Mathematical Model Of Aircraft Research Articles

Aircraft Mathematical Model Identification for Flight Trajectories and Performance Analysis in Cruise

In this paper, a mathematical model for estimating the performance and flight trajectories in cruise is identified from data available in flight manuals. The first part of this paper focuses on the design of a fuel flow and emissions model. Starting from the equations of motion of an aircraft in cruise, a simplified model representing the fuel flow in a corrected form was developed. A practical algorithm was next developed to identify the aircraft model parameters and to determine the mathematical structure that reflects its fuel flow. This process was done using performance data available in the aircraft flight crew operating manual. The emissions model was also developed based on data available in the International Civil Aviation Organization’s engine emissions databank. The second part of the paper deals with the development of algorithms for predicting the trajectories and calculating the optimal speeds (i.e., maximum range, long range, and economy) of the aircraft in cruise. Practical techniques for storing and retrieving information without using optimization algorithms have been considered. The methodology was applied on both a Cessna Citation X business jet and Bombardier CRJ-700 regional jet aircraft. The comparison results showed a very good agreement for the fuel consumption and optimal speed.

Учет свойств атмосферы при сравнении математических моделей аэродинамических коэффициентов с данными летных испытаний

Methodological approaches to the calculation of atmospheric parameters, primarily air density and velocity head, in the task of comparing flight data with the results of mathematical modeling of the aircraft motion are proposed. Models with different degrees of using onboard measurements and standard atmosphere models are considered. The models are compared according to the data of flight experiments performed on a modern aircraft for such flight modes as horizontal platform, turn, climb, descentin, and acceleration. The comparison results are given the form of absolute and relative discrepancies in temperature, static pressure and air density. It is shown that the difference between the properties of the real atmosphere and the standard atmosphere is the main source of mismatches, compared to which the influence of the type of flight modes, altitude, speed is insignificant. In addition, a comparison of the standard atmosphere model with the data of atmospheric meteorological sounding is made, which gave similar results. It is concluded that the calculation of air density and velocity head through the standard atmosphere, widespread in practice, in the general case creates a significant error, which may lead to erroneous conclusions in assessing the correspondence of the aircraft mathematical model and the real object

Method of description for the dynamics of the signal delay change in discrete time with changing aircraft position in space

The article presents an innovative approach to the description of the aircraft range parameter in discrete time when simulating the process of its repositioning in space. A method of describing the dynamics of changes in signal delay in discrete time when the aircraft is changing its spatial position is proposed. Such a model adequately describes the change in signal delay in discrete time. The direction of estimation for the adequacy of radio signal delay change simulation in algorithms of optimum filtration is defined in accordance with the aerodynamic properties of the aircraft. Simulation of the signal delay dynamic change is carried out (it is completely described by the dynamics of change in the distance to the aircraft). The transformation stages of simulation data for the initial model in continuous time with realization of the standard Gaussian random numbers are justified. Information on the simulation data transformation taking into account the correlation matrix of discrete white noise is provided. A method of calculating the transition matrix through the Laplace transform is proposed. The scientific-applied direction of research is determined – it lies in the development of a method for the legitimate representation for the mathematical model of aircraft’s changing range in discrete time within one-dimensional space: the longitudinal and the transverse dimensions. This approach takes into account the continuous description for a system of stochastic differential equations. A comprehensive algorithm for modeling the values of discrete white noise on modern computer equipment and calculating the dynamics of the aircraft range parameter changes is proposed. This algorithm allows to correctly form the a priori information about the change of the vector parameters of the aircraft spatial position at discrete moments of time. As a result, it was shown that the use of the obtained information in the optimal filtering algorithms minimizes the error when determining distance to the aircraft and, accordingly, allows to increase the accuracy and adequacy of the signal delay simulation in discrete time. The results of this research can be used in modernization of the existing models and development of promising on-board radar stations, integrated rangefinders, systems of radio technical reconnaissance and electronic warfare systems, as well as in technical implementation of aircraft flight simulation systems.

Research on the Neal&Smith Criterion Application on Aircraft Flight Control System Handling Qualities Assessment

This paper utilized Neal&Smith criterion to quantify handling qualities of some aircraft augmented with Control and Stability Augmentation System (CSAS) over the flight envelop. Some aircraft mathematical model which augmented by longitudinal pitch Rate Command-Attitude Hold(RCAH) controller are employed. The aircraft handling qualities are described in terms of transfer functions of the pilot mathematical model, which includes a pilot’s neuromuscular delay, phase and gain compensation terms. If desirable closed loop dynamic performance can be obtained by the pilot mathematical model described by transfer function characteristics, then the satisfactory closed loop dynamic performance will also be achievable for the human pilot with decent workload. Consequently, the assessment results can be used to identify CSAS controller’s satisfactory effect domain, and furthermore, in aid of CSAS gain scheduling strategy design.

UAV Control Based on Dual LQR and Fuzzy-PID Controller

This paper presents the design of a longitudinal controller for an autonomous unmanned aerial vehicle (UAV). This paper proposed the dual loop (inner-outer loop) control based on the intelligent algorithm. The inner feedback loop controller is a Linear Quadratic Regulator (LQR) to provide robust (adaptive) stability. In contrast, the outer loop controller is based on Fuzzy-PID (Proportional, Integral, and Derivative) algorithm to provide reference signal tracking. The proposed dual controller is to control the position (altitude) and velocity (airspeed) of an aircraft. An adaptive Unscented Kalman Filter (AUKF) is employed to track the reference signal and is decreased the Gaussian noise. The mathematical model of aircraft has been (Cessna 172) presented. The stability and robustness of the system have been verified in a simulation experiment.

Kernel Adaptive Filtering Multiple-model Actuator Fault Diagnostic For Multi-effectors Aircraft

In the traditional Multiple Model Adaptive Estimation (MMAE) algorithm, the extended Kalman filter has theoretical limitations, and the establishment of accurate aircraft mathematical model is almost impossible. In this paper, the Kernel Adaptive Filter (KAF) is introduced to replace the Kalman filter, a new multi-model adaptive estimation fault diagnosis method is proposed. Based on the kernel methods, the adaptive filter is designed in the high-dimensional feature space without the need to know the system model in advance. After training of KAF using the offline input control signal and output flight states measurement with noise, the estimation of real flight states values and actuator fault detection and isolation can be realized online. The simulation results show good performance of new fault diagnosis method in actuator fault diagnosis.

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.

Deep auto-encoder observer multiple-model fast aircraft actuator fault diagnosis algorithm

In the extended multiple model adaptive estimation fault diagnosis algorithm, the extended Kalman filter has theoretical limitations, and the establishment of accurate aircraft mathematical model is almost impossible. Meanwhile, there is no automatic method to optimally select the node number of deep neural network hidden layer. In this paper, a deep auto-encoder observer multiple-model fault diagnosis algorithm for aircraft actuator fault is proposed. Based on the empirical formula of the basic auto-encoder hidden layer node number selection (three layered neural network), the recursive formula for deep auto-encoder hidden layer node number selection are proposed. The deep auto-encoder observers for no-fault and different actuator faults are trained to observe the system state. Combined with multiple model adaptive estimation, the deep auto-encoder observer overcomes the theoretical limitation of extended Kalman filter, and avoided the calculation of the nonlinear system Jacobian matrix. The simulation results show that hidden layer node number selection recursive formula is useful. The fault diagnosis algorithm is more efficient and has better performance compared to the standard methods.

Aircraft mathematical model with account of vortex sheet dynamics

Constructed is mathematical model of aircraft in the roll channel regime of air inertia rotation with the account of vortex sheet dynamic, including common differential equations characterizing the aircraft dynamic motion, and the state of vortex sheet aerodynamic characteristics depends on running variables of vortex sheet state

Observer Based Optimal Vibration Control of a Full Aircraft System Having Active Landing Gears and Biodynamic Pilot Model

This paper deals with the design of an observed based optimal state feedback controller having pole location constraints for an active vibration mitigation problem of an aircraft system. An eleven-degree-of-freedom detailed full aircraft mathematical model having active landing gears and a seated pilot body is developed to control and analyze aircraft vibrations caused by runway excitation, when the aircraft is taxiing. Ground induced vibration can contribute to the reduction of pilot’s capability to control the aircraft and cause the safety problem before take-off and after landing. Since the state variables of the pilot body are not available for measurement in practice, an observed based optimal controller is designed via Linear Matrix Inequalities (LMIs) approach. In addition, classical LQR controller is designed to investigate effectiveness of the proposed controller. The system is then simulated against the bump and random runway excitation. The simulation results demonstrate that the proposed controller provides significant improvements in reducing vibration amplitudes of aircraft fuselage and pilot’s head and maintains the safety requirements in terms of suspension stroke and tire deflection.

Wind Shear On-Line Identification for Unmanned Aerial Systems

An algorithm to perform the on line identification of the wind shear components suitable for the UAS characteristics has been implemented. The mathematical model of aircraft and wind shear in the augmented state space has been built without any restrictive assumption on the dynamic of wind shear. Due to the severe accelerations on the aircraft induced by the strong velocity variation typical of wind shear, the wind shear effects have been modeled as external forces and moments applied on the aircraft. The identification problem addressed in this work has been solved by using the Filter error method approach. An Extended Kalman Filter has been developed to propagate state. It has been tuned by using a database of measurements through off-line identification of the process noise covariance matrix. Afterwards the implemented EKF has been employed to estimate onboard either aircraft state or turbulence, with significant savings in terms of time and computing resources. Robustness of implemented algorithm has been verified by means of several tests. The obtained results show the feasibility of the tuned up algorithm. In fact it is possible, by using a few numbers of low cost sensors, to estimate with a noticeable accuracy the augmented state vector. Besides a very short computation time is required to perform the augmented state estimation even by using low computation power.

Flutter of Maneuvering Aircraft

AbstractThe objective of this paper is to investigate how the aeroelastic stability, particularly flutter, is affected by aircraft maneuvers. The authors’ investigation is based on a comprehensive mathematical model of aircraft, which is achieved by seamlessly integrating all the disciplines pertinent to flight of aircraft. The aircraft is treated as an unstrained, flexible multibody system subject to unsteady aerodynamics. The bodies are fuselage, wing, and horizontal and vertical stabilizers, whose structures are modeled as beams in bending and torsion. The equations of motion are derived using Lagrange’s equations in quasi-coordinates. The resulting equations are a set of nonlinear ordinary differential equations of relatively high order. The final model is used to determine flutter speeds of aircraft at steady level turn and steady climb at various altitudes. These maneuvers are especially chosen to keep the equations time invariant. The numerical results are given for a generic transport model (GTM)....

Measurement of dose equivalent distribution on-board commercial jet aircraft

The annual effective doses of aircrew members often exceed the limit of 1 mSv for the public due to the increased level of cosmic radiation at the flight altitudes, and thus, it is recommended to monitor them [International Commission on Radiation Protection. 1990 Recommendations of the International Commission on Radiological Protection. ICRP Publication 60. Ann. ICRP 21: (1-3), (1991)]. According to the Monte Carlo simulations [Battistoni, G., Ferrari, A., Pelliccioni, M. and Villari, R. Evaluation of the doses to aircrew members taking into consideration the aircraft structures. Adv. Space Res. 36: , 1645-1652 (2005) and Ferrari, A., Pelliccioni, M. and Villari, R. Evaluation of the influence of aircraft shielding on the aircrew exposure through an aircraft mathematical model. Radiat. Prot. Dosim. 108: (2), 91-105 (2004)], the ambient dose equivalent rate Ḣ*(10) depends on the location in the aircraft. The aim of this article is to experimentally evaluate Ḣ*(10) on-board selected types of aircraft. The authors found that Ḣ*(10) values are higher in the front and the back of the cabin and lesser in the middle of the cabin. Moreover, total dosimetry characteristics obtained in this way are in a reasonable agreement with other data, in particular with the above-mentioned simulations.

Mathematical model and vibration analysis of aircraft with active landing gears

This paper deals with the study and comparison of the dynamic response of aircraft with passive and active landing gears due to runway irregularities while the aircraft is taxying. This paper develops a detailed full aircraft mathematical vibration model to describe an active landing gear system. The derived dynamic equations are used to analyze the active landing gear system using proportional integral derivative (PID) controllers. The performance of this system is compared with the passive landing gear system by numerical simulations. The active landing gear system is able to increase the ride comfort and good track holding by reducing the fuselage acceleration, vertical fuselage displacement caused by landing and runway excitations.

Single Neuron PID Control of Aircraft Deicing Fluids Rapid Heating System

Aircraft deicing fluids rapid heating system is widely used in aircraft ground deicing to ensure that the operation of flights can be safe and efficient. Aiming at the temperature turbulence problem of aircraft deicing system, this paper presents the single neuron PID control strategy which combine the advantage of conventional PID control with artificial neuron control. The aircraft deicing fluids rapid heating system and the scheme and working principle of the system is introduced. Simulation is executed on the basis of the mathematical model of aircraft deicing fluids rapid heating system, which is built in this paper, according to a number of data collected by experiments which are operated on the experimental platform of deicing fluids rapid heating system. The simulation results show that the single neuron PID control strategy perform effectively on the temperature turbulence problem of aircraft deicing fluids rapid heating system. Experiments are conducted to vertify the single neuron PID control strategy, the results of which show that the single neuron PID control strategy can achieve the request in practical application of the aircraft deicing fluids rapid heating system.

Modeling Study of Aircraft Based on Small Perturbation Equation

In aircraft flight control law design, the first key is to establish actual aircraft mathematical model, then according to the model of dynamic output information, analysis control law design is appropriate. But in the movement the aircraft is a complex dynamics system, modeling is very complex. This paper firstly carry out comprehensive feasibility analysis, on a plane modeling consideration simplified, secondly, in actual applications verified using the perturbation method of nonlinear equation linearization, establish the plane mathematics model.

Intelligent Control Method for Aircraft Deicing Fluidtemperature Based on a New Adaptive Smith Predictor

During the course of industry control, pure hysteresis, time-varying，non- linear complex systems often occur. It is ineffective to solve the issues above with the traditional fuzzy control and PID control methods. Against the pure hysteresis, time-varying, non- linear characteristics of Aircraft Deicing Fluid rapid heating system, on the basis of Smith Predictor and traditional PID, a Fuzzy-PID control method is proposed based on an adaptive Smith predictor. In this way, pure hysteresis of the system will be compensated, to reduce the overshoot and enhance the stability of the system. By establishing the mathematical model of Aircraft Deicing Fluid rapid heating system and simulating for the model obtain the simulation results, which have shown that the method is effective, can improve the qualities of control and enhance the stability of temperature control system significantly

Aircraft Multi-Constrained Generalized Dynamic Inversion Control

The new and evolving paradigm of generalized dynamic inversion (GDI) is applied to aircraft maneuvering control design, through the development of a new multiple constraint formulation. The flexibility of GDI in utilizing nullspace of the controls coefficient matrix is exploited to eliminate the problems of excessive control effort and limited performance that are associated with classical dynamic inversion. Scalar deviation functions of the aircraft state error variables are differentiated along the aircraft mathematical model solution trajectories, and linear time varying stable dynamics in these deviation functions are manipulated to obtain linear algebraic constraint equations in the control vector. The constraint equations are inverted using the Greville formula, resulting in the control law. The particular part of the control law drives the states to their desired values, and the auxiliary part acts to stabilize the vehicles inner dynamics by means of the null-control vector. The null-control vector is constructed via a novel class of positive semidefinite Lyapunov functions and nullprojected Lyapunov equations. The closed loop control system is assessed by performing a fully coordinated simultaneous heading-velocity change maneuver. The new type of GDI control laws shows to require low control effort, in addition to providing excellent transient response and reasonable steady-state tracking accuracy.

A mathematical model of aircraft for evaluating the effects of shielding structure on aircrew exposure

To investigate the influence of the aircraft structures and contents on the exposure of aircrew to the galactic component of cosmic rays, a mathematical model of an aeroplane has been developed. The irradiation of the mathematical model in the cosmic ray environment has been simulated using the Monte Carlo transport code FLUKA. Effective dose andambient dose-equivalent rates have been determined inside the aircraft at several locations along the fuselage at a typicaI civil aviation altitude. A significant effect of the shielding of aircraft structures has been observed on the ambient dose-equivalent rates, while the impact on the effective dose rates seems to be minor. Care should be taken in positioning the detectors onboard when the measurements are aimed at validating the codes.

Suboptimal adaptive control system for flight quality improvement

In this paper, the suboptimal algorithm of adaptive control system is presented, which is specially adjusted for automatic flight control systems of general aviation and commuter aircraft, and unmanned aircraft (UMA) that conduct flights in atmospheric turbulence. At first, the method could be applied for correcting these changes in flight dynamics parameters, which cannot be compensated with the aid of an open adaptation loop. At the same time, full identification of aircraft model in real time is not required. This method is based on the estimation of most typical parameters of the aircraft mathematical model, which are most closely related to parameters, which are unmeasurable during flight, like aircraft real mass and position of center of gravity. The structure of an adaptation algorithm of aircraft flight control laws is based on the expert knowledge in the field of flight dynamics and is the result of optimization calculations. The examples which show attaining better flight comfort of the PZL M20, “Mewa” general aviation aircraft and quality improvement of the UMA, “Vector” pitch angle automatic control, have been presented.