Nyquist判据在特殊系统应用上的改进

摘要

Nyquist criterion on non-minimum phase systems is error-prone,and the curve is easy to stagger.What's more,the supplement of the frequency characteristics for the Bode diagram is extremely complicated.To solve the above problems,this paper studied the characteristics of two special systems based on the theory of the Nyquist criterion in logarithmic coordinates.It proposed a way to improve the complexity of the stability judgment method on non-minimum phase systems.Through extracting the common characteristic of Nyquist curve and Bode diagram,unifying them in one formula,we solved the problems of the difficulty in judgment of curve numbers.The paper precisely defined the half-through and its expansion,which enlarged the application scope of the Nyquist criterion.Through the three steps,which are addition,calculation and determination,the difficulty is highly reduced.What's more,the accuracy is also improved.%针对Nyquist判据对非最小相位系统稳定性判定方法易错、曲线易交错,对含有积分环节的Bode图进行增补频率特性方法复杂等问题,依据Nyquist判据在对数坐标上的应用理论,研究了两种特殊系统的特点,提出了一种改善非最小相位系统稳定性判定复杂性的方法;提取了Nyquist曲线和Bode图稳定性判定的共同点,将两者的判断统一于一个公式,解决了曲线相互交错导致的难以判断环绕圈数的问题;准确定义了半穿越并将其扩展,使得Nyquist判据适用范围得以扩展.通过增补-计算-判断3个步骤,大大降低了判断难度,提高了准确率.