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1

Speed control of doubly fed induction motor using backstepping control with interval type-2 fuzzy controller

Herizi Abdelghafour, Rouabhi Riyadh, Zemmit Abderrahim

Diagnostyka

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2023

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Vol. 24, No. 3

art. no. 2023301

EN

The control of the doubly-fed induction motor is a complex operation because of this motor characterised by a non-linear multivariable dynamics, having settings that change over time and a significant link between the mechanical component and magnetic behavior (flux) (speed and couple). This article then proposes a new strategy of a robust control of this motor, which is decoupled due to the stator flux’s direction. The proposed control is integrated with the backstepping control which based on Lyapunov theory; this approach consists in constructively designing a control law of nonlinear systems by considering some state variables as being virtual commands, and the important branch of artificial intelligence type-2 fuzzy logic. The hybrid control backstepping-fuzzy logic consists in replacing the regulators applied to the backstepping control by regulators based on type-2 fuzzy logic. This control will be evaluated by numerous simulations where there is a parametric and non-parametric variation.

2

A comparative study based on proportional integral and backstepping controllers for doubly fed induction generator used in wind energy conversion system

Moumani Youssef, Laafou Abdeslam Jabal, Madi Abdessalam Ait

Archives of Electrical Engineering

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2023

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Vol. 72, nr 1

211--228

EN

This paper presents a comparative study between the conventional PI (Proportional Integral) and backstepping controllers applied to the DFIG (Doubly Fed Induction Generator) used in WECS (Wind Energy Conversion System). These two different control strategies proposed in this work are developed to control the active and reactive power of the DFIG on the one hand, and to maintain the DC-link voltage constant for the inverting function on the other hand. This is ensured by generating control signals for two power electronic converters, RSC (Rotor Side Converter) and GSC (Grid Side Converter). In order to optimise the power production in the WT (Wind Turbine), an MPPT (Maximum Power Point Tracking) algorithm is applied along with each control technique. To simulate the effectiveness of the proposed controllers, MATLAB/Simulink Software is used, and the obtained results are analysed and discussed to compare PI and backstepping controllers in terms of robustness against wind speed variations and tracking performance in dynamic and steady states.

3

A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design

Mohamed Mohamad Afendee, Vaidyanathan Sundarapandian, Hannachi Fareh, Sambas Aceng, Darwin P.

Archives of Control Sciences

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2023

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Vol. 33, No. 4

711--735

EN

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

4

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng

Archives of Control Sciences

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2022

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Vol. 32, No. 1

123--152

EN

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.

5

Backstepping control strategy for multi-source energy system based flying capacitor inverter and PMSG

Boumediene Bachir, Smaili Attalah, Allaoui Tayeb, Berkani Abderrahmane, Marignetti Fabrizio

Przegląd Elektrotechniczny

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2021

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R. 97, nr 3

21--29

EN

In this paper, renewable photovoltaic (PV) and wind turbine (WT) generators with battery are coupled via a flying capacitor inverter to a power grid in parallel with an alternating load. This paper studies a new control structure focused a backstepping control of the energy storage system. The proposed methods to adjust the active and reactive power by adjusting the currents, the DC bus voltage on the grid side converter, as well as the battery voltage allow three selective control targets to be achieved, the objective is to obtain purely sinusoidal signals and symmetrical gate current, suppresses reactive power ripples and cancels active power ripples in the event of grid imbalance. In order to optimize the power flow in the different parts of the production process, an energy management algorithm is developed in order to mitigate the fluctuations of the load, the considered multi-sources on-grid system was implemented in the Matlab/Simulink, the results show the effectiveness of the proposed method. To analyze our approach, a prototype is modeled, simulated and can be realized in an experimental test setup.

PL

W tym artykule odnawialne generatory fotowoltaiczne (PV) i turbiny wiatrowe (WT) z baterią są sprzężone za pośrednictwem falownika ze swobodnym kondensatorem z siecią energetyczną równolegle ze zmiennym obciążeniem. Przeanalizowano nową strukturę controli sterowania, która skupiła się na wstecznej kontroli systemu magazynowania energii. Proponowane metody regulacji mocy czynnej i biernej poprzez regulację prądów, napięcia szyny DC po stronie sieciowej oraz napięcia akumulatora pozwalają na osiągnięcie trzech celów regulacji selektywnej, celem jest uzyskanie sygnałów czysto sinusoidalnych i symetrycznych. prąd bramki, tłumi tętnienia mocy biernej i anuluje tętnienia mocy czynnej w przypadku braku równowagi sieci. W celu optymalizacji przepływu mocy w różnych częściach procesu produkcyjnego opracowano algorytm zarządzania energią w celu złagodzenia wahań obciążenia, rozważany wielozródłowy system on-grid został zaimplementowany w programie Matlab / Simulink, wyniki pokazują skuteczność proponowanej metody. Aby przeanalizować nasze podejście, modeluje się prototyp, przeprowadza symulację i może zostać zrealizowany w eksperymentalnej konfiguracji testowej.

6

Enhanced Reliability for Winding Machine via New Fault Tolerant Control Based on RST-Backstepping Controller

Haouari Fouad, Messekher Salaheddine, Bali Noureddine, Tadjine Mohamed, Boucherit Mohamed Seghir

Power Electronics and Drives

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2021

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Vol. 6 (41)

229--241

EN

Due to the external disturbances, model uncertainties, strong coupling, and occurred faults, the winding machine presents a great control challenge. In order to deal with these problems, this paper presents the formulation of a novel scheme of fault tolerant control (FTC) for three-motor web-winding systems; it is concerned with the nonlinear robust backstepping control based on the combination of RST and backstepping controllers where the process is modelled by a nonlinear model. The main contribution of the paper is that the approach developed here summarises the performance of RST and backstepping controllers in order to design a robust controller capable of eliminating external disturbances and sensor faults affecting the system. The stability of the whole system is proven using the Lyapunov theory. Finally, analysis in comparison with the conventional backstepping controller and simulations in the MATLAB environment are accomplished to confirm the efficiency of the proposed method.

7

Sensorless backstepping control using a Luenberger observer for double-star induction motor

Chaabane Hadji, Eddine Khodja Djalal, Salim Chakroune

Archives of Electrical Engineering

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2020

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Vol. 69, nr 1

101--116

EN

In this paper, we propose sensorless backstepping control of a double-star induction machine (DSIM). First, the backstepping approach is designed to steer the flux and speed variables to their references and to compensate uncertainties. Lyapunov”s theory is used and it demonstrates that the dynamic tracking of trajectories tracking is asymptotically stable. Second, unfortunately, this law control called sophisticated is a major problem which leads to the necessity of using a mechanical sensor (speed, load torque). This imposes an additional cost and increases the complexity of the montage. In practice, this variable is unknown and its measurement is expensive. To restrain this problem we estimate speed and load torque by using a Luenberger observer (LO). Simulation results are provided to illustrate the performance of the proposed approach in high and low variable speeds and load torque disturbance.

8

Global stability of backsteping control with robust nonlinear observer of induction motor in (α,β) frame

Chenafa Amine, Chenafa Mohammed, Mansouri Abdellah, Chaker Abdelkader

Przegląd Elektrotechniczny

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2019

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R. 95, nr 1

191--196

EN

This paper deals with the design of an advanced control law by backstepping with an observer for a special class of nonlinear systems. We design an observer with a single adjustment gain as a function of speed. Our contribution is developed by demonstrating a nonlinear control law by backstepping using the global Lyapunov stability of the controller, the nonlinear observer and the induction motor. We study the behavior of the torque tracking and the rotor flux of the induction motor in the natural frame(α,β). The control algorithm obtained is studied through simulations and applied in many configurations (flux and speed and torque disturbances), and is shown to be very efficient.

PL

Niniejszy artykuł dotyczy projektowania zaawansowanego prawa kontroli poprzez odtwarzanie z obserwatorem specjalnej klasy systemów nieliniowych. Projektujemy obserwatora z jednym wzmocnieniem regulacji w funkcji prędkości. Nasz układ jest rozwijany przez demonstrowanie nieliniowego prawa kontrolnego poprzez odtwarzanie za pomocą globalnej stabilności Lapunowa kontrolera, nieliniowego obserwatora i silnika indukcyjnego. Badamy zachowanie śledzenia momentu i strumienia wirnika silnika indukcyjnego w naturalnej ramie (α, β). Uzyskany algorytm sterowania jest badany za pomocą symulacji i stosowany w wielu konfiguracjach (strumień i zakłócenia prędkości i momentu obrotowego) i jest bardzo wydajny.

9

Backstepping controller with force estimator applied for mobile robot

Ibari Benaoumeur, Bouzgou Kamel, Ahmed-Foitih Zoubir, Benchikh Laredj

Przegląd Elektrotechniczny

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2019

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R. 95, nr 10

18--21

EN

In this paper, we present the concept of nonlinear control technique for trajectory tracking problem of mobile robot type unicycle. the design of the proposed controller is combines a backstepping controller and the force estimator method. The main aim of this study is to design a robust control law in the presence of disturbances using the backstepping with estimation of the forces. The approach consists to estimate the perturbation using an adaptive controller, the effectiveness of the proposed approach is demonstrated through simulation and experimental results.

PL

W niniejszym artykule przedstawiamy koncepcję techniki sterowania nieliniowego dla problemu śledzenia trajektorii w monocyklu typu robota mobilnego. Konstrukcja proponowanego sterownika łączy w sobie kontroler backstepping i metodę estymatora siły. Głównym celem tego badania jest zaprojektowanie solidnego prawa sterowania w obecności zakłóceń wykorzystując backstepping z oszacowaniem sił. Podejście polega na oszacowaniu perturbacji za pomocą adaptacyjnego kontrolera, skuteczność zaproponowanego podejścia została zademonstrowana za pomocą symulacji i wyników eksperymentalnych.

10

Synchronization of neuronal bursting using backstepping control with recursive feedback

Rasappan Suresh

Archives of Control Sciences

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2019

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Vol. 29, No. 4

617--642

EN

J. L. Hindmarsh, R. M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.

11

Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design

Pham Viet-Thanh, Vaidyanathan Sundarapandian, Volos Christos, Jafari Sajad, Alsaadi Fawaz E., Alsaadi Fuad E.

Archives of Control Sciences

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2019

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Vol. 29, No. 1

73--96

EN

We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap system displays chaotic attractors, which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.

12

A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design

Vaidyanathan S., Jafari S., Pham V.-T., Azar A. T., Alsaadi F. E.

Archives of Control Sciences

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2018

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Vol. 28, No. 2

239--254

EN

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor.

13

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Vaidyanathan S.

Archives of Control Sciences

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2017

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Vol. 27, no. 3

409--439

EN

This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

14

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Vaidyanathan S.

Archives of Control Sciences

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2016

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Vol. 26, no. 3

311--338

EN

A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.14219, L2 = 0.04605, L3 = 0 and L4 = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

15

A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

Vaidyanathan S.

Archives of Control Sciences

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2016

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Vol. 26, no. 1

19--47

EN

This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.20572, L2 = 0 and L3 = −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as DKY = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.

16

Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

Vaidyanathan S., Volos C., Pham V.-T., Madhavan K.

Archives of Control Sciences

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2015

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Vol. 25, no. 1

135--158

EN

A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0:1448;L2 = 0:0328;L3 = 0 and L4 = −1:1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY = 3:1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

17

Reduced order hybrid function projective combination synchronization of three Josephson junctions

Ojo K. S., Njah A. N., Ogunjo S. T., Olusola O. I.

Archives of Control Sciences

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2014

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Vol. 24, no. 1

99--113

EN

In this paper, we examine reduced order hybrid function projective combination synchronization of three chaotic systems consisting of: (i) two third chaotic Josephson junctions as drives and one second order chaotic Josephson junction as response system; (ii) one third order chaotic Josephson junction as the drive and two second order chaotic Josephson junctions as the slaves using active backstepping technique. The analytic results confirm the realization of reduced order hybrid function projective combination synchronization using active backstepping technique. Numerical simulations are performed to validate the analytical results.

18

Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities

Vaidyanathan S., Volos C., Pham V.-T., Madhavan K., Idowu B. A.

Archives of Control Sciences

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2014

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Vol. 24, no. 3

375--403

EN

In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.

19

Dynamic variables limitation for backstepping control of induction machine and voltage source converter

Morawiec M.

Archives of Electrical Engineering

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2012

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Vol. 61, nr 3

389-410

EN

The paper presents the method of control of an induction squirrel-cage machine supplied by a voltage source converter. The presented idea is based on an innovative method of the voltage source converter control, consisting in direct joining of the motor control system with the voltage source rectifier control system. The combined control system gives good dc-bus voltage stabilization. In the applied control system the limits of the reference variables have been introduced. A correction of the estimated machine load torque is proposed. The new proposed solutions are confirmed by mathematical dependences, simulation and experimental results.

20

Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

Suresh R., Sundarapandian V.

Archives of Control Sciences

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2012

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Vol. 22, no. 3

343-365

EN

This paper investigates the backstepping control design with novel feedback input approach for controlling chaotic systems to guarantee the complete synchronization as well as the anti-synchronization of chaotic systems, viz. n-scroll Chua (K. Wallace et.al. 2001) and Lur’e chaotic systems. Our theorems on hybrid synchronization for n-scroll Chua and Lur’e (J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based on the Lyapunov function, the backstepping control is determined to tune the controller gain based on the precalculated feedback control inputs. The backstepping scheme is recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the chaotic systems. Mainly this technique gives the flexibility to construct a control law. Numerical simulations are also given to illustrate and validate the hybrid synchronization results derived in this paper.