A mathematical model of a six-degree-of-freedom hexapod system for vibration isolation was derived in the discrete-time domain on the basis of the experimental data obtained from a satellite. Using Box-Jenkins model structure, the transfer functions between six piezoelectric actuator input voltages and six geophone sensor output voltages are identified empirically. The 6×6 transfer function matrix is symmetric, and its off-diagonal terms indicate the coupling among different input/output channels. Though the coupling was observed among various input/output channels up to 10 Hz, the single-input single-output (SISO) controllers were designed neglecting the effect of coupling. The SISO controllers demonstrated limited performance in vibration attenuation. Using multi-input multi-output (MIMO) control techniques such as Linear Quadratic Gaussian (LQG) and H, high-order controllers were developed. The simulation results using these controllers obtain 33 dB, and 12 dB attenuation at 5, and 25 Hz corner frequencies, respectively.

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