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An Adaptive Vibration Control Procedure Based on Symbolic Solution of Diophantine Equation

Leniowska L.

Archives of Acoustics

2011

Vol. 36, No. 4

901-912

In this paper, the adaptive control based on symbolic solution of Diophantine equation is used to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The plate is excited by a uniform force over the bottom surface generated by a loudspeaker. The axially-symmetrical vibrations of the plate are measured by the application of the strain sensors located along the plate radius, and two centrally placed piezoceramic discs are used to cancel the plate vibrations. The adaptive control scheme presented in this work has the ability to calculate the error sensor signals, to compute the control effort and to apply it to the actuator within one sampling period. For precise identification of system model the regularized RLS algorithm has been applied. Self-tuning controller of RST type, derived for the assumed system model of the 4th order is used to suppress the plate vibration. Some numerical examples illustrating the improvement gained by incorporating adaptive control are demonstrated.

Self-tuning control with regularized RLS algorithm for vibration cancellation of a circular plate

Leniowska L., Kos P.

Archives of Acoustics

2009

Vol. 34, No. 4

613-624

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.