Modeling and 6-DOF Vibration Reduction for a Spacecraft with Precision Sensors
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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. A model of transmissibility matrix relating tri-axial geophones on the base and the platform was also developed to identify other important corner frequencies. Using multi-input multi-output control techniques such as Linear Quadratic Gaussian and H ∞, high-order controllers were developed. The simulation results using these controllers obtain 33 dB, and 12 dB vibration attenuation at 5, and 25 Hz corner frequencies, respectively.
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