Flight Dynamics System Research Articles

Synthetic orbit uncertainty generation through regression analysis of historical Conjunction Data Messages

In the last decades, the Earth-orbiting population of both active and non-active objects has grown significantly, leading to a substantial increase in number of possible in-orbit collisions. It is therefore crucial to monitor the orbit of space resident objects to assess in advance the threat of risky conjunctions. Within this framework, the 18th Space Defense Squadron (SDS) is consistently updating the orbit of thousands of tracked objects by processing observations of the U.S. Space Surveillance Network (SSN). The determined orbital data is continuously maintained in the Special Perturbation (SP) catalogue and used by the 19th SDS to issue close approach warnings to satellite operators around the globe in the form of Conjunction Data Messages (CDM). The Flight Dynamics (FD) group of the German Space Operation Centre (GSOC) receives on regular basis a subset of the SP catalogue data along with CDMs associated to the fleet of its controlled satellites. The SP ephemerides are in fact provided without any covariance information preventing any computation of the Probability of Collision (Pc). In GSOC FD we are implementing a service to link a series of synthetic orbital error covariance matrices to a given SP ephemeris by statistically analyzing historical CDMs of past events. More than 30 GB of past conjunction data are processed to extract state vector, covariance matrix and object size parameter of already encountered secondary objects. The orbital errors of these last are subsequently categorized and divided into orbital classes to decouple the high correlation the covariance has with respect to solar flux, object dimension, altitude of perigee, eccentricity and orbit inclination. The classification aims at collecting similar CDMs regarding the aforementioned dependencies, and approximates the predicted 1-sigma position errors in the orbital frame by optimal curve-fitting techniques. By evaluation of the curve fitting coefficients of a requested orbit class a covariance matrix can be generated for any prediction time in upcoming CDM refinements and other analyses. The work discusses the limiting cases of the classification approach, bringing possible solutions to the scenario of empty classes. An in-depth characterization of the parameters that affect the orbital errors is in fact performed to individualize the neighboring class that provides the closest and most meaningful covariance timeline. Successively, the effect of using synthetic covariance in a conjunction risk assessment is also explored, adapting the problem on real operations. Lastly, the entire data processing pipeline and how the described service fits into the GSOC Flight Dynamics System (FDS) framework is described.

Zonotopic estimation for asynchronous switched system with application to missile flight system

Interval estimation for asynchronous switched systems is investigated on the basis of zonotope. A particular zonotopic estimation framework that includes center estimation and P-radius estimation is presented. In the light of robust stability theory, an asynchronous robust observer, which is used in the center estimation, is established. And the P-radius estimation is conducted by zonotopic set-membership estimation theory. The proposed framework reduces the conservatism that exists in interval observer design methods. Besides, to maintain a high accuracy, the direct method that disregards order reduction is applied instead of the iterative method in this framework. Finally, the simulation of a missile flight dynamics system is carried out to illustrate the validity of the estimation framework.

Experimental Stability Analysis of Vertical Takeoff and Landing System Based on Robust Control Strategy

The Vertical Take-Off and Landing (VTOL) system is a multi-variable system subjected to harsh weather conditions, which creates challenges in proving the stability of the system before takeoff, which is essential for a flight dynamics system. The presented research work is based on the experimental results of the VTOL system to investigate and prove the stability using Lyapunov theory. This is achieved by tracking the pitch along the x-axis using cascaded control and integral super twisting sliding mode control (ISTSMC) algorithms. The motor current of the propeller assembly is regulated based on proportional integral (PI) and proportional integral derivative (PID) controllers. The cascaded control shows the maximum tracking error due to high-frequency fluctuations in the controller input signal, which lead to expensive mechanical losses for the actuators. The comparison of the results shows that ISTSMC outperforms the cascaded control strategy by reducing the tracking error to less than 1% percent and reducing the high-frequency fluctuations in the controller input signal. The hardware results show a minor delay in the transient response during vertical takeoff due to the inertia of the system and the tracking error due to air friction, etc., of the external environment, compared to the simulation results obtained in MATLAB.

Advancements in the Theory and Practice of Flight Vehicle System Identification

System identification methods have played an essential role in the research and industry projects at the Institute of Flight System Dynamics of the Technical University of Munich. Besides the application of the established system identification approaches to multiple aircraft, novel methods have been developed at the institute to deal with the challenges associated with fixed- and rotary-wing aircraft system identification in the time and frequency domains. This paper provides an overview of these new developments, as well as practical application examples from the past and ongoing projects at the institute. After a brief introduction to the work at the institute, the paper describes the new advancements in the fields of time domain system identification and optimal input design by introducing optimal control methods. It continues with an alternative problem formulation for applying frequency domain system identification and parameter estimation methods to a novel flight control design and tuning approach. Additional topics from the past and ongoing research at the institute such as novel methods and practical findings in rotorcraft system identification and flight path reconstruction for different applications will be discussed and referenced.

SWOT re-entry: Maneuver strategy and risk computation

The Surface Water & Ocean Topography (SWOT) mission is a joint NASA/CNES mission launched on December 16th, 2022 dedicated to oceanography and continental hydrology. Once the scientific mission is over, SWOT will have to perform a controlled re-entry to comply with the French Space Operation Act (FSOA). Indeed, the launch authorization is subject to the respect of the FSOA, fully applicable since 2020. The main requirement applying to the end-of-life of the satellite consists in limiting the casualty area and then the probability of having a victim on ground under the threshold of 10−4 in case of a natural re-entry. With a mass over two tons and a casualty area of about 47 m2, SWOT cannot comply with this requirement. Thus, the platform has been designed with a specific propulsion system to carry out end-of-life maneuvers leading to an atmospheric re-entry and impact in the South Pacific Ocean Uninhabited Area (SPOUA). CNES is in charge of defining the re-entry maneuvers strategy, performing end-of-life operations and evaluating the risk of casualties in case of failure during nominal strategy. This paper addresses these topics. The computation of the ten maneuvers used to decrease the perigee altitude and finally target the SPOUA is performed using the DOORS tool. Before describing the maneuvers strategy, this paper presents an overview of the current functionalities of this tool, which has been already used during the five ATV missions and ASTRA-1K de-orbit twenty years ago. DOORS is mainly used for mission analysis purposes, but for end-of-life operations it can be activated by the operational Flight Dynamics System (FDS). Finally, the casualty risk estimation relies on the use of two other CNES tools, DEBRISK and ELECTRA, whose methods are presented. The list of surviving fragments has been computed using the new DEBRISK-V3 methodology in case of controlled and uncontrolled re-entry. The risk of human casualty is evaluated using ELECTRA and its Monte Carlo simulations. This tool generates numerous trajectories of the satellite and its fragments with various dispersed variables. The impact locations compared to an up-to-date grid of the World population lead to the probability of victims. The complete risk of SWOT controlled re-entry encompasses both the risk related to a failure during the last re-entry maneuver and the risk associated with the natural re-entry in case a failure occurs before this last burn (during the mission or during the first re-entry maneuvers). Both of them are weighted by their probability of occurrence.

Advances and Modern Applications of Frequency-Domain Aircraft and Rotorcraft System Identification

This paper provides an overview of advances and applications of aircraft and rotorcraft flight dynamics system identification at the U.S. Army Combat Capabilities Development Command Aviation & Missile Center over the past 20 years. An overarching topic is how frequency-domain system identification has evolved to aid modeling work of modern aircraft and rotorcraft configurations. The paper starts with a brief overview of the frequency-response method for system identification. Subsequently, the paper highlights and demonstrates several new advances using flight-test data from a conventional helicopter, fixed-wing aircraft, advanced coaxial compound rotorcraft, and a small multirotor unmanned aerial vehicle. The first advancement is the use of identification results to improve simulation model fidelity. The next advancement is the Joint Input-Output Method for identification of aircraft with highly correlated inputs. Next, the paper discusses the advancement of flexible constraints, which provide the ability to directly determine physical parameters from flight-test data. The paper then discusses a methodology to identify lower-order linearized dynamic inflow models from higher-order free wake aerodynamic models. Finally, the paper discusses model stitching, which is the technique of combining or stitching together individual linear models and trim data for discrete flight conditions to produce a continuous, full flight-envelope real-time stitched simulation model.

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

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

FLIGHT DYNAMICS AND STABLE CONTROL ANALYSES OF MULTI-BODY AIRCRAFT

Multi-body aircraft is a new concept aircraft consisting of multiple small unmanned aerial vehicles hinged-connected by wing tips. This concept aircraft can integrate the performance and advantages of two types of flying platforms: small unmanned aerial vehicles and high-altitude long endurance unmanned aerial vehicles. It has great development potential. Based on the Newton-Euler equation and on the lifting line method, it establishes a multi-body aircraft flight dynamics model, and analyzes the trim and stability characteristics of the multi-body aircraft system that allowing the relative degree of freedom of rolling motion with the dual-aircraft combination. The results show that, different from the traditional configuration aircraft, the multi-body aircraft system has an unstable relative motion flight mode, which is dominated by relative rolling motion. This configuration aircraft cannot fly stably in an uncontrolled situation. Based on the completion of the dynamics modeling, the Proportion-Integration-Differentiation control method is used for stable control. The stable control loop is designed separately for each single aircraft to achieve the purpose of stable flight. The simulation results show that the control method is effective and can quickly stabilize the divergent flight dynamics system.

Nonlinear Longitudinal Aerodynamic Analysis at Low Speed Delta Jet Fighter

This study examines the application of the bifurcation theory to the reduced-order of longitudinal flight dynamic systems. An investigation of steady and unsteady longitudinal aerodynamic coefficients is carried out, including an extended range of pitch up and down reduced frequencies from 0 - 0.06 values. An aircraft with a general delta wing with a 1.5 aspect ratio is chosen for the present analysis. Different elevator control deflection from -28.6 to 0 degrees is used to determine the equilibrium points α and q. The unsteady aerodynamic load results increase the requirements for control power as well as thrust vectoring during pitch up than steady longitudinal one. The flow unsteadiness effect improves the vehicle stability during pitch up corresponding a loosing of it during pitch down. A positive pitch rate is required to point the nose of the fighter. This improvement in pointing will help in the close maneuvering missions.

LARUS: an unmanned aircraft for the support of maritime rescue missions under heavy weather conditions

In maritime emergencies, the time until arrival at the scene of an accident is a decisive factor for a successful rescue operation. In this context, the research project LARUS aims to support the rescue forces at sea with unmanned aerial systems and thus to optimize the rescue process. This refers on the one hand to the localization of potential accident sites and on the other hand to informing the rescuers about the situation on site as well as the provision of an efficient communication infrastructure. For this purpose, the UAS is equipped with various sensors and communication media. To ensure a seamless rescue procedure, the aircraft must be capable of operating even under severe weather conditions. In this regard, the Institute of Flight System Dynamics is currently investigating measures to reduce the gust loads to make the UAS robust against challenging weather conditions. The integration of the LARUS aerial system into airspace using an active collision avoidance system is also an important research aspect. In addition, the adaptation of flight control to the expanded requirements and influencing factors as well as the implementation of international SAR search strategies for flight guidance are also the subject of development work.

F-16/MATV; Optimal Position Controller Design using Robust and Discrete Linear Quadrature Gaussian [RLQG] Controller

This paper presents the robust controller design for nonlinear F-16/MATV (Multi–Axis – Thrust - Vectoring) position control system. The linearization of nonlinear flight position system is guaranteed by feedback linearization using Taylor series expansion and the optimal LQG controllers are designed to achieve the steady state flight condition. The comparison of the using continuous and discrete LQG is fully discussed for control system. First the continuous optimal LQG controller is designed for continuous time state space represented flight dynamic system based on separation principle. But the designed optimal LQG controller requires a very large controller gain to achieve the design objective, which lacks high sensitivity and leads to highly cost system. This leads to design a controller using discrete LQG controller for discrete time state space represented flight control system. After implementing this controller into the system in MATLAB Simulink environment, using singular value decomposition technique, it is founded that the performance and robustness of the design objective is satisfied.

Polynomial Chaos-Based Flight Control Optimization with Guaranteed Probabilistic Performance

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failure probability under chance constraints is conducted. Afterward, a time-dependent polynomial chaos expansion is performed to validate the results. With this approach, the failure probability is reduced while guaranteeing the closed-loop performance, thus increasing the safety margin. Simulations are carried out on a longitudinal model subject to uncertain parameters to demonstrate the effectiveness of this approach.

Validation of decision logic of an autoland system for a UAV using model-based safety-assessment techniques

Software of automatic flight control systems requires thorough verification and validation. Traditionally, this is achieved with elaborate development processes following pertinent industry standards. To reduce the development effort, however, new methods have emerged: a model-based software development process is used at the Institute of Flight System Dynamics of the Technical University of Munich for the design of auto-flight systems with MATLAB/Simulink. Besides, the model-based safety assessment (MBSA) framework ExCuSe has been developed, which implements methods for fault modeling and automatic cut-set extraction using the Simulink Design Verifier. This paper proposes an application of MBSA techniques for the efficient requirements and design validation of decision logic in auto-flight-system software. With ExCuSe, software design models of an investigated decision logic are supplemented by models for off-nominal inputs (e.g., a sensor fault) and for the design requirements. With the analysis, either a formal proof is obtained that the investigated decision logic fulfills the requirements under any circumstances (guaranteed properties), or a counterexample illustrates a requirement violation. The functional principle and applicability of the method are demonstrated by the analysis of decision logic of the autoland system of the SAGITTA Demonstrator UAV. ExCuSe is used to prove that the logic guarantees a timely flare initiation so that a safe touchdown sink rate is achieved despite altitude-measurement inaccuracy and closed-loop flare dynamics uncertainty. As virtually all auto-flight systems feature decision logic, this initial demonstration of the technique opens up many opportunities for further applications in future work.

Study on flight dynamics of flexible projectiles based on closed-loop feedback control

Since projectiles with large slenderness ratio are prone to elastic deformation, the effect of structural deformation is necessary to be taken into consideration for dynamic modeling. In order to obtain the precise aerodynamic performance and flight dynamic characteristics of flexible projectiles, a new numerical flight simulation system is developed based on computational fluid dynamics and generalized dynamic-mesh technique. Furthermore, flight dynamic stability of a typical flexible projectile is carried out in detail by introducing PID controller. By means of installing the sensors at various locations, the effect of different mode shapes on the characteristics of the closed-loop flight dynamic system is researched. Numerical results indicate that, when the disturbance due to elastic vibration is added into the mixed signals gained from the angular velocity/acceleration sensors, the feedback response of the closed-loop system becomes adversely divergent. In contrast, the stability of the closed-loop system is not sensitive to the elastic disturbance added to the centroid velocity and acceleration. Moreover, the stability of closed-loop system is much less affected by the unsteady aerodynamic loading due to elastic vibration than the interference of the elastic vibration on the dynamic signals detected by the sensors. The phenomenon can be explained by the requirement on the stability of the long and short period modes of flight dynamics, which can provide some guidance for the layout of the sensor and the design of control system of the projectiles with large slenderness ratio.

Design and validation of flight dynamics system

Design and validation of flight dynamics system

Dynamic Optimization of High-Altitude Solar Aircraft Trajectories Under Station-Keeping Constraints

This paper demonstrates the use of nonlinear dynamic optimization to calculate energy-optimal trajectories for a high-altitude, solar-powered unmanned aerial vehicle (UAV). The objective is to maximize the total energy in the system while staying within a 3 km mission radius and meeting other system constraints. Solar energy capture is modeled using the vehicle orientation and solar position, and energy is stored both in batteries and in potential energy through elevation gain. Energy capture is maximized by optimally adjusting the angle of the aircraft surface relative to the sun. The UAV flight and energy system dynamics are optimized over a 24 h period at an 8 s time resolution using nonlinear model predictive control. Results of the simulated flights are presented for all four seasons, showing an 8.2% increase in end-of-day battery energy for the most limiting flight condition of the winter solstice.

Terminal sliding mode control for cyber physical system based on filtering backstepping

Based on a nonlinear flight dynamic model with aerodynamic coefficients and external disturbance uncertainties, which is a typical cyber physical system, a filtering backstepping terminal sliding mode control method is proposed for a robust controller. The tracking differentiator can provide the capability of solving the problem of complexity explosion in backstepping controllers to simplify the backstepping implementation. Nonlinear disturbance observers are used to observe the uncertainties of the nonlinear flight dynamic system. The terminal sliding mode controller is designed to improve its convergence rate and the tracking accuracy. Finally, nonlinear 6-degree-of-freedom simulation results for an F-16 aircraft model elaborate the effectiveness of the proposed control system.

Stochastic contraction-based observer and controller design algorithm with application to a flight vehicle

This paper focuses on a stochastic version of contraction theory to construct observer-controller structure for a flight dynamic system with noisy velocity measurement. A nonlinear stochastic observer is designed to estimate the pitch rate, the pitch angle, and the velocity of an aircraft example model using stochastic contraction theory. Estimated states are used to compute feedback control for solving a tracking problem. The structure and gain selection of the observer is carried out using Itô's stochastic differential equations and the contraction theory. The contraction property of integrated observer-controller structure is derived to ensure the exponential convergence of the trajectories of closed-loop nonlinear system. The upper bound of the state estimation error is explicitly derived and the efficacy of the proposed observer-controller structure has been shown through the numerical simulations.

Analytical Solution of Uniaxial Flight Systems Using Volterra Kernels in Frequency Domain

In previous research, a nonlinear analytical solution of the low-order flight system using Volterra kernels in the time domain was developed. In this paper, equivalent analytical solutions using Volterra kernels in the frequency domain is addressed. A two-term truncated Volterra series is developed for first-order and second-order generalized nonlinear single degree of freedom systems. The resultant models are given in the form of first and second kernels in the frequency domain. A parametric study of the influence of each linear and nonlinear term on kernel structures is investigated. Periodic input is then employed to quantify and qualify the nonlinear response characteristics. A uniaxial pitch motion example is presented as a low-order flight dynamic system. This example shows the ability of the proposed analytical Volterra-based model over the analytical linear model to predict, interpret, and analyze the nonlinear behavior.

TLE를 이용한 우주물체 궤도예측 정밀도 향상 연구

This paper describes an improvement of space objects orbit prediction. To screen possible collisions between operational satellites and space objects, the TLE (Two-Line Element) was used as pseudo-measurement and than the orbit determination and orbit prediction were performed through the flight dynamics system. For determining the orbits, the state vectors were assumed by a series of TLEs within a certain period. The propagation error was analyzed according to the fitting period and a number of pseudo-observations. In order to find out the improvement of orbit prediction with the proposed method, KOMPSAT-2, 3 having the precise orbit in the meter-level range were first applied. Then the result applied to space objects under the same conditions was analyzed. As a result of the RMS error comparison with the orbit prediction of space object, the precision of orbit prediction was improved by approximately 90% for seven days prediction. The improved orbit prediction of space objects can be utilized in the daily analysis for initial screening of the close space objects at high risk.