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

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 sys-
tem 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.