Time-delayed positive-position and velocity fefe edback controller to suppress the lateral vibrations in nonlinear Jeffcott-rotor system

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Within this paper, the negative-velocity and positive-positionfeedback (PPF) controllers are combined together to eliminate thelateral vibrations of a vertically supported nonlinear Jeffcott-rotorsystem. Time-delays (1 and 2 ) in the control loop are included inthe system model. The slow-flow modulating equations governingthe whole system vibration amplitudes are derived utilizingasymptotic analyses. The maximum limits of  1 and 2 at which thesystem solution remains stable are illustrated. The analysesapproved that the integration of velocity controller to the PPF one,improves the control efficiency and stretches the stable limits of both 1 and 2 . Finally, numerical confirmations for the obtained analyticalresults are included, which are in excellent agreement with theanalytical solution

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