Fast fixed-time sliding mode control of a bistable dual-stage vibration isolator with disturbances

Despite that multistable isolators have been demonstrated to achieve the superior isolation performance compared with the linear ones, their performances are still inferior at ultra-low frequencies with the multi-solution phenomenon. Furthermore, their performances are dependent on the variation of initial conditions. Therefore, this paper proposes a fast fixed-time sliding mode controller to solve the ineffectiveness of the bistable dual-stage vibration isolator with external disturbances facing the above issues. Firstly, the bistable dual-stage isolator is modelled in the analytical form, and simulated compared with its linear counterpart to show its problems at some conditions. Secondly, the fast fixed-time sliding mode controller is presented with the modeling of sliding manifold and control inputs. Thirdly, the numerical simulation of the bistable dual-stage isolator with the proposed control is conducted, the results of which are compared with the finite-time sliding mode control. Finally, the outstanding feature of the proposed controller is concluded that the short convergence time becomes bounded with increasing initial conditions at both low and high excitation amplitudes. This work provides a valuable method to improve the isolation performance and robustness of the multistable vibration isolators.