In many applications comprised of multiple platforms with stringent vibration isolation requirements, several vibration isolators are employed to work in tandem. They usually must accomplish two objectives: (i) reduce the vibration level of each platform; and (ii) maintain the required alignment with respect to each other or with a fixed reference. If the isolators are located on a rigid supporting structure, the problem can be approached as a classical vibration isolation (VI) problem, in which an increase in damping implies a reduction of vibration level experienced by the platforms. However, there are an increasing number of scenarios in which the dynamic interaction between the isolator and the base structure has the potential to alter the system response and consequently degrade VI performance. In this work, a generalized method to analyze the combined VI and alignment problem, for multiple isolators located on a flexible supporting structure, is proposed. The dynamic interaction between the platforms and the isolators is considered in the control design, and it is proved employing two different functional values that the maximum damping solution is not always the best approach when the dynamics of the supporting structure are considered. Numerical simulations are presented to validate the theory developed and robustness of the proposed control approach is demonstrated.
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