时滞系统PID控制器增益的稳定范围研究

On Gain Stabilizing Regions of PID Controller for Time Delay Systems

  • 摘要: 基于逆Nyquist曲线,提出一种时滞系统在PID控制下确定增益稳定范围的方法.根据时滞系统的逆Nyquist曲线特征和广义Hermite-Biehler定理,确定用于判断系统稳定性所需的频率范围,以及该范围内逆Nyquist曲线上两类关键点的横坐标.关键点将PID增益分成若干区间,通过纵向直线与逆Nyquist曲线的交点数,以及文中给出的一个推理和两个定理,可判断PID增益稳定的范围.该方法能有效解决时滞系统在PID控制下增益稳定范围的确定问题.

     

    Abstract: A new method based on the inverse Nyquist curve is given to ascertain the stabilizing gain regions of time delay systems using PID controller. According to the characteristics of the inverse Nyquist curve of time delay systems and the generalized Hermite-Biehler theorem, the required frequency range for estimating the system stability can be acquired, and the abscissas of two kinds of key points can be obtained in this range. These key points divides the PID gain into several regions. Using an inference and two theorems derived in this paper, the stabilizing PID gain regions are acquired by the number of intersections of the inverse Nyquist curve and the vertical line in the required frequency range. This method can effectively solve the problem of getting the stabilizing gain regions in PID control for time delay systems using PID controller.

     

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