scholarly journals Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application

2019 ◽  
Vol 9 (21) ◽  
pp. 4683 ◽  
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Lyapunov Exponent ◽  
External Force ◽  
Control Method ◽  
Duffing Oscillator ◽  
Pseudorandom Sequence ◽  
Past Century ◽  
Continuous Control ◽  
Duffing System ◽  
Numerical Solution Methods ◽  
Solution Methods

Over the past century, a tremendous amount of work on the Duffing system has been done with continuous external force, including analytical and numerical solution methods, and the dynamic behavior of physical systems. However, hows does the Duffing oscillator behave if the external force is intermittent? This paper investigates the Duffing oscillator with intermittent external force, and a modified Duffing chaotic system is proposed. Different from the continuous-control method, an intermittent external force of cosine function was designed to control the Duffing oscillator, such that the modified Duffing (MD) system could behave chaotically. The dynamic characteristics of MD system, such as the strange attractors, Lyapunov exponent spectra, and bifurcation diagram spectra were outlined with numerical simulations. Numerical results showed that there existed a positive Lyapunov exponent in some parameter intervals. Furthermore, by combining it with chaos scrambling and chaos XOR encryption, a chaos-based encryption algorithm was designed via the pseudorandom sequence generated from the MD. Finally, feasibility and validity were verified by simulation experiments of image encryption.

scholarly journals Vibration of the Duffing Oscillator: Effect of Fractional Damping

2007 ◽  
Vol 14 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Marek Borowiec ◽  
Grzegorz Litak ◽  
Arkadiusz Syta
Keyword(s):  
Lyapunov Exponent ◽  
Perturbation Methods ◽  
Duffing Oscillator ◽  
Homoclinic Bifurcation ◽  
Sufficient Condition ◽  
External Excitation ◽  
Fractional Damping ◽  
Duffing System ◽  
Transition To Chaos ◽  
Melnikov Criterion

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear tools as Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude μ_c, which a sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.

scholarly journals Chaotic Motion in Forced Duffing System Subject to Linear and Nonlinear Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Tai-Ping Chang
Keyword(s):  
Lyapunov Exponent ◽  
Nonlinear System ◽  
Chaotic Motion ◽  
Chaotic Behavior ◽  
Duffing Oscillator ◽  
Nonlinear Damping ◽  
Critical Value ◽  
Duffing System ◽  
Linear And Nonlinear

This paper investigates the chaotic motion in forced Duffing oscillator due to linear and nonlinear damping by using Melnikov technique. In particular, the critical value of the forcing amplitude of the nonlinear system is calculated by Melnikov technique. Further, the top Lyapunov exponent of the nonlinear system is evaluated by Wolf’s algorithm to determine whether the chaotic phenomenon of the nonlinear system actually occurs. It is concluded that the chaotic motion of the nonlinear system occurs when the forcing amplitude exceeds the critical value, and the linear and nonlinear damping can generate pronounced effects on the chaotic behavior of the forced Duffing oscillator.

Effect of Different Forms of Periodic Piecewise Linear Forces on Duffing Oscillator

2021 ◽  
Vol 13 (2) ◽  
pp. 361-375
Author(s):  
S. V. Priyatharsini ◽  
B. Bhuvaneshwari ◽  
V. Chinnathambi ◽  
S. Rajasekar
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Piecewise Linear ◽  
Duffing Oscillator ◽  
Control Force ◽  
Maximal Lyapunov Exponent ◽  
Simulation Tools ◽  
Duffing System ◽  
Parametric Control ◽  
Applied Forces

The paper highlights the effect of different forms of   periodic   piecewise linear forces in the ubiquitous Duffing oscillator equation. The external periodic piecewise linear forces considered are Triangular, Hat, Trapezium, Quadratic and Rectangular. With the aid of some numerical simulation tools such as bifurcation diagram, phase portrait and Poincare´ map, the different routes to chaos and various strange attractors are found to occur due to the applied forces. The effect of an ε-parametric control force in the Duffing system is also analyzed. To characterize the regular and chaotic behaviours of this system, the maximal Lyapunov exponent is employed.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

scholarly journals Continuous Control Set Predictive Current Control for Induction Machine

2021 ◽  
Vol 11 (13) ◽  
pp. 6230
Author(s):  
Toni Varga ◽  
Tin Benšić ◽  
Vedrana Jerković Štil ◽  
Marinko Barukčić
Keyword(s):  
Control Method ◽  
Induction Machine ◽  
Current Control ◽  
Continuous Control ◽  
Loop Model ◽  
Voltage Reference ◽  
Control Loop ◽  
Speed Tracking ◽  
Finite Control ◽  
Control Set

A speed tracking control method for induction machine is shown in this paper. The method consists of outer speed control loop and inner current control loop. Model predictive current control method without the need for calculation of the weighing factors is utilized for the inner control loop, which generates a continuous set of voltage reference values that can be modulated and applied by the inverter to the induction machine. Interesting parallels are drawn between the developed method and state feedback principles that helped with the analysis of the stability and controllability. Simple speed and rotor flux estimator is implemented that helps achieve sensorless control. Simulation is conducted and the method shows great performance for speed tracking in a steady state, and during transients as well. Additionally, compared to the finite control set predictive current control, it shows less harmonic content in the generated torque on the rotor shaft.

An Investigation Into the Compliance of SCARA Robots. Part II: Experimental and Numerical Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 23-30 ◽  
Author(s):  
H. A. ElMaraghy ◽  
B. Johns
Keyword(s):  
Elastic Compliance ◽  
Servo Control ◽  
Compliance Matrix ◽  
End Effector ◽  
Prismatic Parts ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Using Data ◽  
Assembly Performance ◽  
Robot Configurations

A model of inherent elastic compliance was developed for general position-controlled SCARA, with conventional joint feedback control, for both rotational and prismatic part insertion (Part I). The developed model was applied to the SKILAM and ADEPT I robots for validation. Experimental procedures and numerical solution methods are described. It was found that the ADEPT I robot employs a coupled control strategy between joints one and two which produces a constant, decoupled end effector compliance. The applicable compliance matrix, in this case, is presented and the experimental results are discussed. The model may be used to develop compliance maps that define the amount of end effector compliance, as a function of the joints compliance, as well as its variation for different robot configurations. This is illustrated using data for the SKILAM SCARA robot. Results are plotted and discussed. The most appropriate robot postures for assembly were found for both rotational and prismatic parts. The conditions necessary to achieve compliance or semicompliance centers with the SKILAM robot were examined. The results and methods demonstrated in these examples may be used to select appropriate robots for given applications. They can also guide robot designers in selecting joint servo-control gains to obtain the desired joints compliance ratio and improve assembly performance.

Continuous control of sampled data systems with robustness against bounded measurement errors

2017 ◽  
Vol 40 (10) ◽  
pp. 3125-3133
Author(s):  
Milad Ghanbari ◽  
Masoud Bahraini ◽  
Mohammad Javad Yazdanpanah
Keyword(s):  
Measurement Errors ◽  
Control Method ◽  
Linear Time ◽  
Continuous Control ◽  
Data Systems ◽  
Sampled Data ◽  
Linear Time Invariant ◽  
Experimental Implementation ◽  
Time Invariant ◽  
Ultimate Bound

This paper considers the design of a generalized hold function to be used for the control of sampled-data systems. The proposed method suggests a continuous controller for sampled data systems. Ultimate boundedness of the proposed method in the presence of bounded measurement errors is also shown for linear and nonlinear systems. In linear time invariant cases, a cost function is suggested for the sake of ultimate bound minimization. In addition, this can answer how we choose a sensor for a real system to get a desired control outcome. Eventually, the effectiveness of the proposed control method is investigated through simulation and experimental implementation.

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