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

Abstract

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.

An Adaptive Method for Reducing Vibrations of Circular Plates with Recursive Identification

“…The number of calculations strongly depends on the order of the controller. In the paper [19], instead of performing calculations online, the symbolic formulas for controller parameter estimation, which included only simple mathematical operations, such as multiplication and addition, were applied. This solution works well if the 4th-order ARX model (AutoRegressive with eXogenous input model) of the system has enough fidelity; however, for complex objects, modeled with the higher-order polynomials, the resulting symbolic formulas must be strongly optimized and reduced.…”

“…This condition is achieved when D(z −1 ) = 1. As a solution to the system of linear equations (19) obtained coefficients of the digital controller described by ( 15) and ( 16), which allow us to determine the control signal:…”

Application of an Memetic Algorithm to Placement of Sensors for Active Noise-Vibration Control

“…Active noise-vibration control systems often rely on structural sound sources (Pawełczyk 2008, Leniowska 2011, Kozupa and Wiciak 2010, Mazur and Pawełczyk 2011. However, for successful active control of a vibrating structure it is essential to possess relevant information about its current state.…”

Active Noise Control with a Single Nonlinear Control Filter for a Vibrating Plate with Multiple Actuators

“…The plates can be used as secondary sound sources, as replacement for classical loudspeakers, but also can be used as active barriers (Fahy, Gardonio, 2007; Hansen, Snyder, 1997; Rdzanek, Zawieska, 2003), where usually single or double plates (Pietrzko, 2009) are placed between the noise source and the area where the noise sound pressure level (SPL) should be reduced. Rectangular plates are frequently used ; Gorski, Kozupa, 2012), but also other plate shapes, including circular plates Rdzanek et al, 2011;Leniowska, 2011) and triangular plates (Barański, Szela, 2008), are useful for some applications and are investigated in the literature. Also more complex structures like L-jointed plates, T-shaped plates (Keira et al, 2005) or four connected plates (Liu et al, 2010), are of scientific interest.…”