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.

Vibrating plates have been recently used for a number of active noise control applications. They are resistant to difficult environmental conditions including dust, humidity, and even precipitation. However, their properties significantly depend on temperature. The plate temperature changes, caused by ambient temperature changes or plate heating due to internal friction, result in varying response of the plate, and may make it significantly different than response of a fixed model. Such mismatch may deteriorate performance of an active noise control system or even lead to divergence of a model-based adaptation algorithm.

In this paper effects of vibrating plate temperature variation on a feedforward adaptive active noise reduction system with the multichannel Filtered-reference LMS algorithm are examined. For that purpose, a thin aluminum plate is excited with multiple Macro-Fiber Composite actuators. The plate temperature is forced by a set of Peltier cells, what allows for both cooling and heating the plate. The noise is generated at one side of the plate, and a major part of it is transmitted through the plate. The goal of the control system is to reduce sound pressure level at a specified area on the other side of the plate.

To guarantee successful operation of the control system in face of plate temperature variation, a gain-scheduling scheme is proposed to support the Filtered-reference LMS algorithm.