scholarly journals Developing and automating time delay system stability analysis of dynamic systems using the Matrix Lambert W (MLW) function method

2009 ◽  
Author(s):  
Kristel M. Pietarila
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Dynamic Systems ◽  
Function Method ◽  
Delay System ◽  
System Stability ◽  
Time Delay System ◽  
The Matrix ◽  
System Stability Analysis

Developing and Automating Time Delay System Stability Analysis of Machinery Systems Using the Matrix Lambert W Function Method

2008 ◽  
Author(s):  
Kristel M. Pietarila ◽  
Roger Fales
Keyword(s):  
Stability Analysis ◽  
Analytic Solutions ◽  
Delay System ◽  
New Method ◽  
System Stability ◽  
Lambert W Function ◽  
The Matrix ◽  
System Equations ◽  
System Stability Analysis ◽  
Delay Differential

Stability analysis of time delayed (TD) systems is not easy to conduct since the addition of delays within a dynamic model results in irrational system equations. Traditional analysis methods involve adding model approximates representing delays. These approximates make the system equations rational, but can drive stable TD systems to instability as approximate accuracy is improved. A more advanced method would be an invaluable tool for simplifying the stability analysis procedure for TD systems. A new method for analyzing TD system stability without adding TD approximates to the system has been presented by Asl et al. [1, 2]. This method involves using the Lambert W function to obtain analytic solutions for a set of delay differential equations. The research presented in this paper discusses the development and automation of TD system stability analysis for a complex machinery system utilizing this new method, the matrix Lambert W (MLW) function TD stability analysis method.

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.

Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty

2015 ◽  
Vol 58 ◽  
pp. 50-57 ◽  
Author(s):  
Rajeeb Dey ◽  
Sandip Ghosh ◽  
Goshaidas Ray ◽  
Anjan Rakshit ◽  
Valentina Emilia Balas
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
Bounded Uncertainty
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