All stabilizing PID controllers for time delay systems
All stabilizing PID controllers for time delay systems
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DOI：
10.1016/j.automatica.2009.07.026
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
Norbert Hohenbichler
中科院分区：
文献类型：
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作者：
Norbert Hohenbichler
本文提出了一种计算任意（包括不稳定）线性时滞系统整组稳定PID控制器参数的方法。主要贡献是处理(kd,ki)-平面上的无限数量的稳定边界，以固定比例增益kp。对于延迟开环，证明了（kd,ki）平面上的稳定区域由凸多边形组成。关于中性回路，引入了一种新的现象。对于某些系统和特定的kp， （kd,ki）平面上的精确稳定区域可以用具有无限顶点数的多边形序列的极限来描述。这个序列可以用凸多边形很好地近似。此外，本文还给出了kp区间在（kd,ki）平面上可能存在稳定区域的一个必要条件。因此，在这些区间内网格化后，可以计算出稳定控制器参数集。实现该方法的Matlab工具是可用的。
This paper presents a method to compute the entire set of stabilizing PID controller parameters for an arbitrary (including unstable) linear time delay system. The main contribution is to handle the infinite number of stability boundaries in the (kd,ki)-plane for a fixed proportional gain kp. For retarded open loops, it is shown that the stable region in the (kd,ki)-plane consists of convex polygons. Concerning neutral loops, a new phenomenon is introduced. For certain systems and certain kp, the exact stable region in the (kd,ki)-plane can be described by the limit of a sequence of polygons with an infinite number of vertices. This sequence may be well approximated by convex polygons. Moreover, the paper describes a necessary condition for kp-intervals potentially having a stable region in the (kd,ki)-plane. Thus, the set of stabilizing controller parameters can be calculated after gridding kpin these intervals. A Matlab tool implementing the presented method is available.