Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 8
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit model using MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.

Go to article

Authors and Affiliations

Sundarapandian Vaidyanathan
Aceng Sambas
Sen Zhang
Download PDF Download RIS Download Bibtex

Abstract

In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.

Go to article

Authors and Affiliations

Sundarapandian Vaidyanathan
Aceng Sambas
Mustafa Mamat
Download PDF Download RIS Download Bibtex

Abstract

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.
Go to article

Authors and Affiliations

Sundarapandian Vaidyanathan
Sajad Jafar
Viet-Thanh Pham
Ahmad Taher Azar
Fawaz E. Alsaadi

Abstract

We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap systemdisplays 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.

Go to article
Download PDF Download RIS Download Bibtex

Abstract

In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988).We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija- Greller population biology system (1988).We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).
Go to article

Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
2
Aceng Sambas
3
P. Darwin
4

  1. Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Non Destructive Testing Laboratory, Automatic Department, Jijel University, BP 98, 18000, Jijel, Algeria
  3. Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia
  4. Department of Computer Science and Engineering, Rajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India
Download PDF Download RIS Download Bibtex

Abstract

A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.

Go to article

Authors and Affiliations

Sundarapandian Vaidyanathan
Irene M. Moroz
Aceng Sambas
Download PDF Download RIS Download Bibtex

Abstract

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.
Go to article

Authors and Affiliations

Mohamad Afendee Mohamed
1
Sundarapandian Vaidyanathan
2 3
Fareh Hannachi
4
Aceng Sambas
1
P. Darwin
5

  1. Faculty of Information and Computing,Universiti Sultan Zainal Abidin, Terengganu, Malaysia
  2. Centre for ControlSystems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062 Tamil Nadu, India
  3. Faculty of Information and Computing, Universiti Sultan Zainal Abidin Terengganu, Malaysia
  4. Larbi Tebessi University – Tebessi routede constantine, 12022, Tebessa, Algeria
  5. Department of Computer Science and EngineeringRajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India
Download PDF Download RIS Download Bibtex

Abstract

The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.
Go to article

Bibliography

  1.  A.C. Fowler, J.D. Gibbon, and M.J. McGuinness, “The complex Lorenz equations”, Physica D 4, 139–163 (1982).
  2.  P. Liu, H. Song, and X. Li, “Observe-based projective synchronization of chaotic complex modified Van Der Pol-Duffing oscillator with application to secure communication”, J. Comput. Nonlinear Dyn. 10, 051015 (2015).
  3.  G.M. Mahmoud and A.A. Shaban, “On periodic solutions of parametrically excited complex non-linear dynamical systems”, Physica A 278(3‒4), 390–404 (2000).
  4.  G.M. Mahmoud and A.A. Shaban, “Periodic attractors of complex damped non-linear systems”, Int. J. Non-Linear Mech. 35(2), 309–323 (2000).
  5.  G.M. Mahmoud, “Periodic solutions of strongly non-linear Mathieu oscillators”, Int. J. Non-Linear Mech. 32(6), 1177–1185 (1997).
  6.  G.M. Mahmoud and E.E. Mahmoud, “Lag synchronization of hyperchaotic complex nonlinear systems”, Nonlinear Dynamics 67, 1613– 1622 (2012).
  7.  P. Liu and S. Liu, “Anti-synchronization between different chaotic complex systems”, Phys. Scr. 83, 065006 (2011).
  8.  S. Liu and P. Liu, “Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters”, Nonlinear Anal.-Real World Appl. 12, 3046–3055 (2011).
  9.  N. Siddique and F.U. Rehman, “Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach”, Math. Probl. Eng. 2018, 6581493 (2018).
  10.  G.M. Mahmoud, E.E. Mahmoud, and A.A. Arafa, “Projective synchronization for coupled partially linear complex-variable systems with known parameters”, Math. Meth. Appl. Sci. 40(4), 1214–1222 (2017).
  11.  D.W. Qian, Y.F Xi, and S.W. Tong, “Chaos synchronization of uncertain coronary artery systems through sliding mode”, Bull. Pol. Acad. Sci. Tech. Sci. 67(3), 455–462 (2019).
  12.  G.M. Mahmoud, E.E. Mahmoud, and A.A. Arafa, “On modified time delay hyperchaotic complex Lü system”, Nonlinear Dynamics 80(1‒2), 855–869 (2015).
  13.  G.M. Mahmoud, T. Bountis, M.A. Al-Kashif, and A.A. Shaban, “Dynamical properties and synchronization of complex nonlinear equations for detuned lasers”, Dynam. Syst. 24(1), 63–79 (2009).
  14.  J.-B. Hu, H. Wei, Y.-F. Feng, and X.-B. Yang, “Synchronization of fractional chaotic complex networks with delay”, Kybernetika 55, 203–215 (2019).
  15.  N.A. Almohammadi, E.O. Alzahrani, and M.M. El-Dessoky, “Combined modified function projective synchronization of different systems through adaptive control”, Arch. Control Sci. 29, 133–146 (2019).
  16.  H. Su, Z. Rong, M.Z.Q. Chen, X. Wang, G. Chen and H. Wang, “Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks”, IEEE Trans. Cybern. 43, 2182–2195 (2013).
  17.  A. Khan and U. Nigar, “Sliding mode disturbance observer control based on adaptive hybrid projective compound combination synchronization in fractional-order chaotic systems”, Int. J. Control Autom. Syst. 31, 885–899 (2020).
  18.  G.M. Mahmoud, E.A. Mansour, and T.M. Abed-Elhameed, “On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization”, Optik 130, 398–406 (2017).
  19.  S. Wang, X. Wang, X. Wang, and Y. Zhou, “Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems”, AIP Adv. 6, 045011 (2016).
  20.  J. Zhou, A. Oteafy, and N. Smaoui, “Adaptive synchronization of an uncertain complex dynamical network”, IEEE Trans. Autom. Control 51, 652–656 (2006).
  21.  X. Chen, J. Qiu, J. Cao, and H. He, “Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection”, Neurocomputing 173, 1299–1309 (2016).
  22.  F. Zhang, C. Mu, X. Wang, I. Ahmed, and Y. Shu, “Solution bounds of a new complex PMSM system”, Nonlinear Dynamics 74, 1041–1051 (2013).
  23.  Y.Wang, Y. Fan, Q.Wang, and Y. Zhang, “Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers”, IEEE Trans. Circuits Syst. I-Regul. Pap. 59, 1786–1795 (2012).
  24.  L. Zarour, K. Abed, M. Hacil, and A Borni, “Control and optimisation of photovoltaic water pumping system using sliding mode”, Bull. Pol. Acad. Sci. Tech. Sci. 67(3), 605–611 (2019).
  25.  N. Siddique, F.U. Rehman, M. Wasif, W. Abbasi, and Q. Khan, “Parameter Estimation and Synchronization of Vaidyanathan Hyperjerk Hyper-Chaotic System via Integral Sliding Mode Control”, 2018 AEIT Conference IEEE, 1–5 (2018).
  26.  K. Urbanski, “A new sensorless speed control structure for PMSM using reference model”, Bull. Pol. Acad. Sci. Tech. Sci. 65(4), 489–496 (2017).
  27.  X. Sun, Z. Shi, Y. Zhou, W. Zebin, S. Wang,B. Su, L. Chen, and K. Li, “Digital control system design for bearingless permanent magnet synchronous motors”, Bull. Pol. Acad. Sci. Tech. Sci. 66(5), 687–698 (2018).
  28.  T. Tarczewski, M. Skiwski, L.J. Niewiara, and L.M. Grzesiak, “High-performance PMSM servo-drive with constrained state feedback position controller”, Bull. Pol. Acad. Sci. Tech. Sci. 66(1), 49–58 (2018).
  29.  W. Xing-Yuan and Z. Hao, “Backstepping-based lag synchronization of a complex permanent magnet synchronous motor system”, Chin. Phys. B 22, 048902 (2013).
  30.  Z. Zhang, Z. Li, M.P. Kazmierkowski, J. Rodríguez, and R. Kennel, “Robust Predictive Control of Three-Level NPC Back-to-Back Power Converter PMSG Wind Turbine Systems With Revised Predictions”, IEEE Trans. Power Electron. 33(11), 9588– 9598 (2018).
  31.  N. Hoffmann, F.W. Fuchs, M.P. Kazmierkowski, and D. Schröder, “Digital current control in a rotating reference frame – Part I: System modeling and the discrete time-domain current controller with improved decoupling capabilities”, IEEE Trans. Power Electron. 31(7), 5290–5305 (2016).
  32.  H. Won, Y.-K. Hong, M. Choi, H.-s. Yoon, S. Li and T. Haskew, “Novel Efficiency-shifting Radial-Axial Hybrid Interior Permanent Magnet Sychronous Motor for Electric Vehicle”, 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, USA, 2020, pp. 47–52.
  33.  C. Jiang and S. Liu, “Synchronization and Antisynchronization of-Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection”, Complexity 4, 1–15 (2017).
  34.  M. Karabacak and H.I. Eskikurt, “Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control”, Math. Comput. Model. 53, 2015–2030 (2011).
Go to article

Authors and Affiliations

Nazam Siddique
1
ORCID: ORCID
Fazal U. Rehman
1

  1. Capital University of Science and Technology, Islamabad Expressway, Kahuta Road, Zone-V Islamabad, Pakistan

This page uses 'cookies'. Learn more