摘 要：针对一类具有外部干扰的系统，提出一种基于干扰观测器和线性矩阵不等式的鲁棒控制方法。针对具有外部干扰的分数阶非线性不确定系统，利用系统状态变量设计了干扰观测器。基于干扰观测器的输出，设计了分数阶非线性系统的鲁棒状态反馈控制器，并将控制器的设计问题转化为一类分数阶不确定系统的鲁棒稳定性问题。应用分数阶 Lyapunov 理论分析了闭环系统的稳定性，并获得闭环系统进一步基于 LMI 控制器参数的求解方法。最后，用 Newcastle 机器人控制系统仿真验证了提出的控制方法有效性。
关键词：干扰观测器；鲁棒控制；分数阶；时滞非线性系统
DOI:10.19850/j.cnki.2096-4706.2022.06.018
基金项目：广东科技学院校级科研项目（青年项目）（GKY-2020KYQNK-8）
中图分类号：TP391.9 文献标识码：A 文章编号：2096-4706（2022）06-0075-04
Robust Control of Fractional Nonlinear Systems Based on DOB
LI Hengbo
(School of Computer Science, Guangdong University of Science and Technology, Dongguan 523083, China )
Abstract: A robust control method based on disturbance observer and linear matrix inequality is proposed for a system with external disturbances. In view of the fractional order nonlinear uncertain system with external disturbances, this paper designs disturbance observer by using the system state variable. Based on the output of the disturbance observer, it designs a robust state feedback controller for fractional nonlinear systems, and the design problem of controller is converted into a kind of robust stability problems of fractional uncertain systems. It applies fractional Lyapunov theory to analyze the stability of the closed-loop system and obtain a further solution method based on the LMI controller parameters of the closed-loop system. Finally, the effectiveness of the proposed control method is verified by the Newcastle robot control system simulation.
Keywords: disturbance observer; robust control; fractional order; time delay nonlinear system
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作者简介：李亨博（1990—），女，瑶族，湖南永州人，讲师，硕士研究生，研究方向：智能控制。