A theoretical study of the active control of structural vibration transmission in a multiple isolator system comprising a piece of equipment mounted on a base structure via active mounts is presented. Two types of problem have been studied with a common framework: first, the active isolation of vibration transmission from the equipment to the base structure and, second, the active isolation of vibration transmission from the base structure to the equipment. Four different control strategies using the measured axial velocity or/and axial force underneath or at the top of the mounts have been investigated and compared with the effectiveness of the reference control approaches of minimizing the total power transmitted from the equipment to the flexible base structure or minimizing the total kinetic energy of the suspended rigid equipment when driven by the base structure. For the first type of isolation problem the best control is achieved when a cost function which minimizes the weighted mm of the square values of the axial velocities and axial forces is implemented. For the second isolation problem the best control performance is given by the minimization of an estimate of the kinetic energy of the suspended equipment related to the translational degrees of freedom.

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