Search results for: Lyapunov%20stability

Authors: Wael M. Elawady, Mohamed F. Asar, Amany M. Sarhan

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This paper adopts a continuous sliding mode control scheme for trajectory tracking control of robot manipulators with structured and unstructured uncertain dynamics and external disturbances. In this algorithm, the equivalent control in the conventional sliding mode control is replaced by a PID control action. Moreover, the discontinuous switching control signal is replaced by a continuous proportional-integral (PI) control term such that the implementation of the proposed control algorithm does not require the prior knowledge of the bounds of unknown uncertainties and external disturbances and completely eliminates the chattering phenomenon of the conventional sliding mode control approach. The closed-loop system with the adopted control algorithm has been proved to be globally stable by using Lyapunov stability theory. Numerical simulations using the dynamical model of robot manipulators with modeling uncertainties demonstrate the superiority and effectiveness of the proposed approach in high speed trajectory tracking problems.

Keywords: PID, robot, sliding mode control, uncertainties

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Authors: Gwanghee Heo, Geonhyeok Bang, Chunggil Kim, Chinok Lee

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This paper attempts to develop a wireless feedback control system as a primary step eventually toward a bio-inspired structure system where inanimate structure behaves like a life form autonomously. It is a standalone wireless control system which is supposed to measure externally caused structural responses, analyze structural state from acquired data, and take its own action on the basis of the analysis with an embedded logic. For an experimental examination of its effectiveness, we applied it on a model of two-span bridge and performed a wireless control test. Experimental tests have been conducted for comparison on both the wireless and the wired system under the conditions of Un-control, Passive-off, Passive-on, and Lyapunov control algorithm. By proving the congruence of the test result of the wireless feedback control system with the wired control system, its control performance was proven to be effective. Besides, it was found to be economical in energy consumption and also autonomous by means of a command algorithm embedded into it, which proves its basic capacity as a bio-inspired system.

Keywords: structural vibration control, wireless system, MR damper, feedback control, embedded system

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Authors: Henni Mansour Abdelwaheb

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This study discusses the design of a bounded position/force feedback controller developed to ensure position and force tracking for bilateral teleoperation arms operating with variable delay, and actuator saturation. Also, an adaptive robust Radial Basis Function (RBF) neural network is used to estimate the environment torque. The parameters of the environment torque are then sent from the slave site to the master site as a non-power signal to avoid passivity problems. Moreover, a nonlinear function is applied to each controller term as a smooth saturation function, providing a bounded control signal and preserving the system’s actuators. Lastly, the Lyapunov approach demonstrates the global stability of the controlled system, and numerical experiment results further confirm the validity of the presented strategy.

Keywords: teleoperation manipulators system, time-varying delay, actuator saturation, adaptive robust rbf neural network approximation, uncertainties

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Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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Authors: Riaz Ahmad, Jiazhong Zhang, Asma Farooqi

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In this study, mass transport between separation bubbles and the flow around a two-dimensional airfoil are numerically investigated using Lagrangian Coherent Structures (LCSs). Finite Time Lyapunov Exponent (FTLE) technique is used for the computation to identify invariant manifolds and LCSs. Moreover, the Characteristic Base Split (CBS) scheme combined with dual time stepping technique is applied to simulate such transient flow at low Reynolds number. We then investigate the evolution of vortex structures during the transport process with the aid of LCSs. To explore the vortex formation at the surface of the airfoil, the dynamics of separatrix is also taken into account which is formed by the combination of stable-unstable manifolds. The Lagrangian analysis gives a detailed understanding of vortex dynamics and separation bubbles which plays a significant role to explore the performance of the unsteady flow generated by the airfoil. Transport process and flow separation phenomena are studied extensively to analyze the flow pattern by Lagrangian point of view.

Keywords: transport phenomena, CBS Method, vortex formation, Lagrangian Coherent Structures

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Authors: Nader H. Ghareeb, Mohamed S. Gaith, Sayed M. Soleimani

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In modern engineering, weight optimization has a priority during the design of structures. However, optimizing the weight can result in lower stiffness and less internal damping, causing the structure to become excessively prone to vibration. To overcome this problem, active or smart materials are implemented. The coupled electromechanical properties of smart materials, used in the form of piezoelectric ceramics in this work, make these materials well-suited for being implemented as distributed sensors and actuators to control the structural response. The smart structure proposed in this paper is composed of a cantilevered steel beam, an adhesive or bonding layer, and a piezoelectric actuator. The static deflection of the structure is derived as function of the piezoelectric voltage, and the outcome is compared to theoretical and experimental results from literature. The relation between the voltage and the piezoelectric moment at both ends of the actuator is also investigated and a reduced finite element model of the smart structure is created and verified. Finally, a linear controller is implemented and its ability to attenuate the vibration due to the first natural frequency is demonstrated.

Keywords: active linear control, lyapunov stability theorem, piezoelectricity, smart structure, static deflection

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Authors: Rihab Hamdi, Amel Hadri Hamida, Ouafae Bennis, Fatima Babaa, Sakina Zerouali

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This paper features a sliding mode controller (SMC) for closed-loop voltage control of DC-DC three-cells buck converter connected in parallel, operating in continuous conduction mode (CCM), based on pulse-width modulation (PWM). To maintain the switching frequency, the approach is to incorporate a pulse-width modulation that utilizes an equivalent control, inferred by applying the SM control method, to produce a control sign to be contrasted and the fixed-frequency within the modulator. Detailed stability and transient performance analysis have been conducted using Lyapunov stability criteria to restrict the switching frequency variation facing wide variations in output load, input changes, and set-point changes. The results obtained confirm the effectiveness of the proposed control scheme in achieving an enhanced output transient performance while faithfully realizing its control objective in the event of abrupt and uncertain parameter variations. Simulations studies in MATLAB/Simulink environment are performed to confirm the idea.

Keywords: DC-DC converter, pulse width modulation, power electronics, sliding mode control

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Authors: Shweda Mohan, J. L. Nandagopal, S. Amritha

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This paper focuses on the dynamic modelling of unicycle robot. Two main concepts used for balancing unicycle robot are: reaction wheel pendulum and inverted pendulum. The pitch axis is modelled as inverted pendulum and roll axis is modelled as reaction wheel pendulum. The unicycle yaw dynamics is not considered which makes the derivation of dynamics relatively simple. For the roll controller, sliding-mode controller has been adopted and optimal methods are used to minimize switching-function chattering. For pitch controller, an LQR controller has been implemented to drive the unicycle robot to follow the desired velocity trajectory. The pitching and rolling balance could be achieved by two DC motors. Unicycle robot is a non-holonomic, non-linear, static unbalance system that has the minimal number of point contact to the ground, therefore, it is a perfect platform for researchers to study motion and balance control. These real-time solutions will be a viable solution for advanced robotic systems and controls.

Keywords: decoupled dynamics, linear quadratic regulator (LQR) control, Lyapunov function sliding mode control, unicycle robot, velocity and trajectory control

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Authors: Sarita Kumari, Ranjit Kumar Upadhyay

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This paper deals with plankton-fish dynamics where the fish population is growing logistically and nonlinearly harvested. The interaction between phytoplankton and zooplankton population is considered to be Crowley-Martin type functional response. It has been assumed that phytoplankton grows logistically and is affected by a space-dependent growth rate. Conditions for the existence of a positive equilibrium point and their stability analysis (both local and global) have been discussed for the non-spatial system. We have discussed maximum sustainable yields as well as optimal harvesting policy for maximizing the economic gain. The stability and existence of Hopf –bifurcation analysis have been discussed for the spatial system. Different conditions for turning pattern formation have been established through diffusion-driven instability analysis. Numerical simulations have been carried out for both non-spatial and spatial models. Phase plane analysis, the largest Lyapunov exponent, and bifurcation theory are used to numerically analyzed the non-spatial system. Our study shows that spatial heterogeneity, the mortality rate of phytoplankton, and constant harvesting of the fish population each play an important role in the dynamical behavior of the marine system.

Keywords: optimal harvesting, pattern formation, spatial heterogeneity, Crowley-Martin functional response

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust fault-tolerant predictive control (FTPC) strategy is proposed for systems with linear parameter varying (LPV) models and input constraints subject to sensor faults. Generally, virtual observers are used for improving the observation precision and reduce the impacts of sensor faults and uncertainties in the system. However, this type of observer lacks certain system measurements which substantially reduce its accuracy. To deal with this issue, a real observer is then designed based on the virtual observer, and consequently a real observer-based robust predictive control is designed for polytopic LPV systems. Moreover, the proposed observer can entirely assure that all system states and sensor faults are estimated. As a result, and based on both observers, a robust fault-tolerant predictive control is then established via the Lyapunov method where sufficient conditions are proposed, for stability analysis and control purposes, in linear matrix inequalities (LMIs) form. Finally, simulation results are given to show the effectiveness of the proposed approach.

Keywords: linear parameter varying systems, fault-tolerant predictive control, observer-based control, sensor faults, input constraints, linear matrix inequalities

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Authors: Alireza Gholami, Amir H. D. Markazi

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In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: adaptive algorithm, fuzzy systems, membership functions, observer

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Authors: Shabadini Sampath, Jinglang Feng

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With huge kinetic energy, space debris poses a major threat to astronauts’ space activities and spacecraft in orbit if a collision happens. The active removal of space debris is required in order to avoid frequent collisions that would occur. In addition, the amount of space debris will increase uncontrollably, posing a threat to the safety of the entire space system. But the safe and reliable removal of large-scale space debris has been a huge challenge to date. While capturing and deorbiting space debris, the space manipulator has to achieve high control precision. However, due to uncertainties and unknown disturbances, there is difficulty in coordinating the control of the space manipulator. To address this challenge, this paper focuses on developing a robust and intelligent control algorithm that controls joint movement and restricts it on the sliding manifold by reducing uncertainties. A neural network adaptive sliding mode controller (NNASMC) is applied with the objective of finding the control law such that the joint motions of the space manipulator follow the given trajectory. A computed torque control (CTC) is an effective motion control strategy that is used in this paper for computing space manipulator arm torque to generate the required motion. Based on the Lyapunov stability theorem, the proposed intelligent controller NNASMC and CTC guarantees the robustness and global asymptotic stability of the closed-loop control system. Finally, the controllers used in the paper are modeled and simulated using MATLAB Simulink. The results are presented to prove the effectiveness of the proposed controller approach.

Keywords: GNC, active removal of space debris, AI controllers, MatLabSimulink

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Authors: Jia Li, Huacong Li, Xiaobao Han

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Due to the more variable geometry parameters of VCE (variable cycle aircraft engine), presents an adaptive controller method based on the full-state linear model of VCE and has simulated to solve the multivariate controller design problem of the whole flight envelops. First, analyzes the static and dynamic performances of bypass ratio and other state parameters caused by variable geometric components, and develops nonlinear component model of VCE. Then based on the component model, through small deviation linearization of main fuel (Wf), the area of tail nozzle throat (A8) and the angle of rear bypass ejector (A163), setting up multiple linear model which variable geometric parameters can be inputs. Second, designs the adaptive controllers for VCE linear models of different nominal points. Among them, considering of modeling uncertainties and external disturbances, derives the adaptive law by lyapunov function. The simulation results showed that, the adaptive controller method based on full-state linear model used the angle of rear bypass ejector as input and effectively solved the multivariate control problems of VCE. The performance of all nominal points could track the desired closed-loop reference instructions. The adjust time was less than 1.2s, and the system overshoot was less than 1%, at the same time, the errors of steady states were less than 0.5% and the dynamic tracking errors were less than 1%. In addition, the designed controller could effectively suppress interference and reached the desired commands with different external random noise signals.

Keywords: variable cycle engine (VCE), full-state linear model, adaptive control, by-pass ratio

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Authors: Shruti Malviya, Chris Bowler

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Environmental processes acting at multiple spatial scales control marine diatom community structure. However, the contribution of local factors (e.g., temperature, salinity, etc.) in these highly complex systems is poorly understood. We, therefore, investigated the diatom community organization as a function of environmental predictors and determined the relative contribution of various environmental factors on the structure of marine diatoms assemblages in the world’s ocean. The dataset for this study was derived from the Tara Oceans expedition, constituting 46 sampling stations from diverse oceanic provinces. The V9 hypervariable region of 18s rDNA was organized into assemblages based on their distributional co-occurrence. Using Ward’s hierarchical clustering, nine clusters were defined. The number of ribotypes and reads varied within each cluster-three clusters (II, VIII and IX) contained only a few reads whereas two of them (I and IV) were highly abundant. Of the nine clusters, seven can be divided into two categories defined by a positive correlation with phosphate and nitrate and a negative correlation with longitude and, the other by a negative correlation with salinity, temperature, latitude and positive correlation with Lyapunov exponent. All the clusters were found to be remarkably dominant in South Pacific Ocean and can be placed into three classes, namely Southern Ocean-South Pacific Ocean clusters (I, II, V, VIII, IX), South Pacific Ocean clusters (IV and VII), and cosmopolitan clusters (III and VI). Our findings showed that co-occurring ribotypes can be significantly associated into recognizable clusters which exhibit a distinct response to environmental variables. This study, thus, demonstrated distinct behavior of each recognized assemblage displaying a taxonomic and environmental signature.

Keywords: assemblage, diatoms, hierarchical clustering, Tara Oceans

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Authors: Filimonova Alexanra

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Inviscid incompressible fluid flows are considered. The object of the study is a vortex parquet – a structure consisting of distributed vortex spots of different directions, occupying the entire plane. The main attention is paid to the study of advection processes of passive particles in the corresponding velocity field. The dynamics of the vortex structures is considered in a rectangular region under the assumption that periodic boundary conditions are imposed on the stream function. Numerical algorithms are based on the solution of the initial-boundary value problem for nonstationary Euler equations in terms of vorticity and stream function. For this, the spectral-vortex meshless method is used. It is based on the approximation of the stream function by the Fourier series cut and the approximation of the vorticity field by the least-squares method from its values in marker particles. A vortex configuration, consisting of four vortex patches is investigated. Results of a numerical study of the dynamics and interaction of the structure are presented. The influence of the patch radius and the relative position of positively and negatively directed patches on the processes of interaction and mixing is studied. The obtained results correspond to the following possible scenarios: the initial configuration does not change over time; the initial configuration forms a new structure, which is maintained for longer times; the initial configuration returns to its initial state after a certain period of time. The processes of mass transfer of vorticity by liquid particles on a plane were calculated and analyzed. The results of a numerical analysis of the particles dynamics and trajectories on the entire plane and the field of local Lyapunov exponents are presented.

Keywords: ideal fluid, meshless methods, vortex structures in liquids, vortex parquet.

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Authors: Magdy Roman, Mostafa Shoeib, Mostafa Rostom

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Global vision, whether provided by overhead fixed cameras, on-board aerial vehicle cameras, or satellite images can always provide detailed information on the environment around mobile robots. In this paper, an intelligent vision-based method of path planning and obstacle avoidance for mobile robots is presented. The method integrates visual perception with a new proposed field-based path-planning method to overcome common path-planning problems such as local minima, unreachable destination and unnecessary lengthy paths around obstacles. The method proposes an exponential angle deviation field around each obstacle that affects the orientation of a close robot. As the robot directs toward, the goal point obstacles are classified into right and left groups, and a deviation angle is exponentially added or subtracted to the orientation of the robot. Exponential field parameters are chosen based on Lyapunov stability criterion to guarantee robot convergence to the destination. The proposed method uses obstacles' shape and location, extracted from global vision system, through a collision prediction mechanism to decide whether to activate or deactivate obstacles field. In addition, a search mechanism is developed in case of robot or goal point is trapped among obstacles to find suitable exit or entrance. The proposed algorithm is validated both in simulation and through experiments. The algorithm shows effectiveness in obstacles' avoidance and destination convergence, overcoming common path planning problems found in classical methods.

Keywords: path planning, collision avoidance, convergence, computer vision, mobile robots

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Mohd Sabri Minhat, Nurul Adilla Mohd Subha

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The PUSPATI TRIGA Reactor (RTP), Malaysia reached its first criticality on June 28, 1982, with power capacity 1MW thermal. The Feedback Control Algorithm (FCA) which is conventional Proportional-Integral (PI) controller, was used for present power control method to control fission process in RTP. It is important to ensure the core power always stable and follows load tracking within acceptable steady-state error and minimum settling time to reach steady-state power. At this time, the system could be considered not well-posed with power tracking performance. However, there is still potential to improve current performance by developing next generation of a novel design nuclear core power control. In this paper, the dual-mode predictions which are proposed in modelling Optimal Model Predictive Control (OMPC), is presented in a state-space model to control the core power. The model for core power control was based on mathematical models of the reactor core, OMPC, and control rods selection algorithm. The mathematical models of the reactor core were based on neutronic models, thermal hydraulic models, and reactivity models. The dual-mode prediction in OMPC for transient and terminal modes was based on the implementation of a Linear Quadratic Regulator (LQR) in designing the core power control. The combination of dual-mode prediction and Lyapunov which deal with summations in cost function over an infinite horizon is intended to eliminate some of the fundamental weaknesses related to MPC. This paper shows the behaviour of OMPC to deal with tracking, regulation problem, disturbance rejection and caters for parameter uncertainty. The comparison of both tracking and regulating performance is analysed between the conventional controller and OMPC by numerical simulations. In conclusion, the proposed OMPC has shown significant performance in load tracking and regulating core power for nuclear reactor with guarantee stabilising in the closed-loop.

Keywords: core power control, dual-mode prediction, load tracking, optimal model predictive control

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Authors: S. Behnia, S. Fathizadeh, A. Akhshani

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In the recent decades, DNA has increasingly interested in the potential technological applications that not directly related to the coding for functional proteins that is the expressed in form of genetic information. One of the most interesting applications of DNA is related to the construction of nanostructures of high complexity, design of functional nanostructures in nanoelectronical devices, nanosensors and nanocercuits. In this field, DNA is of fundamental interest to the development of DNA-based molecular technologies, as it possesses ideal structural and molecular recognition properties for use in self-assembling nanodevices with a definite molecular architecture. Also, the robust, one-dimensional flexible structure of DNA can be used to design electronic devices, serving as a wire, transistor switch, or rectifier depending on its electronic properties. In order to understand the mechanism of the charge transport along DNA sequences, numerous studies have been carried out. In this regard, conductivity properties of DNA molecule could be investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. In SSH model, the non-diagonal matrix element dependence on intersite displacements is considered. In this approach, the coupling between the charge and lattice deformation is along the helix. This model is a tight-binding linear nanoscale chain established to describe conductivity phenomena in doped polyethylene. It is based on the assumption of a classical harmonic interaction between sites, which is linearly coupled to a tight-binding Hamiltonian. In this work, the Hamiltonian and corresponding motion equations are nonlinear and have high sensitivity to initial conditions. Then, we have tried to move toward the nonlinear dynamics and phase space analysis. Nonlinear dynamics and chaos theory, regardless of any approximation, could open new horizons to understand the conductivity mechanism in DNA. For a detailed study, we have tried to study the current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: DNA conductivity, Landauer resistance, negative dierential resistance, Chaos theory, mean Lyapunov exponent

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Authors: Yamina Boughari, Ruxandra Mihaela Botez, Florian Theel, Georges Ghazi

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Clearance of flight control laws of a civil aircraft is a long and expensive process in the Aerospace industry. Thousands of flight combinations in terms of speeds, altitudes, gross weights, centers of gravity and angles of attack have to be investigated, and proved to be safe. Nonetheless, in this method, a worst flight condition can be easily missed, and its missing would lead to a critical situation. Definitively, it would be impossible to analyze a model because of the infinite number of cases contained within its flight envelope, that might require more time, and therefore more design cost. Therefore, in industry, the technique of the flight envelope mesh is commonly used. For each point of the flight envelope, the simulation of the associated model ensures the satisfaction or not of specifications. In order to perform fast, comprehensive and effective analysis, other varying parameters models were developed by incorporating variations, or uncertainties in the nominal models, known as Linear Fractional Representation LFR models; these LFR models were able to describe the aircraft dynamics by taking into account uncertainties over the flight envelope. In this paper, the LFRs models are developed using the speeds and altitudes as varying parameters; The LFR models were built using several flying conditions expressed in terms of speeds and altitudes. The use of such a method has gained a great interest by the aeronautical companies that have seen a promising future in the modeling, and particularly in the design and certification of control laws. In this research paper, we will focus on the Cessna Citation X open loop stability analysis. The data are provided by a Research Aircraft Flight Simulator of Level D, that corresponds to the highest level flight dynamics certification; this simulator was developed by CAE Inc. and its development was based on the requirements of research at the LARCASE laboratory. The acquisition of these data was used to develop a linear model of the airplane in its longitudinal and lateral motions, and was further used to create the LFR’s models for 12 XCG /weights conditions, and thus the whole flight envelope using a friendly Graphical User Interface developed during this study. Then, the LFR’s models are analyzed using Interval Analysis method based upon Lyapunov function, and also the ‘stability and robustness analysis’ toolbox. The results were presented under the form of graphs, thus they have offered good readability, and were easily exploitable. The weakness of this method stays in a relatively long calculation, equal to about four hours for the entire flight envelope.

Keywords: flight control clearance, LFR, stability analysis, robustness analysis

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