Pendulum controlled by a delayed proportional feedback force: Dynamical analysis and FPGA implementation
FRANK XAVIER NGAGOUM TCHAMDJEU ULRICH GAËL NGOUABO SAMUEL NOUBISSIE ROLAND CHRISTIAN GAMOM NGOUNOU EWO HILAIRE BERTRAND FOTSIN
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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.
FRANK XAVIER NGAGOUM TCHAMDJEU1 2 ULRICH GAËL NGOUABO1 3 SAMUEL NOUBISSIE3 4 ROLAND CHRISTIAN GAMOM NGOUNOU EWO5 HILAIRE BERTRAND FOTSIN1
Volume 97, 2023
Continuous Article Publishing mode
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