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Pendulum controlled by a delayed proportional feedback force: Dynamical analysis and FPGA implementation

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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.

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Authors and Affiliations

  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

    Frank Xavier Ngagoum Tchamdjeu, Ulrich Gaël Ngouabo & Hilaire Bertrand Fotsin

  2. Unité de Recherche d’Ingénierie des Systèmes Industriels et Environnement (UR-ISIE), IUT-FV de Bandjoun, Université de Dschang, B.P. 134, Bandjoun, Cameroun

    Ulrich Gaël Ngouabo & Samuel Noubissie

  3. 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

    Samuel Noubissie

  4. Laboratoire Génie Informatique et Automatique (GIA), École Normale Supérieure d’Enseignement Technique, Université de Douala, B.P. 1 872, Douala, Cameroun

    Roland Christian Gamom Ngounou Ewo

  5. Department of Electrical and Electronics Engineering, Higher Institute of Advanced Technologies, University Institute of Guinea Gulf, P.O. Box 12 489, Douala, Cameroon

    Frank Xavier Ngagoum Tchamdjeu

Authors
  1. Frank Xavier Ngagoum Tchamdjeu
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  2. Ulrich Gaël Ngouabo
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  3. Samuel Noubissie
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  4. Roland Christian Gamom Ngounou Ewo
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  5. Hilaire Bertrand Fotsin
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Tchamdjeu, F.X.N., Ngouabo, U.G., Noubissie, S. et al. Pendulum controlled by a delayed proportional feedback force: Dynamical analysis and FPGA implementation. Pramana - J Phys 96, 13 (2022). https://doi.org/10.1007/s12043-021-02259-x

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  • DOI: https://doi.org/10.1007/s12043-021-02259-x

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