一类二阶指数1广义系统的切插值投影及其在机电一体化中的应用
Tangential interpolatory projections for a class of second-order index-1 descriptor systems and application to Mechatronics
摘要：
研究了基于迭代有理Krylov算法（IRKA）的切向插值投影法对二阶指数-1广义系统的模型降阶问题。我们的主要重点是减少到一个二阶形式的系统，使原系统的结构可以保留。为此，对基于IRKA的切向插值方法进行了改进，以隐式方式有效地处理底层广义系统的二阶结构。本文还表明，通过利用系统的对称性，可以显着降低实施的计算成本。理论结果验证了基于压电驱动器的自适应主轴支承的模型降阶是二阶指数-1微分代数形式。通过对数值结果的分析，验证了该方法的有效性和准确性.
英文摘要：
This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system into a second-order form so that the structure of the original system can be preserved. For this purpose, the IRKA based tangential interpolatory method is modified to deal with the second-order structure of the underlying descriptor system efficiently in an implicit way. The paper also shows that by exploiting the symmetric properties of the system the implementing computational costs can be reduced significantly. Theoretical results are verified for the model reduction of the piezo actuator based adaptive spindle support which is second-order index-1 differential-algebraic form. The efficiency and accuracy of the method are demonstrated by analyzing the numerical results.
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