非线性互联系统状态观测器设计方法研究  

Research on Design Method of State Observer for Nonlinear Interconnected Systems

作　　者：孙延修[1] 黎虹[1] SUN Yanxiu;LI Hong(Basic Course Department,Shenyang Institute of Technology,Fushun 113122,China)

机构地区：[1]沈阳工学院基础课部,辽宁抚顺113122

出　　处：《自动化仪表》2023年第1期35-41,共7页Process Automation Instrumentation

基　　金：沈阳工学院青年骨干教师科研基金资助项目(QN202009)。

摘　　要：非线性互联系统广泛应用于各类工业生产中。随着科学技术的迅速发展,控制系统的复杂程度越来越高,同时各子系统之间的互联性也变得越来越强。因此,针对日益复杂的非线性互联系统进行研究,已成为一个非常重要的课题。针对非线性互联系统观测器的设计方法进行研究,通过设计状态观测器实现对互联系统中状态向量的鲁棒估计。首先,基于李雅普诺夫函数给出广义互联系统状态观测器存在的充分条件。其次,将非线性广义互联系统观测器的存在条件进行推广,得到正常非线性互联系统观测器存在的充分条件。观测器的存在条件均通过Schur补引理,以线性矩阵不等式的形式给出,简化了观测器增益矩阵的求解,得到了互联系统观测器的设计方法。最后,利用MATLAB软件计算出观测器的增益矩阵。两个算例仿真结果验证了所提方法的可行性与有效性。Nonlinear interconnected systems are widely used in various types of industrial production. Along with the rapid development of science and technology, the complexity of control systems is increasing, and at the same time the interconnectivity between subsystems also become stronger and stronger. Therefore, the study of increasingly complex nonlinear interconnected systems has become a very important topic. The design method of observer for nonlinear interconnected systems is studied to achieve robust estimation of state vectors in interconnected systems by designing state observers. Firstly, sufficient conditions for the existence of state observers of generalized interconnected systems are given based on the Lyapunov function. Secondly, the conditions for the existence of observers of nonlinear generalized interconnected systems are generalized to obtain sufficient conditions for the existence of observers of normal nonlinear interconnected systems. The existence conditions of the observer are all given in the form of linear matrix inequalities through Schur complementary lemma, which simplifies the solution of the observer gain matrix and obtains the design method of the observer of the interconnected system. Finally, the gain matrix of the observer is calculated by using MATLAB software. The simulation results of two cases verify the feasibility and effectiveness of the proposed method.

关 键 词：观测器 广义互联系统 线性矩阵不等式 增益矩阵 非线性 鲁棒估计 李雅普诺夫函数 状态估计 

分 类 号：TH-39[机械工程]