Theoretical study and microcontroller implementation of a non-smooth electromechanical system actuated by a Rayleigh-Duffing oscillator

Abstract

Abstract This paper deals with the theoretical and experimental studies of non-smooth electromechanical system (EMS) actuated by Rayleigh-Duffing oscillator (RDO). The RDO exhibits sinusoidal and triangular signals depending on its nonlinear coefficient. The rate-equations of EMS under study are derived thanks to the Kirchhoff and Newton second laws. Based on the Routh-Hurwitz criterion, the stability of the two equilibrium points found are reported where one is unconditionally unstable and other one is stable or unstable based on systems parameters. The influence of the variation of the system parameters on the dynamics of the EMS is numerically studied by using the amplitude curves of the current and displacement of the EMS. Numerical results show that when the RDO excites the EMS with a sinusoidal signal, the movement of the EMS is either periodic oscillations or chaotic oscillations depending on the value of the elasticity coefficient. When the RDO excites the EMS with triangular signal, relaxation oscillations, periodic bursting oscillations or chaotic bursting oscillations are observed in the EMS depending on the value of the elasticity coefficient. The numerical analysis results are confirmed by the microcontroller implementation of EMS actuated by RDO.