Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination
Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination
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基于量词消除的控制中非线性参数约束的求解和可视化
DOI：
10.1007/s00200-007-0056-7
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
H. Anai
中科院分区：
文献类型：
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作者：
N. Hyodo;Myunghoon Hong;H. Yanami;S. Hara;H. Anai
提出了一种基于符号-数值计算的参数鲁棒控制综合方法。该方法是一种参数空间方法，对包括PI和PID控制器在内的有理型固定结构控制器的分析和设计特别有效。实量词消去（QE）是符号计算的最新进展之一，在符号计算的发展中起着关键作用。基于q的方法可以统一处理许多重要的鲁棒控制设计规范，如频率受限H∞范数约束，稳定性（增益/相位）裕度和稳定半径规范，以及极点位置要求，通过将这些规范简化为称为“符号确定条件（SDC）”的特定类型的公式。这对于提高QE计算的效率也很有用，因为我们可以使用Sturm-Habicht序列利用专门针对SDC的高效QE算法。基于QE实现的参数空间方法，我们开发了一个鲁棒参数控制的MATLAB工具箱。在图形用户界面（GUI）的帮助下，基于q的参数空间方法和从控制器参数空间中获取的特定控制器参数值的性能数值模拟可以方便地集成在我们的工具箱中。利用我们的工具箱，对具有三个或两个参数的控制器的参数可行域在参数空间中进行了可视化。这使得控制工程师能够顺利地实现多目标鲁棒控制器综合。我们还讨论了如何将数值计算和符号运算结合起来，使我们的新设计方法在实际控制设计中更加有效。
We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.
DOI：
10.1109/tac.2003.815013
发表时间：
2003-08
期刊：
IEEE Trans. Autom. Control.
影响因子：
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作者：
T. Iwasaki;S. Hara;H. Yamauchi
通讯作者：
T. Iwasaki;S. Hara;H. Yamauchi
一些具有正实部的根
DOI：
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发表时间：
2005
期刊：
Proceedings of the International Symposium on Symbolic and Algebraic Computation 2005
影响因子：
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作者：
Hirokazu Anai;Shinji Hara;Kazuhiro Yokoyama
通讯作者：
Kazuhiro Yokoyama