Continuous finite-time sliding mode control for synchronization of perturbed bistable electrostatic and piezoelectric transducers with external disturbances

Abstract

Despite that the synchronization of chaotic systems has been extensively investigated and demonstrated to contribute to physical, chemical, financial, and biological applications, the synchronization of different perturbed bistable systems appears to be an open issue. This is significant with the fact that the bistability widely exists from the visual perception to the electrical and mechanical systems. Therefore, this paper proposes a continuous finite-time terminal sliding mode control method to synchronize two bistable electromechanical transducers, with the electrostatic one acting as the master system and the piezoelectric one acting as the slave system. The model of two systems as well as the control method considering external disturbances and unmodeled dynamics are presented. Numerical simulation results show that two bistable systems can be synchronized with our proposed control method in intrawell, chaotic, and interwell oscillation modes. Furthermore, the chattering issue in conventional discontinuous controllers is eliminated with our designed continuous finite-time terminal protocols for bistable chaotic systems so as to improve the robustness of the controller and avoid its failure. Interesting findings are discussed for the varying system responses and control inputs in different oscillation modes. This work also is expected to facilitate the development of applications where bistability is found such as power or communication systems to resist the external disturbances.