Online Identification of Mathematical Model of Circular Plate for Vibration Cancellation

Identification is the first step in designing of the controller for suppressing vibrations of considered circular plate. It constructs a parametric model of the system dynamics from measured input and output data. This data-driven technique can describe systems that are not easily modelled from the first principles or specifications. Identification methods can handle a wide range of the system dynamics without knowledge of the actual system physics. In this paper the ARX model structure and algorithm called online identification have been considered. In this procedure, model parameters are calculated and updated during the process using the data measured a few steps earlier. Before output data can be resorted for identification it should be prefiltered by using the digital Butterworth filter. This step removes mean values and high-frequency noise.
The second order transfer function, obtained by using described identification algorithm, was implemented in procedure of designing the optimal PID controller for suppressing vibrations of the plate. Simulations of working this regulator for sin and chirp signals shows that the controller causes substantial reduction of the vibrations.