Tonal vibration control with a self-tuning absorber employing the extremum seeking algorithm

This paper presents a theoretical study on the implementation of a self-tuning vibration absorber for tonal vibration control. The study considers a tuneable vibration absorber, composed by a spring-mass-damper system with variable stiffness and damping components, which is attached to a single degree of freedom mechanical system subjected to a harmonic excitation. The online tuning of the absorber stiffness and damping parameters is performed using an extremum seeking algorithm set to minimise the vibration kinetic energy of the hosting system. The paper proposes a two-paths tuning approach, which, starting from initial estimates of the stiffness and damping parameters of the absorber, searches for their optimal values along constant-damping and constant-stiffness paths respectively. The study presents a comprehensive analysis on the implementation of the algorithm at off-resonance and at resonance frequencies of the hosting system. Also, it investigates how the intrinsic parameters of the algorithm influence the convergence to the optimal stiffness and damping values. The proposed tuning methodology does not require a reference signal for the tonal excitation and, thus, can be suitably implemented both for fixed and time-varying tonal disturbances.