This paper presents a theoretical analysis of a planar quasi-zero stiffness magnetic levitation system with improved passive rotational stability for the application of vibration isolation. Through proper choices of equilibrium position and magnet geometry (horizontal gap parameter), the system is made stable in the vertical and rotational degrees of freedom, thus requiring active stability control only in the horizontal degree of freedom. It is found that the control effort is inversely proportional to the magnitude of the passive rotational stability. The effect of these parameters on the stability and vibration response of the system is examined. The nonlinearity of the system is also investigated by comparing the vibration response to its linear representation, in which it is shown that the system becomes increasingly nonlinear as it is perturbed further away from its equilibrium position.
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