Vibration Control using Fractional Derivative Feedback

(8th Report: Fractional-Order LQR using State Observer)

Abstract

This research deals with a vibration suppression problem occurring in a viscoelastic damper system modeled with a fractional-order differential equation using a fractional-order linear quadratic regulator (LQR) as a typical modern control. In the previous report, the fractional-order LQR was configured with a state feedback style. However, ordinary sensors cannot measure a fractional-order state in practice, because a fractional-order state is composed of displacement, velocity and acceleration. Therefore, a state observer is required to estimate all of the states including fractional-order states. This report aims at realizing the fractional-order LQR with an output feedback style by constructing a state observer in order to estimate fractional-order states.