A Control Theoretic Framework for Optimally Locating Passive Vibration Isolators to Minimize Residual Vibration

This paper investigates the problem of optimally locating passive vibration isolators to minimize residual vibration caused by exogenous disturbance forces. The stiffness and damping properties of the isolators are assumed to be known and the task is to determine the isolator locations, which are nonlinearly related to system states. This paper proposes an approach for reformulating the nonlinear isolator placement problem as a LTI control problem by linking the control forces to measured outputs using a feedforward term. Accordingly, the isolator locations show up as a static output feedback gain matrix which is optimized for residual vibration reduction using standard H∞ optimal control methods. Simulations and experiments on SISO and MIMO case studies are used to demonstrate the merits of the proposed approach. Even though presented in the specific context of ultra-precision manufacturing machines, the proposed method is applicable to the optimal design of other passive systems with nonlinear relationships between design variables and system states.Copyright © 2015 by ASME

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