Absolute Vibration Suppression (AVS) Control – Modeling, Implementation and Robustness

Abstract

Absolute Vibration Suppression (AVS) is a control method for flexible structures governed by the wave equation. Such system may be a rotating shaft, a rod in tension or a crane for which the cable mass is not negligible. First an accurate, infinite dimension, transfer function, relating arbitrary actuation and measurement points, with general boundary conditions, is derived. The transfer function consists of time delays, due to the wave motion, and low order rational terms, which correspond to the reflection from the boundary. Thus the compact mathematical representation has a clear physical interpretation. Furthermore, it leads to the special structure of the AVS controller which is a collocated, rate to force feedback that completely eliminates the vibration. The paper investigates the properties of the AVS controller and its robustness to modeling errors, in particular small non-collocation.

Fractional order control of the two-dimensional wave equation

“…The membrane then resembles a structure governed by the 1D wave equation, such as a string. In that case, α n (s) = s and the TFs (17a)-(17b) Functions of the form (18) were reported in Halevi (2005), Halevi and Peled (2010) and Halevi (2010, 2012) for a rotating rod system with a linear set of BC. The exponents are linear in s, which indicates pure time delays.…”

“…in Alli and Singh (2000) to control the 1D wave equation by root locus and optimization methods, or in Saito and Katsura (2013) to control a multi-mass resonant system by wave absorption strategy. In a series of publications (Halevi, 2005;Halevi & Peled, 2010;Sirota & Halevi, 2010, the infinite dimensional TFs were used to model flexible rods in torsion (1D wave equation) with a general linear set of boundary conditions (BC). The TF model consisted of exponents that are linear in s and of low order rational terms.…”