基于改进Fal函数的滤波器及扩张状态观测器研究  

Research on filter and extended state observer based on improved Fal function

作　　者：秦耀 杨杰 刘书云[1,2] 曾海金 QIN Yao;YANG Jie;LIU Shu-yun;ZENG Hai-jin(School of Electrical Engineering and Automation,Jiangxi University of Science and Technology,Ganzhou 341000,China;Institute of Permanent Magnet Levitation Technology and Rail Transport,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]江西理工大学电气工程与自动化学院,江西赣州341000 [2]江西理工大学永磁磁浮技术与轨道交通研究院,江西赣州341000

出　　处：《控制与决策》2025年第2期684-692,共9页Control and Decision

基　　金：国家自然科学基金项目(62063009)。

摘　　要：Fal函数是非线性扩张状态观测器(Fal_NESO)的核心单元,其构成的滤波器(FalFilter)对于控制系统的性能具有重要影响.通过对FalFilter和Fal函数的性能分析,提出一种在定义域内连续可导且只有一个待整定参数的CFal函数,并证明了由CFal函数构成滤波器(CFalFilter)和非线性扩张状态观测器(CFal_NESO)的可行性;然后,联合CFalFilter和CFal_NESO,得到一种带滤波器的新型观测器(CFalFilter-CFal_NESO),用于处理测量环节含噪声干扰的情况;最后,通过典型实例将CFal函数与两个改进的Fal函数进行对比实验.实验结果表明,在跟踪速度趋近条件下,CFalFilter滤波效果最佳;仅改变Fal函数参数,CFal_NESO能够更好地提取噪声环境中的信号状态,同时减小因观测器阶数增加而带来的参数整定困难;在不改变参数条件下,CFalFilter-CFal_NESO进一步提高了对带有测量噪声信号的状态跟踪性能.所提CFalFilter、CFal_NESO和CFalFilter-CFal_NESO对于大多数非线性、高阶系统的滤波和观测均能适用,具有重要的学术意义和实际应用价值.The Fal function is the core unit of the nonlinear extended state observer(Fal_NESO),and its constituent filter(FalFilter)also has an important influence on the performance of the control system.By analysing the performance of the FalFilter and the Fal function,a CFal function is proposed,which is continuously derivable in the definition domain and has only one parameter to be rectified,and the feasibility of constituting a filter(CFalFilter)and a nonlinearly extended state observer(CFal_NESO)from the CFal function is proved.Then,by combining the CFalFilter and the CFal_NESO,a new type of observer with a filter(CFalFilter-CFal_NESO)is obtained to deal with the case of noise interference in the measurement link.Finally,the CFal function is compared with the two improved Fal functions through typical examples,and the experimental results show that the CFalFilter has the best effect under the condition of convergence of tracking speed;by changing only the parameter of the Fal function,the CFal_NESO can better extract the state of the signal in the noisy environment,and at the same time,it also reduces the difficulty in parameter tuning due to the increase in the number of orders of the observer;without changing the parameter,the CFalFilter-CFal_NESO further improves the state tracking performance of the signal with measurement noise.The CFalFilter,CFal_NESO and CFalFilter-CFal_NESO proposed in this paper are applicable to the filtering and observation of most nonlinear and high-order systems,which are of great academic significance and practical application value.

关 键 词：非线性扩张状态观测器 Fal函数滤波器 CFal函数 收敛性 稳定性 新型观测器 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]