引用本文:李银伢, 盛安冬, 王远钢, 郭治.PI控制中衰减度与H∞指标的相容性[J].控制理论与应用,2007,24(3):498~502.[点击复制]
LI Yin-ya, SHENG An-dong, WANG Yuan-gang, GUO Zhi.Consistency of decay ratio and H-infinity indices in PI control[J].Control Theory and Technology,2007,24(3):498~502.[点击复制]
PI控制中衰减度与H∞指标的相容性
Consistency of decay ratio and H-infinity indices in PI control
摘要点击 1410  全文点击 1365  投稿时间：2005-10-11  修订日期：2006-02-23
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DOI编号  10.7641/j.issn.1000-8152.2007.3.033
  2007,24(3):498-502
中文关键词  满意控制  PI控制  相容性  H∞指标  衰减度  D-分割法
英文关键词  satisfactory control  PI control  consistency  H-infinity index  decay ratio  D-partition method
基金项目  国家自然科学基金资助项目(60174028); 博士点基金资助项目(20040288002).
作者单位
李银伢, 盛安冬, 王远钢, 郭治 南京理工大学自动化系, 江苏南京210094 
中文摘要
      研究n阶线性定常系统在PI控制下衰减度与H∞指标的相容性问题. 首先基于D-分割法和边界穿越定理, 分别推导了描述PI控制器参数稳定域边界、PI控制器满足期望的衰减度指标的参数边界和期望的H∞指标的参数边界的解析表达式. 再应用满意控制思想, 对上述期望指标的相容性进行了分析, 给出了相容指标较好的取值范围.当上述两类指标相容时, 可以迅速得到整个PI控制器相容性解集(满意解集). 用一个算例说明了所提出的设计方法的有效性.
英文摘要
      The consistency of decay ratio index and H-infinity index under PI control for n-order linear time-invariant systems is considered in this paper. Based on the D-partition technique and the boundary cross theorem, the analytic expressions for describing the stabilizing boundaries, the parameter boundaries with the expected decay ratio index and Hinfinity index of PI controller are derived, respectively. Using the idea of satisfactory control, the consistency of the above expected indices is analyzed and a good range of the consistent index is proposed. The whole consistency solution set (the satisfactory solution set) of PI controller can be quickly determined when the above two types of indices are consistent. A numerical example also shows the validity of the proposed design method.