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      https://www.ias.ac.in/article/fulltext/pram/096/0013

    • Keywords

       

      Delayed proportional controller; coexistence of strange attractors; multiscroll; RK4algorithm; VHDL; FPGA implementation.

    • Abstract

       

      This work deals with the dynamical analysis and FPGA implementation of a pendulum controlled by a delayed proportional feedback force. The system has infinity equilibrium points and so the nature of these points is established according to the value of the gain of the controller. Analysis of the effect of delay on the linear system through a stability chart revealed stability switching. The Hopf bifurcation curves are presented gradually as the delay varies and thus confirm the analytical predictions. Furthermore, these bifurcation diagrams show the existence of complex behaviours and the coexistence of infinity strange attractors for different initial values. This system can be considered as a self-producer of attractors depending on the initial conditions. For certain values of the delay, the system exhibits the multiscroll behaviour which can be observed through the phase portraits. The FPGA implementation of the system is based on the VHDL hardware description which takes into account the RK4 resolution method with calculations under the 32-bit 16Q16 fixed-point number standard.

    • Author Affiliations

       

      FRANK XAVIER NGAGOUM TCHAMDJEU1 2 ULRICH GAËL NGOUABO1 3 SAMUEL NOUBISSIE3 4 ROLAND CHRISTIAN GAMOM NGOUNOU EWO5 HILAIRE BERTRAND FOTSIN1

      1. Unité de Recherche de Matière de Condensée d’Electronique et de Traitements de Signal (UR-AMCETS), Faculté de Science, Université de Dschang, B.P. 67, Dschang, Cameroun
      2. Department of Electrical and Electronics Engineering, Higher Institute of Advanced Technologies, University Institute of Guinea Gulf, P.O. Box 12 489, Douala, Cameroon
      3. Unité de Recherche d’Ingénierie des Systèmes Industriels et Environnement (UR-ISIE), IUT-FV de Bandjoun, Université de Dschang, B.P. 134, Bandjoun, Cameroun
      4. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes and TWAS Research Unit, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroun
      5. Laboratoire Génie Informatique et Automatique (GIA), École Normale Supérieure d’Enseignement Technique, Université de Douala, B.P. 1 872, Douala, Cameroun
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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