvector structure as much as possible, Nelder–Mead optimization algorithm is implemented for the search of the optimal robust solution. Different optimization cost functions are investigated in terms of eigenvalue sensitivity and stability robustness. Design solutions are compared with each other and with a fundamental solution in terms of robustness measures. Furthermore, a small amount of flexibility is included in the selection of the eigenvalue locations and the improvement in the robustness is evaluated by singular value analysis. The effectiveness of the control system is demonstrated with nonlinear simulations on the F-16 aircraft mathematical model.

Safe control of trailing UAV in close formation flight against actuator fault and wake vortex effect

In the close formation flight, the wake vortex induced by the leading aircraft will have adverse effects on the safe flight of the trailing unmanned aerial vehicle (UAV). Hence, this paper investigates a difficult problem of safe control for the trailing UAV against actuator faults, input saturation, and wake vortex effect. By using disturbance observers, external wake vortex, disturbances, and internal actuator faults are estimated. Then, with the help of estimated knowledge of disturbance, backstepping control laws are developed for the longitudinal dynamics and the lateral-directional dynamics, respectively. One of the key features of the proposed strategy is that, the inherent problem, i.e., “explosion of complexity” in conventional backstepping control, is solved by the presented dynamic surface control scheme. Another key feature is that external wake vortex, disturbances, and internal actuator faults, input saturation are simultaneously considered. It is shown by Lyapunov stability analysis that the closed-loop system is uniformly ultimately bounded with safety requirements guaranteed even in the presence of wake vortex and actuator faults. The effectiveness of the proposed approach is further validated by simulation results.

An adaptive control architecture for cyber-physical system security in the face of sensor and actuator attacks and exogenous stochastic disturbances

In this paper, we propose a novel adaptive control architecture for addressing security and safety in cyber-physical systems subject to exogenous disturbances. Specifically, we develop an adaptive controller for time-invariant, state-dependent adversarial sensor and actuator attacks in the face of stochastic exogenous disturbances modelled as Markov processes. We show that the proposed controller guarantees uniform ultimate boundedness of the closed-loop dynamical system in a mean-square sense. We further discuss the practicality of the proposed approach and provide a numerical example involving the lateral directional dynamics of an aircraft to illustrate the efficacy of the proposed adaptive control architecture.

Singular Perturbation Control for the Longitudinal and Lateral-Directional Flight Dynamics of a UAV

This paper presents a singular perturbation control strategy for regulating both the longitudinal and the lateral-directional flight dynamics of an Unmanned Aerial Vehicle (UAV). The proposed control strategy is based on a double four-time-scale (4TS) decomposition of the longitudinal and lateral-directional dynamics. The longitudinal dynamics include the altitude, velocity, pitch, and flight path angle dynamics, with the control signals being the elevator deflection and the throttle position, while the lateral-directional dynamics include the side-slip angle, bank angle, yaw rate and roll rate dynamics, with the control signals being the aileron and rudder deflection. The nonlinear control strategy drives the system to follow references in the aerodynamic velocity, the flight path angle and the load factor, which in return provides references in bank angle, side-slip angle and yaw rate. In addition, the control strategy allows to select the desired dynamics for all the singularly perturbed subsystems. Numerical results are included for a realistic nonlinear UAV model, including control saturation and presenting control robustness capabilities under unmodelled dynamics.

Impact of Ground Effect on Airplane Lateral Directional Stability during Take-Off and Landing

Computational simulations of aerodynamic characteristics of the Common Research Model (CRM), representing a typical transport airliner are conducted using CFD methods in close proximity to the ground. The obtained dependencies on bank angle for aerodynamic forces and moments are further used in stability and controllability analysis of the lateral-directional aircraft motion. Essential changes in the lateral-directional modes in close proximity to the ground have been identified. For example, with approach to the ground, the roll subsidence and spiral eigenvalues are merging creating the oscillatory Roll-Spiral mode with quite significant frequency. This transformation of the lateral-directional dynamics in piloted simulation may affect the aircraft responses to external crosswind, modify handling quality characteristics and improve realism of crosswind landing. The material of this paper was presented at the Seventh European Conference for Aeronautics and Space Sciences EUCASS-2017. Further work is carried out for evaluation of the ground effect aerodynamics for a high-lift configuration based on a hybrid geometry of DLR F11 and NASA GTM models with fully deployed flaps and slats. Some aspects of grid generation for a high lift configuration using structured blocking approach are discussed.

Fault‐tolerant control of non‐linear systems based on adaptive virtual actuator

A new adaptive fault-tolerant control architecture for Lipschitz non-linear systems is developed. Specifically, the proposed approach involves a novel adaptive virtual actuator which is inserted between the faulty plant and the nominal controller to hide faults and disturbances from the nominal controller. The envisaged adaptive virtual actuator does not require any information about the nominal controller nor does it require a separate fault detection, isolation and identification unit. Moreover, it can tackle loss of effectiveness and time-varying additive actuator faults as well as an external disturbance, and in addition to the stability of the closed-loop system, it also guarantees that the difference between the states of the nominal and the faulty systems tend to zero. Simulation results corresponding to the lateral directional dynamics of an aircraft demonstrate and illustrate the effectiveness of the proposed adaptive virtual actuator.

Numerical Assessment of the Effect of Leading Edge Vortex Breakdown on the Lateral-Directional Derivatives at High Angles of Attack

Modern fighters design is characterized by slender wings of sharp leading edges (L.E.) and sharp-sided fore-bodies to provide extremely strong L.E. vortices and thus allowing maneuvering at high angles of attack (AoA), and besides improving stealth characteristics as well. These design features caused remarkable changes in the behavior of lateral-directional derivatives at high AoA. In this paper, the behavior of lateral-directional derivatives at high AoA is investigated for a generic fighter model that employs the sharp-edged trend using computational fluid dynamics (CFD). The study concluded that vortex breakdown is a key-element in deteriorating the lateral-directional stability at high angles of attacks. Also, asymmetric lateral-directional aerodynamic loads at high angles of attack were observed as well. The study also observed higher sensitivity to sideslip at high AoA; a small sideslip angle would destabilize the lateral-directional dynamics. The computed lateral-directional derivatives were utilized to predict the onset value of AoA for wing rock with very good agreement.

An H<sub>∞</sub> Design Approach for the Heading Hold Autopilot of a Flying Wing UAV

The paper presents a modified loop shaping approach for the design of the automatic flight control system of an unmanned air vehicle’s lateral-directional dynamics. The design objectives include robust stabilization with respect to modeling uncertainties, heading angle tracking of an ideal model, coordinated turn and reduced sensitivity with respect to low frequency measurement errors. Based on the resulting full order controller one determined a reduced order controller. The numerical results show that both the full order and the reduced order autopilots accomplish the design objectives.

Trajectory tracking for fixed-wing UAV using model predictive control and adaptive backstepping

This paper presents a two layer guidance and control system design for fixed-wing unmanned aerial vehicles (UAV). On the top level, the guidance system makes the airplane follows precomputed references using a novel iterative model predictive scheme, which can handle the nonlinear optimization problem by successive linearizations (starting the algorithm using a robust L1 navigation law which ensures the availability of the solution). The outputs of this algorithm are references in airspeed, flight path angle and bank angle, which are seek by the low level controller also presented in this paper. This controller uses an adaptive backstepping approach for the longitudinal dynamics, and a conventional integral-LQR controller for the lateral-directional dynamics. Simulations show good performances of the overall architecture.

Influence of Accelerometer Location on Autopilot Stability of Reusable Launch Vehicle Attitude Control System

Fly-back phase of any Reusable Launch Vehicle (RLV), with wings, encounters ballistic flight in the absence of aerodynamic forces, in rare atmosphere at high re-entry altitude. Lifting vehicles enter the atmosphere at high angle of attack to increase the drag so that the vehicle velocity can be reduced. High angle of attack also increases the lift to balance the weight for equilibrium glide flight. During high altitude flight, angle of attack and side-slip estimations based on information from inertial sensors and modeled wind, are accurate enough to be used for feedback in attitude control. Once RLV descends below certain altitude and Mach number reduces below certain value, wind's contribution in angle of attack and side-slip becomes prominent and inertial navigation based estimates of these angles, no more remain accurate for their use in attitude control. To overcome this problem, normal and lateral accelerations are directly used in place of angle of attack and side-slip angle, respectively. Two aspect of control law design are covered in this paper which are applicable to descent flight of a typical RLV. First aspect is the impact of change in feedback signals from side-slip angle to lateral acceleration, on stability of lateral-directional dynamics. It is seen that the selection of feedback variables or sensors, significantly changes the achievable stability margins. Second aspect is the role of sensor placement w.r.t. CG, especially lateral accelerometer, on the stability of lateral-directional dynamics. This aspect of sensor placement is being discussed for the first time in any paper. It is seen that proper placement of accelerometer results in better stability margins.