An Eigenvalue Perturbation Approach to Stability Analysis, Part II: When Will Zeros of Time-Delay Systems Cross Imaginary Axis?

2010 ◽  
Vol 48 (8) ◽  
pp. 5583-5605 ◽  
Author(s):  
Jie Chen ◽  
Peilin Fu ◽  
Silviu-Iulian Niculescu ◽  
Zhihong Guan
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Imaginary Axis ◽  
Delay Systems ◽  
Perturbation Approach ◽  
Time Delay Systems

A VERY SIMPLE CRITERION FOR CHARACTERIZING THE CROSSING DIRECTION OF TIME-DELAY SYSTEMS WITH DELAY-DEPENDENT PARAMETERS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250048 ◽  
Author(s):  
ZAI HUA WANG
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Imaginary Axis ◽  
Characteristic Root ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Critical Stability ◽  
Simple Criterion ◽  
Clear Physical Meaning ◽  
Delay Dependent

In this paper, a very simple criterion has been established for checking the crossing direction of a characteristic root crossing the imaginary axis for a class of time-delay systems with delay-dependent parameters, an important topic both in stability analysis and Hopf bifurcation. The criterion uses two easy-to-obtain functions with clear physical meaning from the critical stability condition and it generalizes a popular result in the literature.

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

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