scholarly journals Parametric Controller Design of Hopf Bifurcation System

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jinbo Lu ◽  
Xiaorong Hou ◽  
Min Luo
Keyword(s):  
Computer Simulation ◽  
Hopf Bifurcation ◽  
Nonlinear Dynamic ◽  
Lorenz System ◽  
Controller Design ◽  
Design Method ◽  
Equilibrium Points ◽  
Nonlinear Dynamic System ◽  
Simulation Results ◽  
The Stability

A general parametric controller design method is proposed for Hopf bifurcation of nonlinear dynamic system. This method does not increase the dimension of the system. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Symbolic computation is used to deduce the constraints of controller, and cylindrical algebraic decomposition is used to find the stability parameter regions in parameter space of controller. The method is then employed for Hopf bifurcation control. Taking Lorenz system as an example, the controller design steps of the method and numerical simulations are discussed. Computer simulation results are presented to confirm the analytical predictions.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250088 ◽  
Author(s):  
YONG XU ◽  
RENCAI GU ◽  
HUIQING ZHANG ◽  
DONGXI LI
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Fractional Order ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Control Technique ◽  
Order System ◽  
System Parameters ◽  
Simulation Results ◽  
The Stability

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

scholarly journals Study on the High-Speed and Close of the UVA Cooperative Formation Controller Design

2018 ◽  
Vol 36 (2) ◽  
pp. 345-352
Author(s):  
Jialong Zhang ◽  
Jianguo Yan ◽  
Pu Zhang ◽  
Xiaoqiao Qi ◽  
Maolong Lü
Keyword(s):  
Dynamic Characteristic ◽  
High Speed ◽  
Controller Design ◽  
Design Method ◽  
Formation Flight ◽  
Unsteady Aerodynamic ◽  
Aerodynamic Model ◽  
Thrust Vector ◽  
The Stability ◽  
Rudder Angle

Aiming at the high-speed flight of the UAVs cooperative formation, when a single UAV has occurred, need to exit the formation flight and be close or super close to form of the formation quickly. A fast close cooperative formation controller design method is proposed to make up for low the fighting robustness, and be shortcomings of timeliness poorly and analyze the dynamic characteristic of UAV formation flight. Taking the external factors known into consideration, setting up for the longitude maneuver of nonlinear thrust vector and unsteady aerodynamic model, according to the formation velocity, flat tail rudder angle and thrust vector and pitch angle velocity for corresponding input commend signals for the controller to research the dynamic characteristic of UAV formation flight. Meanwhile, the formation flight distance error is the convergence to a fixed value, and the stability of the cooperative formation flight is good. The simulation of results show that the controller can effectively improve the speed of the close or super close to formation, and maintain the stability of the formation flight, which provides a method of the close or super close formation flight controller design.

scholarly journals Secure Load Frequency Control of Smart Grids under Deception Attack: A Piecewise Delay Approach

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2266 ◽  
Author(s):  
Fei Zhao ◽  
Jinsha Yuan ◽  
Ning Wang ◽  
Zhang Zhang ◽  
Helong Wen
Keyword(s):  
Smart Grids ◽  
Controller Design ◽  
Design Method ◽  
Frequency Control ◽  
Functional Method ◽  
Load Frequency Control ◽  
Linear Matrix ◽  
Load Frequency ◽  
The Stability

The problem of secure load frequency control of smart grids is investigated in this paper. The networked data transmission within the smart grid is corrupted by stochastic deception attacks. First, a unified Load frequency control model is constructed to account for both network-induced effects and deception attacks. Second, with the Lyapunov functional method, a piecewise delay analysis is conducted to study the stability of the established model, which is of less conservativeness. Third, based on the stability analysis, a controller design method is provided in terms of linear matrix inequalities. Finally, a case study is carried out to demonstrate the derived results.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Fear Induced Stabilization in an Intraguild Predation Model

2020 ◽  
Vol 30 (04) ◽  
pp. 2050053
Author(s):  
Mainul Hossain ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Intraguild Predation ◽  
Equilibrium Points ◽  
Stable Limit ◽  
Interior Equilibrium ◽  
The Rich ◽  
The Stability ◽  
The Cost ◽  
The Impact

In the present paper, we investigate the impact of fear in an intraguild predation model. We consider that the growth rate of intraguild prey (IG prey) is reduced due to the cost of fear of intraguild predator (IG predator), and the growth rate of basal prey is suppressed due to the cost of fear of both the IG prey and the IG predator. The basic mathematical results such as positively invariant space, boundedness of the solutions, persistence of the system have been investigated. We further analyze the existence and local stability of the biologically feasible equilibrium points, and also study the Hopf-bifurcation analysis of the system with respect to the fear parameter. The direction of Hopf-bifurcation and the stability properties of the periodic solutions have also been investigated. We observe that in the absence of fear, omnivory produces chaos in a three-species food chain system. However, fear can stabilize the chaos thus obtained. We also observe that the system shows bistability behavior between IG prey free equilibrium and IG predator free equilibrium, and bistability between IG prey free equilibrium and interior equilibrium. Furthermore, we observe that for a suitable set of parameter values, the system may exhibit multiple stable limit cycles. We perform extensive numerical simulations to explore the rich dynamics of a simple intraguild predation model with fear effect.

scholarly journals Stability and Convergence Analysis of Direct Adaptive Inverse Control

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Shafiq ◽  
Muhammad A. Shafiq ◽  
Hassan A. Yousef
Keyword(s):  
Computer Simulation ◽  
Convergence Analysis ◽  
Indirect Method ◽  
Stability And Convergence ◽  
Adaptive Inverse Control ◽  
Inverse Control ◽  
Simulation Results ◽  
The Stability ◽  
Feed Forward Controller ◽  
Physical Plants

In adaptive inverse control (AIC), adaptive inverse of the plant is used as a feed-forward controller. Majority of AIC schemes estimate controller parameters using the indirect method. Direct adaptive inverse control (DAIC) alleviates the adhocism in adaptive loop. In this paper, we discuss the stability and convergence of DAIC algorithm. The computer simulation results are presented to demonstrate the performance of the DAIC. Laboratory scale experimental results are included in the paper to study the efficiency of DAIC for physical plants.

Study on Stability and Reactive Power Optimization of Active Distribution Network Based on Bifurcation Theory

2015 ◽  
Vol 734 ◽  
pp. 701-706
Author(s):  
Xian Bin Dai
Keyword(s):  
Power Distribution ◽  
Distribution System ◽  
Nonlinear Dynamic ◽  
Bifurcation Theory ◽  
Reactive Power ◽  
Distribution Network ◽  
Nonlinear Dynamic System ◽  
Reactive Power Optimization ◽  
Power Distribution Network ◽  
The Stability

as the basic method used to analyze the stability of nonlinear dynamic system, it is able to more deeply discuss the stability problems of power system in the vicinity of a critical point in comparison with traditional analysis method. Active power distribution network is a complicated nonlinear dynamic system. The change of voltage stability is the process to convert from stable status to bifurcation in essence. Taking 10-node active distribution system as an example, the author studies the influence of reactive power optimization on voltage stability based on bifurcation theory. The author explains the reactive optimization algorithm based on numerical simulation, namely, it is the decision - making algorithm in order to realize multiple purposes of having minimum power network loss, largest reactive power margin with stable operation of power distribution network and minimum voltage floating in system fluctuation, which is proved to be effective in elevating power distribution system stability, reducing power loss and improving voltage quality.

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