Search results for: Lyapunov%20stability
50 Reconstruction and Rejection of External Disturbances in a Dynamical System
Authors: Iftikhar Ahmad, A. Benallegue, A. El Hadri
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In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method.Keywords: non-linear systems, sliding mode observer, disturbance rejection, nonlinear control
Procedia PDF Downloads 30749 Advanced Stability Criterion for Time-Delayed Systems of Neutral Type and Its Application
Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon
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This paper investigates stability problem for linear systems of neutral type with time-varying delay. By constructing various Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient stability conditions for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by various effective optimization algorithms. Finally, some illustrative examples are given to show the effectiveness of the proposed criterion.Keywords: neutral systems, time-delay, stability, Lyapnov method, LMI
Procedia PDF Downloads 32348 Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule
Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao
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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.Keywords: taylor rule, monetary system, chaos theory, lyapunov exponent, GMM estimator
Procedia PDF Downloads 49047 Feigenbaum Universality, Chaos and Fractal Dimensions in Discrete Dynamical Systems
Authors: T. K. Dutta, K. K. Das, N. Dutta
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The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions
Procedia PDF Downloads 27146 Trajectory Tracking of Fixed-Wing Unmanned Aerial Vehicle Using Fuzzy-Based Sliding Mode Controller
Authors: Feleke Tsegaye
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The work in this thesis mainly focuses on trajectory tracking of fixed wing unmanned aerial vehicle (FWUAV) by using fuzzy based sliding mode controller(FSMC) for surveillance applications. Unmanned Aerial Vehicles (UAVs) are general-purpose aircraft built to fly autonomously. This technology is applied in a variety of sectors, including the military, to improve defense, surveillance, and logistics. The model of FWUAV is complex due to its high non-linearity and coupling effect. In this thesis, input decoupling is done through extracting the dominant inputs during the design of the controller and considering the remaining inputs as uncertainty. The proper and steady flight maneuvering of UAVs under uncertain and unstable circumstances is the most critical problem for researchers studying UAVs. A FSMC technique was suggested to tackle the complexity of FWUAV systems. The trajectory tracking control algorithm primarily uses the sliding-mode (SM) variable structure control method to address the system’s control issue. In the SM control, a fuzzy logic control(FLC) algorithm is utilized in place of the discontinuous phase of the SM controller to reduce the chattering impact. In the reaching and sliding stages of SM control, Lyapunov theory is used to assure finite-time convergence. A comparison between the conventional SM controller and the suggested controller is done in relation to the chattering effect as well as tracking performance. It is evident that the chattering is effectively reduced, the suggested controller provides a quick response with a minimum steady-state error, and the controller is robust in the face of unknown disturbances. The designed control strategy is simulated with the nonlinear model of FWUAV using the MATLAB® / Simulink® environments. The simulation result shows the suggested controller operates effectively, maintains an aircraft’s stability, and will hold the aircraft’s targeted flight path despite the presence of uncertainty and disturbances.Keywords: fixed-wing UAVs, sliding mode controller, fuzzy logic controller, chattering, coupling effect, surveillance, finite-time convergence, Lyapunov theory, flight path
Procedia PDF Downloads 1545 Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method
Authors: P. W. Tsai, J. W. Chen, C. W. Chen, C. Y. Chen
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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.Keywords: half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method
Procedia PDF Downloads 64144 Global Analysis of HIV Virus Models with Cell-to-Cell
Authors: Hossein Pourbashash
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Recent experimental studies have shown that HIV can be transmitted directly from cell to cell when structures called virological synapses form during interactions between T cells. In this article, we describe a new within-host model of HIV infection that incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. We conduct the local and global stability analysis of the model. We show that if the basic reproduction number R0 1, the virus is cleared and the disease dies out; if R0 > 1, the virus persists in the host. We also prove that the unique positive equilibrium attracts all positive solutions under additional assumptions on the parameters.Keywords: HIV virus model, cell-to-cell transmission, global stability, Lyapunov function, second compound matrices
Procedia PDF Downloads 48843 Bifurcation and Chaos of the Memristor Circuit
Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi
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In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.Keywords: memristor, chaotic circuit, dynamical behavior, chaotic system
Procedia PDF Downloads 46142 Discrete Tracking Control of Nonholonomic Mobile Robots: Backstepping Design Approach
Authors: Alexander S. Andreev, Olga A. Peregudova
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In this paper, we propose a discrete tracking control of nonholonomic mobile robots with two degrees of freedom. The electro-mechanical model of a mobile robot moving on a horizontal surface without slipping, with two rear wheels controlled by two independent DC electric, and one front roal wheel is considered. We present back-stepping design based on the Euler approximate discrete-time model of a continuous-time plant. Theoretical considerations are verified by numerical simulation. The work was supported by RFFI (15-01-08482).Keywords: actuator dynamics, back stepping, discrete-time controller, Lyapunov function, wheeled mobile robot
Procedia PDF Downloads 37941 Power-Aware Adaptive Coverage Control with Consensus Protocol
Authors: Mert Turanli, Hakan Temeltas
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In this paper, we propose a new approach to coverage control problem by using adaptive coordination and power aware control laws. Nonholonomic mobile nodes position themselves suboptimally according to a time-varying density function using Centroidal Voronoi Tesellations. The Lyapunov stability analysis of the adaptive and decentralized approach is given. A linear consensus protocol is used to establish synchronization among the mobile nodes. Also, repulsive forces prevent nodes from collision. Simulation results show that by using power aware control laws, energy consumption of the nodes can be reduced.Keywords: power aware, coverage control, adaptive, consensus, nonholonomic, coordination
Procedia PDF Downloads 32440 Sampled-Data Model Predictive Tracking Control for Mobile Robot
Authors: Wookyong Kwon, Sangmoon Lee
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In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.Keywords: model predictive control, sampled-data control, linear parameter varying systems, LPV
Procedia PDF Downloads 28039 Sampling Effects on Secondary Voltage Control of Microgrids Based on Network of Multiagent
Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon
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This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.Keywords: microgrids, secondary control, multiagent, sampling, LMI
Procedia PDF Downloads 30638 Control of Proton Exchange Membrane Fuel Cell Power System Using PI and Sliding Mode Controller
Authors: Mohamed Derbeli, Maissa Farhat, Oscar Barambones, Lassaad Sbita
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Conventional controller (PI) applied to a DC/DC boost converter for the improvement and optimization of the Proton Exchange Membrane Fuel Cell (PEMFC) system efficiency, cannot attain a good performance effect. Thus, due to its advantages comparatively with the PI controller, this paper interest is focused on the use of the sliding mode controller (SMC), Stability of the closed loop system is analytically proved using Lyapunov approach for the proposed controller. The model and the controllers are implemented in the MATLAB and SIMULINK environment. A comparison of results indicates that the suggested approach has considerable advantages compared to the traditional controller.Keywords: DC/DC boost converter, PEMFC, PI controller, sliding mode controller
Procedia PDF Downloads 20437 Motion Planning and Posture Control of the General 3-Trailer System
Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai
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This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general 3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.Keywords: artificial potential fields, 3-trailer systems, motion planning, posture
Procedia PDF Downloads 39936 Sliding Mode Controlled Quadratic Boost Converter
Authors: Viji Vijayakumar, R. Divya, A. Vivek
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This paper deals with a quadratic boost converter which belongs to cascade boost family, controlled by sliding mode controller. In the cascade boost family, quadratic boost converter is the best trade-off when circuit complexity and modulator saturation is considered. Sliding mode control being a nonlinear control results in a robust and stable system when applied to switching converters which are inherently variable structured systems. The stability of this system is analyzed through Lyapunov’s approach. Analysis is done for load regulation, line regulation and step response of the system. Also these results are compared with that of PID controller based system.Keywords: DC-DC converter, quadratic boost converter, sliding mode control, PID control
Procedia PDF Downloads 95935 Particle Swarm Optimisation of a Terminal Synergetic Controllers for a DC-DC Converter
Authors: H. Abderrezek, M. N. Harmas
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DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control
Procedia PDF Downloads 47534 Projective Lag Synchronization in Drive-Response Dynamical Networks via Hybrid Feedback Control
Authors: Mohd Salmi Md Noorani, Ghada Al-Mahbashi, Sakhinah Abu Bakar
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This paper investigates projective lag synchronization (PLS) behavior in drive response dynamical networks (DRDNs) model with identical nodes. A hybrid feedback control method is designed to achieve the PLS with mismatch and without mismatch terms. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.Keywords: drive-response dynamical network, projective lag synchronization, hybrid feedback control, stability theory
Procedia PDF Downloads 36233 Periodically Forced Oscillator with Noisy Chaotic Dynamics
Authors: Adedayo Oke Adelakun
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The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential.Keywords: hierarchical structure, periodically forced oscillator, noisy parameters, dynamical behaviour, F6 - duffing oscillator
Procedia PDF Downloads 30032 Control of Spherical Robot with Sliding Mode
Authors: Roya Khajepour, Alireza B. Novinzadeh
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A major issue with spherical robot is it surface shape, which is not always predictable. This means that given only the dynamic model of the robot, it is not possible to control the robot. Due to the fact that in certain conditions it is not possible to measure surface friction, control methods must be prepared for these conditions. Moreover, although spherical robot never becomes unstable or topples thanks to its special shape, since it moves by rolling it has a non-holonomic constraint at point of contact and therefore it is considered a non-holonomic system. Existence of such a point leads to complexity and non-linearity of robot's kinematic equations and makes the control problem difficult. Due to the non-linear dynamics and presence of uncertainty, the sliding-mode control is employed. The proposed method is based on Lyapunov Theory and guarantees system stability. This controller is insusceptible to external disturbances and un-modeled dynamics.Keywords: sliding mode, spherical robot, non-holomonic constraint, system stability
Procedia PDF Downloads 35331 Aircraft Pitch Attitude Control Using Backstepping
Authors: Labane Chrif
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A nonlinear approach to the automatic pitch attitude control problem for aircraft transportation is presented. A nonlinear model describing the longitudinal equations of motion in strict feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free design parameters. The controller is evaluated using the aircraft transportation. The adaptation scheme proposed allowed us to design an explicit controller with a minimal knowledge of the aircraft aerodynamics. Finally, the simulation results will show that backstepping controller have better dynamic performance, simpler design, higher precision, easier implement, etc. At the same time, the control effect will be significantly improved. In addition, backstepping control is superior in short transition, good stability, anti-disturbance and good control.Keywords: nonlinear control, backstepping, aircraft control, Lyapunov function, longitudinal model
Procedia PDF Downloads 55530 Potential Field Functions for Motion Planning and Posture of the Standard 3-Trailer System
Authors: K. Raghuwaiya, S. Singh, B. Sharma, J. Vanualailai
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This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the Distance Optimization Technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.Keywords: artificial potential fields, 3-trailer systems, motion planning, posture, parking and collision, free trajectories
Procedia PDF Downloads 35729 Sensorless Controller of Induction Motor Using Backstepping Approach and Fuzzy MRAS
Authors: Ahmed Abbou
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This paper present a sensorless controller designed by the backstepping approach for the speed control of induction motor. In this strategy of control, we also combined the method Fuzzy MRAS to estimate the rotor speed and the observer type Luenburger to observe Rotor flux. The control model involves a division by the flux variable that may lead to unbounded solutions. Such a risk is avoided by basing the controller design on Lyapunov function that accounts for the model singularity. On the other hand, this mixed method gives better results in Sensorless operation and especially at low speed. The response time at 5% of the flux is 20ms while the error between the speed with sensor and the estimated speed remains in the range of ±0.8 rad/s for the rated functioning and ±1.5 rad/s for low speed.Keywords: backstepping approach, fuzzy logic, induction motor, luenburger observer, sensorless MRAS
Procedia PDF Downloads 34628 Multi-Agent Coverage Control with Bounded Gain Forgetting Composite Adaptive Controller
Authors: Mert Turanli, Hakan Temeltas
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In this paper, we present an adaptive controller for decentralized coordination problem of multiple non-holonomic agents. The performance of the presented Multi-Agent Bounded Gain Forgetting (BGF) Composite Adaptive controller is compared against the tracking error criterion with a Feedback Linearization controller. By using the method, the sensor nodes move and reconfigure themselves in a coordinated way in response to a sensed environment. The multi-agent coordination is achieved through Centroidal Voronoi Tessellations and Coverage Control. Also, a consensus protocol is used for synchronization of the parameter vectors. The two controllers are given with their Lyapunov stability analysis and their stability is verified with simulation results. The simulations are carried out in MATLAB and ROS environments. Better performance is obtained with BGF Adaptive Controller.Keywords: adaptive control, centroidal voronoi tessellations, composite adaptation, coordination, multi robots
Procedia PDF Downloads 31727 Modelling the Effect of Distancing and Wearing of Face Masks on Transmission of COVID-19 Infection Dynamics
Authors: Nurudeen Oluwasola Lasisi
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The COVID-19 is an infection caused by coronavirus, which has been designated as a pandemic in the world. In this paper, we proposed a model to study the effect of distancing and wearing masks on the transmission of COVID-19 infection dynamics. The invariant region of the model is established. The COVID-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using the linearization technique method and Lyapunov method. It was found that COVID-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R₀ < 1 and globally asymptomatically stable if R₀ < 1, otherwise unstable if R₀ > 1. More so, numerical analysis and simulations of the dynamics of the COVID-19 infection are presented.Keywords: distancing, reproduction number, wearing of mask, local and global stability, modelling, transmission
Procedia PDF Downloads 10626 Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances
Authors: Shabnam Pashaei, Mohammadali Badamchizadeh
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This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system.Keywords: terminal sliding mode control, fractional-order calculus, chaotic systems, synchronization
Procedia PDF Downloads 38225 Sliding Mode Position Control for Permanent Magnet Synchronous Motors Based on Passivity Approach
Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee
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In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.Keywords: adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control
Procedia PDF Downloads 43324 Stability of Solutions of Semidiscrete Stochastic Systems
Authors: Ramazan Kadiev, Arkadi Ponossov
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Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.Keywords: abrupt changes, exponential stability, regularization, stochastic noises
Procedia PDF Downloads 13923 Anti-Phase Synchronization of Complex Delayed Networks with Output Coupling via Pinning Control
Authors: Chanyuan Gu, Shouming Zhong
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Synchronization is a fundamental phenomenon that enables coherent behavior in networks as a result of interactions. The purpose of this research had been to investigate the problem of anti-phase synchronization for complex delayed dynamical networks with output coupling. The coupling configuration is general, with the coupling matrix not assumed to be symmetric or irreducible. The amount of the coupling variables between two connected nodes is flexible, the nodes in the drive and response systems need not to be identical and there is not any extra constraint on the coupling matrix. Some pinning controllers are designed to make the drive-response system achieve the anti-phase synchronization. For the convenience of description, we applied the matrix Kronecker product. Some new criteria are proposed based on the Lyapunov stability theory, linear matrix inequalities (LMI) and Schur complement. Lastly, some simulation examples are provided to illustrate the effectiveness of our proposed conditions.Keywords: anti-phase synchronization, complex networks, output coupling, pinning control
Procedia PDF Downloads 36622 Stabilization of a Three-Pole Active Magnetic Bearing by Hybrid Control Method in Static Mode
Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi
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The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.Keywords: active magnetic bearing, three pole AMB, hybrid control, Lyapunov function
Procedia PDF Downloads 31121 Impulsive Synchronization of Periodically Forced Complex Duffing's Oscillators
Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous
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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization
Procedia PDF Downloads 424