CASIA OpenIR  > 毕业生  > 硕士学位论文
Thesis Advisor郁文生
Degree Grantor中国科学院研究生院
Place of Conferral中国科学院自动化研究所
Degree Discipline控制理论与控制工程
Keyword鲁棒性分析与综合 严格正实性(Spr) 遗传算法(Ga) 线性矩阵不等式(Lmi) 交替投影算法 Robustness Analysis And Synthesis Strict Positive Realness(Spr) Genetic Algorithm(Ga) Linear Matrix Inequalities(Lmi) Alternatin
Abstract严格正实性是控制系统的一种重要性能。近年来的多数结果是属于鲁棒严格 正实分析的,针对鲁棒严格正实综合的有价值的结果较少。就工程应用来说,综 合性问题则更有实际意义,并且至今仍然是一个具有挑战性的研究难题。 本文研究系统鲁棒严格正实设计算法,主要内容如下: 首先,回顾了鲁棒控制和严格正实的研究状况,给出了严格正实的定义、性 质,并给出了本文的结构。 其次,针对具有不确定性的任意阶多项式族进行鲁棒严格正实综合中遇到的 问题,在系数空间上,提出了一种基于遗传算法的严格正实综合方法。本方法对 多项式线段,区间族,凸多面体族都是有效的,并且容易扩展到强严格正实和离 散系统的鲁棒严格正实综合上。实例表明本设计方法对高阶系统是有效的。 第三,提出了一种新的基于降阶的鲁棒严格正实综合的几何算法,通过从多 项式的弱严格正实域的边界着手,寻找几个弱严格正实域的交集,使综合问题转 化为在只有两变量的椭圆内寻找一个可行解的问题,从而使鲁棒严格正实综合问 题变的简单易求,计算量明显下降。并且,我们所得到的条件对于低阶多项式线 段(n≤5)和区间多项式族(n≤4)来说是都是可以满足的。实例表明这种降阶的几 何算法对于给定的高阶多项式集也是有效的。 第四,提出了一种基于线性矩阵不等式(LMIs)的交替投影算法来进行鲁棒严 格正实综合。把上述的SPR问题用LMIs表示,对某几类特殊的SPR综合问题, 把它改写为具有简单形状的矩阵约束集的可行性问题,随后得到投影到该集合的 正交投影算子的解析表达式,尝试寻求问题的可行解。 论文最后对所取得的研究成果进行了总结。
Other AbstractThe Strict Positive Realness (SPR) of a transfer function is an important performance in control system and much attention has been paid. However, most of the results belong to SPR analysis. From the engineering point of view, synthesis problem is more practical and is still a challenging topic. These papers focus on the developing algorithms for the Robust SPR synthesis. The content of this paper goes as follows: Firstly, researches on robust control and SPR are reviewed, the concepts and properties are described, and the architecture of this thesis are introduced. Secondly, for randomly high order polynomial families with uncertainty, we present an algorithm for robust SPR synthesis based on genetic algorithm, which is effective for polynomial sets such as segment, interval and polygon polynomial sets. The algorithm can be extended easily to the strength SPR problem and discrete systems. Examples illustrate its effectiveness. Thirdly, a new geometry algorithm based on order reduction for SPR synthesis is presented. By searching from the boundary of the region of the weak Strict Positive Realness (WSPR) of a polynomial, we can find the boundary of the WSPR intersection region of the polynomial family, and then transfer the SPR synthesis problem to a feasible problem with just two variables, thus simplifying the problem and saving the computation. The conditions we get by the algorithm can be satisfied for the lower order polynomial segment (n≤5) and interval (n≤4) polynomial sets. Examples also illustrate its effectiveness. Fourthly, an algorithm based on alternating projection has been presented. We describe the SPR problem by Linear Matrix Inequalities (LMIs), then for several special SPR problems, we formulate them as feasibility problems with simple matrixes constraint sets, by obtaining the analytical expressions for the orthogonal projection operators onto these sets, we try to obtain the solution. A conclusion is given finally.
Other Identifier635
Document Type学位论文
Recommended Citation
GB/T 7714
谢良军. 系统鲁棒严格正实设计算法研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2002.
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