H∞回路成形中的μ综合法

μ-synthesis in H-infinity loop-shaping design

中文关键词  H∞回路成形  稳定裕度  μ综合  鲁棒性能  弱阻尼模态

英文关键词  H-infinity loop shaping  stability margin  μ-synthesis  robust performance  lightly damped

中文摘要

      H∞控制理论中的回路成形设计和μ综合都已经是定型的设计方法. 最近有文献提出一种将这两种设计方法结合起来处理弱阻尼谐振模态参数摄动的新方法. 但是实际设计表明, 二者的结合并没有达到预期的效果. 本文分析指出, 回路成形本质上是一种鲁棒稳定性设计, 其H∞范数指标的逆就是系统的稳定裕度. 而μ综合只是一种鲁棒性能的设计工具. μ综合与回路成形结合只是反映在稳定裕度上, 而并不影响设计所允许的摄动大小. 所以在回路成形设计中没有必要再加进μ综合法. 文中附有算例.

英文摘要

      Both loop-shaping design and μ-synthesis are standard design tools of the H-infinity control theory. Recently, a novel design method combining μ-synthesis with loop-shaping is proposed for dealing with the parameter uncertainty of the lightly damped mode. However, the practical design shows that such combination fails to provide the expected result. We point out that the loop-shaping design is essentially a method for robust stability, because the inverse of the resulting H-infinity norm is the stability margin of the system. However, the μ-synthesis is a real tool for designing the robust performance. The combination of μ-synthesis with loop-shaping determines only the stability margin, but not the size of the allowable perturbation. Therefore, there is no need to add an extra procedure of μ-synthesis to the loop shaping design. A design example is presented for explanation.