The weighted minimum variance control is extended to include the rational transfer function as well as the polynomial as the weighting on system input energy so as to guarantee the closed-loop stability in the whole range of the scalar input cost and the monotonic property of the controlled output and control input variances with respect to the scalar input cost. In addition, the Robbins-Monro scheme is modified for on-line adaptation of the scalar input cost under the time varying external disturbance to satisfy the constraint on input variance. The two schemes are then combined and applied to the vibration control of a servo-damper beam system. The experimental and simulation results show that the maximum usage of the available input energy is ensured in the presence of time varying external disturbance so as to achieve the good control performance and the effectiveness of the servo-damper system used for the suppression of the beam vibration.

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