Vibration active control of structure with parameter perturbation using fractional order positive position feedback controller

A Fractional-Order Positive Position Feedback (FOPPF) controller is developed by transforming the integer-order exponent of the Positive Position Feedback (PPF) controller into a fractional format to increase the number of designable parameters. The sensitivity of these fractional-order exponents is investigated to assess their influence on the behavior of the FOPPF controller in frequency domain. An optimal design method of FOPPF controller is presented by taking account of the uncertainty of object structure, and constructing an objective function. This objective function is the weighted sum of the suppression ratio of the peak value of power spectral density and the suppression ratio of the root-mean-square value of the random response in the target frequency band. The performance of this controller is analyzed by numerical simulation and experiment using a vertical tail attaching macro fiber composite piezoelectric actuator. Results indicate that a wider band of effective phase compensation is obtained using the FOPPF controller than using the PPF one, and a higher robustness is achieved as well. The FOPPF controller is more effective on suppressing the both periodic and random vibration responses comparing with the PPF and modified PPF controller.