Fractional controller design for suppressing smart beam vibrations

Purpose – The purpose of this paper is to detail the design of a fractional controller which was developed for the suppression of the flexural vibrations of the first mode of a smart beam. Design/methodology/approach – During the design of the fractional controller, in addition to the classical control parameters such as the controller gain and the bandwidth; the order of the derivative effect was also included as another design parameter. The controller was then designed by considering the closed loop frequency responses of different fractional orders of Continued Fraction Expansion (CFE) method. Findings – The first, second, third and fourth order approximations of CFE method were studied for the performance analysis of the controller. It was determined that the increase in the order resulted in better vibration level suppression at the resonance. The robustness analysis of the developed controllers was also conducted. Practical implications – The experimentally obtained free and forced vibration results indicated that the increase in the order of the approximations yielded better performance around the first flexural resonance region of the smart beam and proved to yield better performance than the classical integer order controllers. Originality/value – Evaluation of the performance of a developed fractional controller was realized by using different approach orders of the CFE method for the suppression of the flexural vibrations of a smart beam.