A Chaotic Time-Delay System with Saturation Nonlinearity

2017 ◽  
Vol 6 (3) ◽  
pp. 111-129 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan
Keyword(s):  
Time Delay ◽  
Complex Dynamics ◽  
Chaotic Signal ◽  
Delay System ◽  
Delay Systems ◽  
Maximum Lyapunov Exponent ◽  
Time Delay Systems ◽  
Time Delay System ◽  
System Parameters ◽  
Saturation Nonlinearity

Complex dynamics are observed in time-delay systems because the presence of time delay could induce unexpected oscillations. Therefore, time-delay systems are effective for constructing chaotic signal generators which have used in various engineering applications. In this paper, a new system with a single scalar time delay and a saturation nonlinearity is introduced. Dynamics of such time-delay system are investigated by using phase planes, bifurcation diagrams and the maximum Lyapunov exponent with the variance of system parameters. It is interesting that the time-delay system can generate double-scroll chaotic attractors despite its elegant model. Circuitry of the system is also presented to show the feasibility of the theoretical model.

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.

Chaotic Attractor in a Novel Time-Delayed System with a Saturation Function

2015 ◽  
pp. 230-258 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan
Keyword(s):  
Time Delay ◽  
Nonlinear Behavior ◽  
Chaotic Signal ◽  
Delay Systems ◽  
Maximum Lyapunov Exponent ◽  
System Parameters ◽  
Saturation Function ◽  
Potential Applications ◽  
Delayed System ◽  
Chaotic Signal Generator

From the viewpoint of engineering applications, time delay is useful for constructing a chaotic signal generator, which is the major part of diverse potential applications. Although different mathematical models of time-delay systems have been known, few models can exhibit chaotic behaviors. Motivated by attractive features and potential applications of time-delay models, a new chaotic system with a single scalar time delay and a nonlinearity described by a saturation function is proposed in this chapter. Nonlinear behavior of the system is discovered through bifurcation diagrams and the maximum Lyapunov exponent with the variance of system parameters. Interestingly, the system shows double-scroll chaotic attractors for some suitable chosen system parameters. In order to confirm the correction and feasibility of the theoretical model, the system is also implemented with analog electronic circuit. Finally, a practical application of such circuit is discussed at the end of this chapter.

scholarly journals Passivity analysis and synthesis for uncertain time-delay systems

2001 ◽  
Vol 7 (5) ◽  
pp. 455-484 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Lihua Xie
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Delay System ◽  
Passivity Analysis ◽  
Analysis And Synthesis ◽  
Uncertain Time

In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

2006 ◽  
Vol 129 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Shinn-Horng Chen ◽  
Jyh-Horng Chou ◽  
Liang-An Zheng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Time Delay System ◽  
The Stability ◽  
Singular Time

In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

Delay-Dependent Stabilization for Singular Time-Delay Systems

2012 ◽  
Vol 182-183 ◽  
pp. 1255-1259 ◽  
Author(s):  
Jin Feng Gao ◽  
Jia Ren ◽  
Chuang Meng
Keyword(s):  
Time Delay ◽  
Delay Interval ◽  
Energy Function ◽  
Delay System ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Delay System ◽  
Delay Dependent ◽  
Singular Time

Some new results of delay-dependent stabilization for linear singular time-delay systems are presented. And the time delay considered here is assumed to be constant but unknown. By using a new Lyapunov-krasovskii functional which splits the whole delay interval into two subintervals and defines a different energy function on each subinterval, a sufficient delay-dependent condition is obtained for the singular time-delay system to be regular, impulse free and stable.

scholarly journals Inversion of hyperoutput time-delay systems

2019 ◽  
Vol 484 (5) ◽  
pp. 538-541
Author(s):  
A. V. Il’in ◽  
E. I. Atamas ◽  
V. V. Fomichev
Keyword(s):  
Time Delay ◽  
Canonical Form ◽  
Delay System ◽  
Delay Systems ◽  
Zero Dynamics ◽  
Inversion Problem ◽  
Time Delay Systems ◽  
Inversion Algorithm ◽  
Time Delay System

An inversion problem for LTI hyperoutput time-delay system is considered. For such systems canonical form with isolated zero dynamics is obtained, system invariant zeros and their relation to spectral observability of zero dynamics subsystem are investigated. Using this results, inversion algorithm is suggested for time-delay systems.

scholarly journals Control Design for Linear Strictly Metzler Time-delay Systems

2021 ◽  
Vol 16 ◽  
pp. 519-526
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Structural Constraints ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
State Control ◽  
Time Delay System ◽  
Diagonal Forms

The relationships among structural constraints and involvement of the design condition are studied to synthesize state control for one class of linear strictly Metzler time-delay systems. These characterizations reflect the specific dynamical and structural attributes of the system class and outline the associated structures of linear matrix inequalities. Adjusting diagonal forms of linear matrix variables it is indicated how the proposed method gives a computable technique for the Metzler time-delay system, guaranteeing stabilising effect through implicit diagonal stabilization. The aim of this research is to describe conditions tying together inequality formulations and concepts of control theory in structures of Metzler systems

Research of Nonlinear PID Control Method for Time Delay Systems

2010 ◽  
Vol 44-47 ◽  
pp. 3839-3843
Author(s):  
Wen Bo Liu ◽  
Meng Xiao Wang
Keyword(s):  
Time Delay ◽  
Pid Control ◽  
Control Method ◽  
Delay System ◽  
Smith Predictor ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Nonlinear Controller ◽  
Time Delay System ◽  
Nonlinear Pid Control

A nonlinear PID control method based on Smith predictor is presented in this paper to control the time delay systems. This method combines the Smith predictor with nonlinear controller. And the simulation study had been done for a first-order time-delay system. The results show that this method offer good static and dynamic characteristics, at the same time its disturbance-rejection and robustness are better.

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