PID控制对线性时滞系统稳定性的研究

包含线性时滞被控对象和PID控制器在内的反馈系统的稳定性已经有多年的研究,在众多论证方法中,奈奎斯特判据、Hermite-Biehler定理、根轨迹等方法最为常见。此类研究的主要目的即是决定控制参数的稳定范围。通过有限的整定步数来明确并表示出其域值范围和计算步骤只能借助一阶被控对象得以实现,且是一次时延被控系统。本文在庞德里亚金的研究结果上,拓展出任意阶被控对象都可适用的控制算法。

Study on Stability of PID-controlled Linear Time-delay Feed Back System

The stability of feedback systems including linear time-delay plants and PID controllers have been demonstrated for many years by means of several methods, of which the Nyquist criterion, a generalization of the Hermite-Biehler Theorem, and the root location method are well known. The main purpose of th6se researches is to determine the range of controller parameters that allow stability. Explicit and complete expressions of the boundaries of these regions and computation procedures with a finite number of steps are now available only for first-order plants, provided with one time delay. In this paper, the same results, based on Pontryagin＇s studies, are presented for arbitrary-order plants.