Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary

This paper thoroughly investigates the broadband active vibration isolation of a bistable nonlinear electromagnetic actuator with an elastic boundary (simply named EB-bistable actuator). A new feedback control law is proposed to control the actuator's input current, to significantly attenuate the broadband vibration transmissibility from the base excitation to the actuator mover (supporting the payload). The control law comprises the polynomial function of the mover's absolute velocity. The mathematical models of the EB-bistable actuator and its application for vibration isolation are derived and experimentally validated. Then, based on the verified model, the paper comprehensively investigates the EB-bistable actuator with the proposed control law, which validates the broadband active vibration isolation performance for different system parameters. The input-to-state stability (ISS) of the control law for any non-negative control weights is proved, and thus it is a model-free control method. Results of one investigated case show that the maximum vibration transmissibility can be attenuated by over 90%. The lower bound of the effective vibration isolation bandwidth (where the vibration transmissibility is smaller than 0 dB) is reduced by 19.69%, i.e. the bandwidth is significantly broadened. Moreover, the study proves the effectiveness of the active vibration isolation for the structural variation and initial condition change. Finally, the paper thoroughly discusses the influence of the control law parameters on the active vibration isolation performance. The parametric studies develop useful guidelines for the active vibration isolation of the EB-bistable actuator.