A Frequency-Shaped Sliding Surface Control (FSSSC) approach is applied to an unstable model of a candidate Electro-Magnetic Isolator (EMI) design which has three Degrees Of Freedom (DOF). The EMI is designed to achieve contactless passive gravity compensation for heavy load by permanent magnets. The 3-DOF model can be regarded as three exactly the same double-integrators disturbed by the nonlinear and coupled passive force which results in its inherent instability. The sliding surface is designed based on relative displacement and payload acceleration feedback to achieve low-frequency vibration isolation. To avoid the algebraic control loop, a linear converging controller is designed instead of the conventional switching control. Regardless of the plant uncertainties, the closed-loop transmissibility converges to the designed transmissibility with increasing open-loop gain. A sufficient condition for the closed-loop stability is developed. Both time domain and frequency domain performance of the designed controller is evaluated by simulation. It shows that robust vibration isolation performance is achieved despite of the nonlinear and coupled passive force.
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