Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers

TL;DR

This paper analyzes how digital control delays can cause instabilities in piezoelectric vibration absorbers and proposes methods to predict and counteract these delays, validated through experiments on a piezoelectric beam.

Contribution

It derives an explicit relation between electromechanical coupling and sampling period for stability and introduces a modification method to mitigate delay effects.

Findings

Delay-induced instabilities occur in low coupling systems due to sampling delays.

A relation between coupling factor and maximum sampling period for stability is established.

Experimental validation confirms the effectiveness of the proposed modification method.

Abstract

The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.