基于奇异摄动法的多变量系统稳定性测量

发布时间：2018-01-05 11:21

本文关键词：基于奇异摄动法的多变量系统稳定性测量　出处：《大连海事大学》2017年硕士论文　论文类型：学位论文

【摘要】：无论在实际生产过程中,还是在自然界运转过程中,稳定性都是系统正常运转的必要条件。因此,对稳定性裕度的度量研究具有重要的理论意义和实际应用价值。而目前研究稳定裕度的方法中,通过奇异摄动理论测量多变量系统稳定裕度的方法尚未见到。本文针对分析和度量稳定裕度的问题,提出了一种基于奇异摄动理论度量多输入多输出系统的稳定裕度的方法。针对控制系统稳定裕度的国内外研究现状,分析了不同方法的优缺点,结合单变量系统中奇异摄动理论求解稳定裕度的方法,提出了基于奇异摄动理论预估多变量系统稳定裕度的方法。这种方法的思想就是引入带有小参数的奇异摄动系统,由小增益定理计算出奇异摄动小参数的范围,从而计算出多输入多输出系统的稳定裕度,并以一个两输入两输出系统为例,用所提出的方法计算出其稳定裕度,然后再将其与其他文献所计算出的多输入多输出系统稳定裕度的值对比。通过对比结果得出,本文所提方法可以反映多输入多输出系统的稳定裕量,并且该方法是由单输入单输出系统引入而来,因此具有向下兼容性。
[Abstract]:Whether in the actual production process or in the natural process, stability is the necessary condition for the normal operation of the system. The research on the measurement of stability margin has important theoretical significance and practical application value. The method of measuring the stability margin of multivariable systems by singular perturbation theory has not been found yet. In this paper, the problem of analyzing and measuring the stability margin of multivariable systems is discussed. This paper presents a method to measure the stability margin of multi-input multi-output systems based on singular perturbation theory, and analyzes the advantages and disadvantages of different methods in view of the domestic and foreign research status of stability margin of control systems. A method for solving stability margin by using singular perturbation theory in univariate systems. A method for estimating the stability margin of multivariable systems based on singular perturbation theory is proposed. The idea of this method is to introduce singularly perturbed systems with small parameters and calculate the range of singular perturbation small parameters by small gain theorem. Thus the stability margin of the multi-input multi-output system is calculated, and the stability margin of a two-input two-output system is calculated by the proposed method. Then it is compared with the value of stability margin calculated in other literatures. The results show that the method proposed in this paper can reflect the stability margin of multi-input multiple-output system. And the method is introduced by single input single output system, so it has downward compatibility.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP273

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