Vibration Control using Fractional Derivative Feedback

(7th Report: Design Method for Fractional-Order LQR)

Abstract

This study aims at applying linear quadratic regulator (LQR) theory to control a vibratory system modelled by a fractional-order differential equation. First, an iteration-based method for solving the algebraic Riccati equation is proposed to obtain a fractional-order LQR. Next, Newmark-𝛽method is modified to be able to simulate a fractional-order differential equation. Finally, as an example, a vibration control problem is considered for a generalized Voigt model. Numerical calculations demonstrate that the Fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.