Synthesis of Robust Controllers with Structured Real Uncertain Parameters

具有结构化实不确定参数的鲁棒控制器的综合

• 批准号: 9111570
• 负责人: B. Ross Barmish
• 金额: $ 24万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9111570&HistoricalAwards=false
• 关键词: Synthesis; Robust; Controllers; Structured; Real

The motivation for this proposal is derived from the problem of robust control in the presence of structured real uncertain parameters. More specifically, it deals exclusively with linear systems described by a transfer function or state space model which includes uncertain parameters entering into various plant coefficients. The takeoff point for research is the body of literature motivated by Kharitonov's Theorem. Given the fact that this body of literature deals almost exclusively with robust stability analysis, the first focal point of the research is synthesis of robust stabilizing controllers. A spark for this line of work is provided by some recent extreme point results (involving the PI) on robust stabilization of an interval plant (ratio of interval polynomials) with a first order controller. Additional motivation is also provided by the so-called value set approach. Given the widespread use of value sets in an analysis context, the open question is: To what extent are value sets useful in a synthesis context? The second focal point of this proposal is robust performance. That is, the objective is to deal with robust performance specifications over and above stability. Analogous to the investigation of robust stabilization, the intention is to begin the work by looking at robust performance problems with low order controllers and then to follow up with the higher order case. In this framework, a number of important research problems are proposed. The third and final focal point is described by the words generating mechanism. That is, to enlarge the class of uncertainties which can be accommodated, it is proposed to impose more structure on the "uncertain" polynomials and rational functions which arise in the analysis.

该提议的动机源于存在结构化真实不确定参数时的鲁棒控制问题。 更具体地说，它专门处理由传递函数或状态空间模型描述的线性系统，其中包括进入各种设备系数的不确定参数。 研究的出发点是受哈里托诺夫定理启发的文献。 鉴于该文献几乎专门涉及鲁棒稳定性分析，因此研究的第一个焦点是鲁棒稳定控制器的综合。 最近的一些极值点结果（涉及 PI）为这一工作提供了灵感，这些极值点结果涉及使用一阶控制器的区间工厂（区间多项式的比率）的鲁棒稳定性。 所谓的价值设定方法也提供了额外的动力。 鉴于值集在分析环境中的广泛使用，悬而未决的问题是：值集在综合环境中有用到什么程度？ 该提案的第二个重点是稳健的性能。 也就是说，目标是处理稳定性之外的稳健性能规范。 与鲁棒稳定性的研究类似，其目的是通过研究低阶控制器的鲁棒性能问题来开始工作，然后跟进高阶情况。 在此框架下，提出了许多重要的研究问题。 第三个也是最后一个焦点由单词生成机制描述。 也就是说，为了扩大可容纳的不确定性类别，建议对分析中出现的“不确定”多项式和有理函数施加更多结构。