This paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.
In this paper, the MFC sensor and actuators are applied to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The mathematical model of the plate was obtained on the base of registration of a system response on a fixed excitation. For the estimation of the system’s behaviour the ARX identification method was used to derive the linear model in the form of a transfer function of the order nine. The obtained model is then used to develop the linear feedback control algorithm for the cancellation of vibration by using the MFC star-shaped actuator (SIMO system). The MFC elements location is dealt with in this study with the use of a laser scanning vibrometer. The control schemes presented have the ability to compute the control effort and to apply it to the actuator within one sampling period. This control scheme is then illustrated through some numerical examples with simulations modelling the designed controller. The paper also describes the experimental results of the designed control system. Finally, the results obtained for the considered plate show that in the chosen frequency limit the designed structure of a closed-loop system with MFC elements provides a substantial vibration suppression.