This paper deals with discrete time learning controllers for systems with periodically varying parameters. Several control rules are proposed which use a basic principle of learning control that is to utilize the information from the most recent cycle to improve the system performance in the next cycle. Convergence properties of proposed learning control algorithms are examined. These algorithms can easily be implemented without additional measurements and without modification of existing feedback/feedforward controller. In a numerical example learning controllers are applied to eliminate the forced vibrations of a magnetically suspended rotor with nonsymmetric stiffness properties. The vibrations result from unbalanced inertia forces. Simulation results show that the learning controller is effective in absorbing periodic disturbances.

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