A mathematical model of a six-degree-of-freedom (6-DOF) hexapod system for vibration isolation was derived in the discrete-time domain on the basis of the experimental data obtained from a satellite. Using a Box–Jenkins model structure, the transfer functions between six piezoelectric actuator input voltages and six geophone sensor output voltages were identified empirically. The transfer function matrix is symmetric, and its off-diagonal terms indicate the coupling among different input/output channels. Various multi-input multi-output (MIMO) control techniques such as Linear Quadratic Gaussian and were proposed for active vibration isolation in the broadband up to 100 Hz. The simulation results using these controllers obtain 13 and 8 dB vibration attenuation at 25 and 35 Hz, respectively.
Modeling and Multivariable Control Design Methodologies for Hexapod-Based Satellite Vibration Isolation
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Joshi, A., and Kim, W. (November 30, 2004). "Modeling and Multivariable Control Design Methodologies for Hexapod-Based Satellite Vibration Isolation." ASME. J. Dyn. Sys., Meas., Control. December 2005; 127(4): 700–704. https://doi.org/10.1115/1.2101842
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