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Pattern Classification and Construction of Lyapunov Function for Nonlinear Control Systems Using the Robust Perturbation Method

使用鲁棒摄动法的非线性控制系统李亚普诺夫函数的模式分类和构造

基本信息

批准号：
05650415
负责人：
MIYAGI Hayao
金额：
$ 1.09万
依托单位：
University of the Ryukyus
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

1.Stability analysis of motor system which consists of reluctance stepping motor or synchronous motor has been carried out by the direct method of Lyapunov, considering the nonlinearities of the motor. The results show that the direct method of Lyapunov is successfully applicable to stability studies of nonlinear systems.2.Power system is a complex engineering system. The report gives two ways of improving transient stability of power systems. One is the cooperative fuzzy control techinique of AVR and GOV based on sliding mode. The other is the static var compensator technique utilizing fuzzy control theory.3.A method of constructing non-Lure type Lyapunov function for nonlinear control system has been presented. The function surpasses the Lure type Lyapunov function from the point of view of the stability region guaranteed.4.The report also presents a method of analysing robust stability of perturbed multimachine power systems, through Popov-Lyapunov approach. Robust stability criteria are presented to derive a robustness measure which gives some bounds on allowable perturbation for the system.5.The robustness of product-type nonlinear feedback systems subjected to parameter variations has been studied through both the positive realness of perturbed transfer functions and the direct method of Lyapunov. The tolerable range of individual parameter deviations and the condition for the product-type nonlinearities can be obtained by the proposed method.

1.本文采用李雅普诺夫直接法对磁阻式步进电动机和同步电动机组成的电动机系统进行了稳定性分析，考虑了电动机的非线性。结果表明，李雅普诺夫直接法可成功地应用于非线性系统的稳定性研究。2.电力系统是一个复杂的工程系统。该报告提出了两种提高电力系统暂态稳定性的方法。一种是AVR和GOV基于滑动模的协同模糊控制技术。二是基于模糊控制理论的静止无功补偿技术。3.提出了一种非线性控制系统的非Lure型李雅普诺夫函数的构造方法。从稳定域的角度看，该函数优于Lure型李雅普诺夫函数。4.本文还提出了一种利用Popov-Lyapunov方法分析多机电力系统鲁棒稳定性的方法。给出了系统鲁棒稳定性的判据，给出了系统允许扰动的界。5.利用扰动传递函数的正实性和直接的李雅普诺夫方法研究了乘积型非线性反馈系统对参数变化的鲁棒性。该方法可以得到各参数偏差的容许范围和乘积型非线性的条件。