Modeling and Multivariable Control Design Methodologies for Hexapod-Based Satellite Vibration Isolation

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 $6×6$ 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 $H∞$ 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.