Analyzing Bifurcation, Stability and Chaos for a Passive Walking Biped Model with a Sole Foot

2018 ◽  
Vol 28 (09) ◽  
pp. 1850113 ◽  
Author(s):  
Maysam Fathizadeh ◽  
Sajjad Taghvaei ◽  
Hossein Mohammadi
Keyword(s):  
Dynamic Models ◽  
Chaotic Behavior ◽  
Bifurcation Diagrams ◽  
Behavior Simulation ◽  
Passive Walking ◽  
Low Energy Consumption ◽  
Nonlinear Dynamic Models ◽  
Soles Of The Feet ◽  
The Stability ◽  
Intrinsic Characteristic

Human walking is an action with low energy consumption. Passive walking models (PWMs) can present this intrinsic characteristic. Simplicity in the biped helps to decrease the energy loss of the system. On the other hand, sufficient parts should be considered to increase the similarity of the model’s behavior to the original action. In this paper, the dynamic model for passive walking biped with unidirectional fixed flat soles of the feet is presented, which consists of two inverted pendulums with L-shaped bodies. This model can capture the effects of sole foot in walking. By adding the sole foot, the number of phases of a gait increases to two. The nonlinear dynamic models for each phase and the transition rules are determined, and the stable and unstable periodic motions are calculated. The stability situations are obtained for different conditions of walking. Finally, the bifurcation diagrams are presented for studying the effects of the sole foot. Poincaré section, Lyapunov exponents, and bifurcation diagrams are used to analyze stability and chaotic behavior. Simulation results indicate that the sole foot has such a significant impression on the dynamic behavior of the system that it should be considered in the simple PWMs.

NONLINEAR DYNAMICS OF DIGITAL PHASE-LOCKED LOOPS WITH DELAY

1994 ◽  
Vol 04 (03) ◽  
pp. 715-726 ◽  
Author(s):  
MARIA DE SOUSA VIEIRA ◽  
ALLAN J. LICHTENBERG ◽  
MICHAEL A. LIEBERMAN
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Behavior ◽  
Nonlinear Oscillators ◽  
Coupled Systems ◽  
Phase Locked Loops ◽  
Bifurcation Diagrams ◽  
Digital Phase ◽  
Coupled Nonlinear Oscillators ◽  
Digital Phase Locked Loops ◽  
The Stability

We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.

scholarly journals Analysis of harmonic vibration synchronization for a nonlinear vibrating system with hysteresis force

2019 ◽  
Vol 39 (4) ◽  
pp. 1087-1101
Author(s):  
Nan Zhang ◽  
Shiling Wu
Keyword(s):  
Nonlinear Vibration ◽  
Phase Difference ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Harmonic Vibration ◽  
Vibration System ◽  
The Difference ◽  
Nonlinear Dynamic Models ◽  
The Stability ◽  
Nonlinear Vibration System

Harmonic vibration synchronization of the two excited motors is an important factor affecting the performance of the nonlinear vibration system driven by the two excited motors. From the point of view of the hysteresis force, the nonlinear dynamic models of the nonlinear vibration system driven by the two excited motors are presented for the analysis of the hysteresis force with the asymmetry. An approximate periodic solution for the nonlinear vibration system with the hysteresis force is investigated using the nonlinear models. The condition of harmonic vibration synchronization is theoretically analyzed using the rotor–rotation equations of the two excited motors in the nonlinear dynamic models and the stability condition of harmonic vibration synchronization also is theoretically analyzed using Jacobi matrix of the phase difference equation of two excited motors. Using Matlab/Simlink, harmonic vibration synchronization of the two excited motors and the stability of harmonic vibration synchronization for the nonlinear vibration system with the hysteresis force are analyzed through the selected parameters. Various synchronous processes of the nonlinear vibration system with the hysteresis force are obtained through the difference rates of the two excited motors (including the initial phase difference, the initial rotational speed difference, the difference of the motors parameters). It has been shown that the research results can provide theoretical basis for the design and research of the vibration system driven by the two-excited motors.

Modelling and robust position and orientation control of a non-affine nonlinear dielectrophoresis-based micromanipulation system

2018 ◽  
Vol 41 (9) ◽  
pp. 2582-2595 ◽  
Author(s):  
Hua Luo ◽  
William W Melek ◽  
John TW Yeow
Keyword(s):  
Dynamic Models ◽  
Sliding Mode ◽  
The Finite Element Method ◽  
Orientation Control ◽  
Level Of Automation ◽  
Position And Orientation ◽  
Nonlinear Dynamic Models ◽  
The Stability ◽  
Automatic Positioning ◽  
Analytical Expressions

Conventional dielectrophoresis and electrorotation have attracted widespread attention in the field of individual micro-object manipulation in recent years. The improvement of current dielectrophoresis-based micromanipulation systems’ flexibility, accuracy and level of automation are essential requirements of dielectrophoresis-based micromanipulation techniques. For the purpose of high-precision automatic positioning and orientation control of a micro-object, we have developed approximate analytical expressions to describe the conventional dielectrophoretic force and electrorotation torque generated by quadrupole polynomial electrodes on a spherical micro-particle. Numerical simulations based on the finite element method are used to demonstrate the effectiveness of the proposed modelling method. In addition, the non-affine nonlinear dynamic models of the dielectrophoresis-based micromanipulation subsystems are established. Furthermore, an uncertainty and disturbance estimator based dynamic sliding mode controller is proposed and applied to achieve a robust sequential position and orientation control system. The stability of the closed-loop system is established. The performance of the proposed control is demonstrated through simulation studies.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Stability of aerobic granular sludge under low energy consumption: Optimization of granular size distribution by a novel internal component

2021 ◽  
Author(s):  
Runjuan Cao ◽  
Yatong Ji ◽  
Taixing Han ◽  
Jingsong Deng ◽  
Liang Zhu ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Granular Sludge ◽  
Pollutant Removal ◽  
Low Energy ◽  
Aerobic Granular Sludge ◽  
Mesh Screen ◽  
Energy Consumption Optimization ◽  
Low Energy Consumption ◽  
Internal Component ◽  
The Stability

To enhance the stability and pollutant removal performance of an aerobic granular sludge (AGS), four groups of AGS reactors with different pore sizes of mesh screen (R1 is control reactor,...

Novel active magnetorheological knee prosthesis presents low energy consumption during ground walking

2021 ◽  
pp. 1045389X2098392
Author(s):  
Rafhael Milanezi de Andrade ◽  
Jordana Simões Ribeiro Martins ◽  
Marcos Pinotti ◽  
Antônio Bento Filho ◽  
Claysson Bruno Santos Vimieiro
Keyword(s):  
Energy Consumption ◽  
Stance Phase ◽  
Gait Cycle ◽  
Dynamic Models ◽  
Knee Prosthesis ◽  
Regenerative Braking ◽  
Harmonic Drive ◽  
Low Energy Consumption ◽  
Energetic Expenditure ◽  
Over Ground Walking

This study analyses the energy consumption of an active magnetorheological knee (AMRK) actuator that was designed for transfemoral prostheses. The system was developed as an operational motor unit (MU), which consists of an EC motor, a harmonic drive and a magnetorheological (MR) clutch, that operates in parallel with an MR brake. The dynamic models of the MR brake and MU were used to simulate the system’s energetic expenditure during over-ground walking under three different working conditions: using the complete AMRK; using just its motor-reducer, to operate as a common active knee prosthesis (CAKP), and using just the MR brake, to operate as a common semi-active knee prosthesis (CSAKP). The results are used to compare the MR devices power consumptions with that of the motor-reducer. As previously hypothesized, to use the MR brake in the swing phase is more energetically efficient than using the motor-reducer to drive the joint. Even if using the motor-reducer in regenerative braking mode during the stance phase, the differences in power consumption among the systems are remarkable. The AMRK expended 16.3 J during a gait cycle, which was 1.6 times less than the energy expenditure of the CAKP (26.6 J), whereas the CSAKP required just 6.0 J.

scholarly journals Chaotic Behavior in Gear System. Adaptation of Bifurcation Diagrams and Method of Statistical Mechanics.

1995 ◽  
Vol 61 (587) ◽  
pp. 3108-3115
Author(s):  
Keijin Sato ◽  
Sumio Yamamoto ◽  
Kazutaka Yokota ◽  
Toshihiro Aoki ◽  
Shu Karube
Keyword(s):  
Statistical Mechanics ◽  
Chaotic Behavior ◽  
Gear System ◽  
Bifurcation Diagrams ◽  
System Adaptation

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

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