Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

被引：7

作者：

Takeshita, Akihiro ^{[1
]}

Yamashita, Tomohiro ^{[1
]}

Kawaguchi, Natsuki ^{[1
]}

Kuroda, Masaharu ^{[1
]}

机构：

[1] Univ Hyogo, Grad Sch Engn, Dept Mech Engn, 2167 Shosha, Himeji, Hyogo 6712280, Japan

来源：

APPLIED SCIENCES-BASEL | 2021年 / 11卷 / 07期

关键词：

vibration; control; fractional calculus; linear quadratic regulator (LQR); algebraic Riccati equation; iteration; state observer; viscoelasticity; PID CONTROLLER; EXPERIMENTAL VALIDATION; TIME IMPLEMENTATION; AUTOTUNING METHOD; PD CONTROLLER; DESIGN; ALGORITHM; SUPPRESSION;

D O I：

10.3390/app11073252

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

引用

页数：20

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