Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses
Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses
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DOI：
10.1109/9780470544334.ch25
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Başar
中科院分区：
文献类型：
--
作者：
T. Başar
在本文中，灵敏度降低的反馈问题制定为一个优化问题，并从镇定问题分离。稳定的反馈方案可从一个给定的植物参数化。导出了灵敏度降低方案的显著性质，并表明对象的不确定性降低了反馈降低灵敏度的能力.该理论是在一般的Banach代数环境下对输入输出系统发展的，然后专门用于一类多变量时不变系统，其特征在于n × n个H ∞矩阵频率响应函数，在右半平面上有或没有零点。该方法是基于使用加权的矩阵算子代数来测量灵敏度，并基于近似逆的概念。近似可逆的植物被证明是一个必要和充分条件的灵敏度降低。引入了一种近似可逆性的指标--奇异性测度，证明了线性定常对象的奇异性测度是由其右半平面零点的位置决定的。在不存在被控对象不确定性的情况下，系统对输出扰动的灵敏度可以降低到接近奇异性测度的最优值。特别地，如果没有右半平面零点，灵敏度可以任意小，灵敏度优化中所用的反馈方案类似于经典控制设计中的超前-滞后网络。给出了它们的一些性质，以及在特殊情况下构造它们的方法。
In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity.The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized byn×nmatrices ofH¿ frequency response functions, either with or without zeros in the right half-plane.The approach is based on the use of aweighted seminormon the algebra of operators to measure sensitivity, and on the concept of anapproximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called ameasure of singularity, is introduced.The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small.The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.