Natsuki Kawaguchi

In this paper, we introduce fractional-order calculus into linear quadratic regulator (LQR) control, which is a typical modern control, and discuss control of a magnetic levitation system using a state observer described by a fractional-order differential equation. In the previous paper, LQR control using a fractional-order state observer with output feedback was applied to a linear control object. It is necessary to verify if the control is also effective for the nonlinear model. For an unstable target, an integrator is required to be designed to trace the target value. In this report, we propose an output-feedback-type servo LQR control system with a fractional-order state observer for a voltage-controlled suspention-type magnetic levitation system with strong nonlinearity.

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.

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-<tt>𝛽</tt>method 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.