Grey relation analysis of natural frequency and semi-active robust optimal control of a multi-dimensional isolator based on parallel mechanism and magneto-rheological damper

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.