Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma
Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma
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DOI：
10.1002/rnc.1123
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发表时间：
2007-03
影响因子：
3.9
通讯作者：
T. Iwasaki;S. Hara
中科院分区：
文献类型：
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作者：
T. Iwasaki;S. Hara
研究了线性系统满足设计指标的控制综合问题，其形式为（半）有限值域内的多个频域不等式。我们的方法是基于广义卡尔曼Yakubovich波波夫（GKYP）引理，并考虑动态输出反馈控制器的顺序等于植物。提出了一种新的乘子展开式，通过标准的变量线性化变换，将综合条件转化为线性矩阵不等式（LMI）条件。在一个单一的目标设置，LMI条件可能会或可能不会是保守的，这取决于乘数展开的基础的选择。我们提供了一个条件的基础矩阵，以产生非保守的LMI条件。一般来说，很难确定满足这种条件的基础矩阵。然而，它表明，合格的基可以找到某些情况下，和资格条件可以用来找到合理的选择的基础上的其他情况。然后，综合方法扩展到多目标的情况下，给出了一个充分条件的控制器的存在，以满足所有规定的规格。最后，通过一个主动磁轴承的设计实例，说明了所提出的设计方法的有效性。版权所有© 2006约翰威利父子有限公司.
This paper considers a control synthesis problem for linear systems to meet design specifications in terms of multiple frequency domain inequalities in (semi)finite ranges. Our approach is based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma, and dynamic output feedback controllers of order equal to the plant are considered. A new multiplier expansion is proposed to convert the synthesis condition to a linear matrix inequality (LMI) condition through a standard linearizing change of variables. In a single objective setting, the LMI condition may or may not be conservative, depending on the choice of the basis for the multiplier expansion. We provide a qualification for the basis matrix to yield non‐conservative LMI conditions. It is difficult to determine the basis matrix meeting such a qualification in general. However, it is shown that qualified bases can be found for some cases, and that the qualification condition can be used to find reasonable choices of the basis for other cases. The synthesis method is then extended to the multiple objective case where a sufficient condition is given for the existence of a controller to meet all the prescribed specifications. Finally, design examples for an active magnetic bearing are given to illustrate the effectiveness of the proposed design method. Copyright © 2006 John Wiley & Sons, Ltd.