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文章编号： 1672-6987（2023）04-0096-08； DOI： 10.16351/j.1672-6987.2023.04.013
步妮， 王晓光(青岛科技大学 自动化与电子工程学院，山东 青岛 266061)
摘要： 实际系统中的不确定性严重影响了系统的稳定性和良好的跟踪性能，因此，研究不确定非线性系统的鲁棒跟踪控制具有重要意义。本工作提出了一种基于演算子理论的设计方案很好的解决了这个问题。具体为：首先，基于演算子理论，综合设计了鲁棒右互质分解控制器，观测器和跟踪补偿控制器；其次，依据Lipschitz 范数和 unimodular 算子的定义，讨论并证明了提高系统跟踪性能的充分条件；再次，基于充分条件，验证了所设计方案的跟踪性；最后，通过二级倒立摆仿真，验证了所提出方案的有效性。
关键词： 演算子理论； 鲁棒右互质分解； 非线性系统； 鲁棒性； 跟踪补偿器
中图分类号： TP 13文献标志码： A
引用格式： 步妮， 王晓光. 基于演算子理论的非线性系统的鲁棒跟踪控制［J］. 青岛科技大学学报(自然科学版), 2023, 44(4): 96-103.
BU Ni， WANG Xiaoguang. Robust tracking control of nonlinear system based on operator theory［J］. Journal of Qingdao University of Science and Technology（Natural Science Edition), 2023， 44（4）： 96-103.
Robust Tracking Control of Nonlinear System Based on Operator Theory
BU Ni, WANG Xiaoguang
(College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China)
Abstract: The uncertainty in the real system seriously affects the stability and good tracking performance of the system. Therefore, it is of great significance to study the robust tracking control of uncertain nonlinear systems. In this paper, a design scheme based on operator theory is proposed to deal well with the effects of uncertainty in real systems. In details, firstly, the robust right coprime factorization controller, observer and tracking compensation controller are designed based on the operator theory. Secondly, based on the definition of Lipschitz norm and unimodular operator, the sufficient conditions of improving the tracking performance of the system are discussed and proved. Thirdly, based on the obtained sufficient conditions, the tracking performance of the designed scheme is improved. Finally, the effectiveness of the proposed scheme is verified by the simulation of the double inverted pendulum.
Key words: operator theory; robust right coprime factorization; nonlinear system; robustness; tracking compensator
收稿日期： 2022-07-04
基金项目： 国家自然科学基金项目（61304093）;山东省自然科学基金项目（ZR2021MF047）.
作者简介： 步妮(1981—),女,副教授.
