Experimental Investigation on the Dynamic Behavior of Chaotic Jumping in Inverted Flexible Pendulum Under Harmonic Excitation

2018 ◽  
Author(s):  
Hartiny A. Kahar ◽  
Elmira Madadi ◽  
Dirk Söffker
Keyword(s):  
Multiple Equilibria ◽  
Dynamical Behavior ◽  
Harmonic Excitation ◽  
Control Parameters ◽  
Pendulum System ◽  
Dynamics And Control ◽  
Design Requirements ◽  
And Control ◽  
Two Equilibria ◽  
Stimulation Of

Control of flexible systems is effected by design requirements and also manufacturing aspects. The dynamics and control of such systems are challenging, especially in the case of an inverted flexible pendulum system. The experimental study of the dynamical behavior of this kind of system showing jumping phenomenon between three equilibria is not considered in detail in literatures so far. The paper focuses on studying the effects of some parameters to the dynamics of the flexible pendulum. By varying the excitation parameters, control parameters, as well as other distinguished mechanical parameters, different phenomena are observed in experiments discussed in this contribution. In this study, a custom built inverted flexible pendulum on cart system under PID-controlled harmonic excitation is considered. Data are collected from both cart excitation signal and displacement of the pendulum, also to observe their correlation towards jumping behavior. Effects of the variation of the parameters leading to changes in chaotic jumping patterns. Multiple equilibria are observed and analyzed. It can be concluded that depending on the excitation amplitudes, frequencies, and controller parameters, the minimum of two equilibria with an unstable third equilibrium can be detected while jumping phenomena between the equilibria are observed. Questions about the stimulation of the jumping by impulses resulting from imperfect sinusoidal excitation due to control limitations are discussed.

On Nonlinear Dynamics and Control of an Inverted Flexible Pendulum System With Chaos

2019 ◽  
Author(s):  
Hartiny Kahar ◽  
Dirk Söffker
Keyword(s):  
Control Method ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Energy Content ◽  
Dynamical Behavior ◽  
Pendulum System ◽  
Time Frequency ◽  
Dynamics And Control ◽  
Specific Frequency ◽  
And Control

Abstract In this paper, the dynamical behavior of a nonlinear mechanical system is considered, namely an inverted flexible pendulum excited in its base by a cart driven by a motor. In this experimental procedure, the chaotic motion of the pendulum tip was identified, in combination with a specific range of parameters. Time-frequency energy analysis is performed to be used for modeling the transition between the equilibria of the chaotic systems. Controlling the chaotic behavior of the system is realized using impulsive control method, where additive impulses are injected into the system, designed with specific impulses energy content at a specific frequency band. The experimental results are presented and discussed in detail, concentrating on how the designed impulses have to be injected to affect the system, specifically the transition between states of equilibria. The results from this experimental modeling procedure show that both additive impulse design and frequency filtering of the injected additive impulses are able to stimulate the equilibrium shift and therefore to control the chaotic behavior of the system.

Conclusion

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Multiple Equilibria ◽  
Nonlinear Models ◽  
Dynamical Behavior ◽  
Transportation Systems ◽  
Network Systems ◽  
Grid Systems ◽  
Feedback Interconnections ◽  
And Control

This book has described a general stability analysis and control design framework for large-scale dynamical systems, with an emphasis on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. The large-scale dynamical systems are composed of interconnected subsystems whose relationships are often circular, giving rise to feedback interconnections. This leads to nonlinear models that can exhibit rich dynamical behavior, such as multiple equilibria, limit cycles, bifurcations, jump resonance phenomena, and chaos. The book concludes by discussing the potential for applying and extending the results across disciplines, such as economic systems, network systems, computer networks, telecommunication systems, power grid systems, and road, rail, air, and space transportation systems.

scholarly journals Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Krzysztof Kecik ◽  
Jerzy Warminski
Keyword(s):  
Vibration Analysis ◽  
Dynamic Behaviour ◽  
Resonance Region ◽  
Nonlinear Damping ◽  
Harmonic Excitation ◽  
Magnetorheological Damper ◽  
Nonlinear Spring ◽  
Dynamics And Control ◽  
And Control ◽  
Experimental Rig

This paper presents vibration analysis of an autoparametric pendulum-like mechanism subjected to harmonic excitation. To improve dynamics and control motions, a new suspension composed of a semiactive magnetorheological damper and a nonlinear spring is applied. The influence of essential parameters such as the nonlinear damping or stiffness on vibration, near the main parametric resonance region, are carried out numerically and next verified experimentally in a special experimental rig. Results show that the magnetorheological damper, together with the nonlinear spring can be efficiently used to change the dynamic behaviour of the system. Furthermore, the nonlinear elements applied in the suspension of the autoparametric system allow to reduce the unstable areas and chaotic or rotating motion of the pendulum.

Dynamics and Control of an SMA-Pendulum System

2016 ◽  
Author(s):  
Dimitri Danulussi Alves Costa ◽  
Marcelo Amorim Savi
Keyword(s):  
Pendulum System ◽  
Dynamics And Control ◽  
And Control

scholarly journals An Electromechanical Pendulum Robot Arm in Action: Dynamics and Control

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
A. Notué Kadjie ◽  
P. R. Nwagoum Tuwa ◽  
Paul Woafo
Keyword(s):  
Control Strategies ◽  
Dynamical Behavior ◽  
Mechanical Vibration ◽  
High Amplitude ◽  
Electrical Signal ◽  
Electrical Circuit ◽  
Robot Arm ◽  
Dynamics And Control ◽  
Short Time ◽  
And Control

The authors numerically investigate the dynamics and control of an electromechanical robot arm consisting of a pendulum coupled to an electrical circuit via an electromagnetic mechanism. The analysis of the dynamical behavior of the electromechanical device powered by a sinusoidal power source is carried out when the effects of the loads on the arm are neglected. It is found that the device exhibits period-n T oscillations and high amplitude oscillations when the electric current is at its smallest value. The specific case which considers the effects of the impulsive contact force caused by an external load mass pushed by the arm is also studied. It is found that the amplitude of the impulse force generates several behaviors such as jump of amplitude and distortions of the mechanical vibration and electrical signal. For more efficient functioning of the device, both piezoelectric and adaptive backstepping controls are applied on the system. It is found that the control strategies are able to mitigate the signal distortion and restore the dynamical behavior to its normal state or reduce the effects of perturbations such as a short time variation of one component or when the robot system is subject to noises.

Dynamics and Control of Four Wheeled Differentially Steered UGVs

2014 ◽  
Author(s):  
Andrew Narvesen ◽  
Majura F. Selekwa
Keyword(s):  
Autonomous Navigation ◽  
Research Area ◽  
Control Parameters ◽  
Ground Vehicles ◽  
Friction Forces ◽  
Straight Line ◽  
Dynamics And Control ◽  
Left And Right ◽  
And Control ◽  
Very High

Autonomous navigation of ground vehicles is a growing research area. Skid steered wheeled ground vehicles are of interest because of the system’s relatively easy control parameters. Steered wheels require actuation and control for the steering and speed of the steered wheels while skid steering just requires actuation and control of the wheel speeds, usually just a left and right wheel speed. Four Wheeled differentially steered vehicles are built primarily for straight line motion since the instantaneous centers of zero velocities for the four wheels are always at infinity when there is no sliding in the wheels. When the vehicle has to negotiate a corner, it uses the differential velocities between sides to force the wheels to slide and perform the cornering maneuver. Maneuvering is difficult when the ground friction is very high because of undue stresses in the axle structure. This paper analyses the dynamics of such vehicles that relates the traction and skid friction forces and proposes a suitable control system. At this time, the paper is supported by simulation results while experimental work is still going on.

Dynamics and Control of a Delayed Oscillator Network by Pinning Strategy

2017 ◽  
Vol 27 (13) ◽  
pp. 1750193 ◽  
Author(s):  
Jing Zhou ◽  
Xu Xu ◽  
Dongyuan Yu ◽  
Wenhao Li
Keyword(s):  
Periodic Solutions ◽  
Large Scale ◽  
Dynamical Behavior ◽  
Orthogonal Transformation ◽  
Original System ◽  
Pinning Control ◽  
Dynamics And Control ◽  
Large Scale Networks ◽  
And Control ◽  
Pinning Strategy

Large scale networks may exhibit complicated dynamical behaviors, such as instability, bifurcation, and chaos. It is not easy to get which nodes or links need to be controlled for ensuring the desired dynamical behavior. This paper presents a detailed analysis on the dynamics and control of a delayed network by a pinning strategy. The network system is first mapped to a simple system by means of an orthogonal transformation. The control signals are then exerted only on a fraction of nodes in the transformed system. We analyze how to get the desired dynamics of the original controlled system (such as zeros solutions, periodic solutions, quasi-periodic solutions and chaos) via controlling the transformed system. It shows that the solutions of the original system can be obtained by the local dynamical behavior exhibiting in the transformed system. The results show that the proposed pinning control strategy is an effective approach for dynamics control.

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