Abstract
Linear matrix Inequality based <TEX>$H_<TEX>$\infty$</TEX>$</TEX> robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard <TEX>$H_<TEX>$\infty$</TEX>$</TEX> control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based<TEX>$H_<TEX>$\infty$</TEX>$</TEX> control is revealed.
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