Self-Tuning Control with Regularized RLS Algorithm for Vibration Cancellation of a Circular Plate

The self-tuning control assumes that the vibrating system
is unknown and the controller procedure has the ability to identify the process
and to update the necessary control law. Such an algorithm provides the relevant
regulator parameters according to the obtained parametric object model. The
algorithm can be described as a combination of the following two procedures: the
online identification and the computation of the controller parameters. Nearly
all of the identification procedures are related to the Least Squares (LS)
estimate of a model output. Classified as an ill-posed problem, it implies that
the obtained solution is potentially very sensitive to the data perturbations.
In order to avoid such problems, the regularized version of the RLS method has
been considered in this paper. By solving the linear system of equations with a
non-singular Sylvester matrix, the formulas for the unknown coefficients of the
considered PID-type controller structure have been obtained. The results of the
tests and simulations for the circular plate vibration cancellation have been
also included.