Multiple-input multiple-output active vibration control of a composite sandwich beam by fractional order positive position feedback

Positive Position Feedback (PPF) is an active vibration control algorithm widely employed for the vibration mitigation of thin-walled structures equipped with active flexural patches. Fractional order PPF (FOPPF) is a recent development of PPF that has been shown to achieve substantially better spillover characteristics, thanks to the inclusion of fractional calculus. However, so far, FOPPF literature has focused almost exclusively on single-input–single-output (SISO) applications, with little consideration of multiple-input-multiple-output (MIMO) capabilities and no experimental work on the subject. To fill this gap, a MIMO FOPPF control architecture was tested numerically and experimentally on a cantilever composite sandwich beam of rectangular section. The feedback algorithm involved two piezoelectric actuators and two piezoelectric sensors in a collocated configuration for the control of the lowest four resonances of the beam, excited by a random external excitation. The participation matrices, necessary for the simulation of the response of the electromechanical system, were obtained with a recently developed experimental method. The fractional orders of derivation, together with other controller parameters such as gain, resonant frequency and damping ratio, were chosen according to an optimization algorithm aimed at the vibration amplitude reduction of the first four resonances of the controlled system. As a result, the performance of the vibration control resulted superior to the equivalent PPF with integer exponents, both in simulations and experiments.