Controlling Nonlinear Dynamics in a Two-Well Impact System.

1998 ◽  
Vol 08 (12) ◽  
pp. 2409-2424 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Nonlinear Dynamics ◽  
High Gain ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
System Response ◽  
Control Procedure ◽  
Combined Use ◽  
Controlled Potential ◽  
And Control ◽  
Amplitude Level

To exploit all potentialities of the optimal control procedure, the analysis initiated in Part I focuses on the system response under one-side control, an excitation which furnishes high gain though, roughly, controlling only one part of the phase space. Many bifurcational and control items related to the unsymmetric and pulsed nature of the excitation are deeply investigated. A nonclassical kind of homoclinic bifurcation is identified and it is discussed how it may lead to major regularity. The system response is very rich, and the main local and global phenomena of the dynamics are analyzed in detail through combined use of bifurcation diagrams and attractor-basin phase portraits. Both the confinement of steady dynamics in the controlled potential well and their successive transition from confined to scattered are studied, and it is discussed how they are obtained through comparison with the case of harmonic excitation. It is shown that the two investigated optimal excitations permit to increase the amplitude level for confined to scattered dynamics and to regularize the steady dynamics, although in a different manner. The analysis shows the effectiveness — in "average" sense — of the proposed method for controlling nonlinear dynamics.

Numerical Investigation of Nonlinear Dynamics of a Pneumatic Artificial Muscle With Hard Excitation

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Bhaben Kalita ◽  
Santosha K. Dwivedy
Keyword(s):  
Nonlinear Dynamics ◽  
Resonance Condition ◽  
Basin Of Attraction ◽  
Artificial Muscle ◽  
Phase Portraits ◽  
System Response ◽  
Pneumatic Artificial Muscle ◽  
Superharmonic Resonance ◽  
System Parameters ◽  
Hard Excitation

Abstract In this work, a numerical analysis has been carried out to study the nonlinear dynamics of a system with pneumatic artificial muscle (PAM). The system is modeled as a single degree-of-freedom system and the governing nonlinear equation of motion has been derived to study the various responses of the system. The system is subjected to hard excitation and hence the subharmonic and superharmonic resonance conditions have been studied. The second-order method of multiple scales (MMS) has been used to find the response, stability, and bifurcations of the system. The effect of various system parameters on the system response has been studied using time response, phase portraits, and basin of attraction. In these responses, while the saddle node bifurcation is found in both super and subharmonic resonance conditions, the Hopf bifurcation is found only in superharmonic resonance condition. By changing different system parameters, it has been shown that the response with three periods leads to chaotic response for superharmonic resonance condition. This study will find applications in the design of PAM actuators.

scholarly journals Nonlinear Dynamics of Imperfect FGM Conical Panel

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Yan Niu ◽  
Yuxin Hao ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Shaowu Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Engineering Application ◽  
Shear Deformation Theory ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

Structures composed of functionally graded materials (FGM) can satisfy many rigorous requisitions in engineering application. In this paper, the nonlinear dynamics of a simply supported FGM conical panel with different forms of initial imperfections are investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers of the imperfection, amplitudes of the imperfection, and damping on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories, phase portraits, and Poincare maps are obtained to show the dynamic responses of the system.

Analysis and Control of Chaos in Sheppard-Taylor DC-DC Converter

2013 ◽  
Vol 401-403 ◽  
pp. 1596-1599 ◽  
Author(s):  
Chuang Bi ◽  
Zheng Hang Fan ◽  
Yong Xiang ◽  
Jin Gang Hu
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Diagram ◽  
Time Domain ◽  
Chaos Control ◽  
Phase Portraits ◽  
Control Of Chaos ◽  
Complex Behaviour ◽  
Power Spectral ◽  
The Stability ◽  
And Control

This paper addresses the nonlinear dynamics of the Sheppard-Taylor converter to explain the complex behaviour exhibited in the converter under different practical conditions. The bifurcation diagram of the converter is generated to analyze the stability of the system. Several representative waveforms are captured from simulation to illustrate the chaos control of the converter, such as time-domain waveforms, phase portraits, Poincaré section diagrams, and power spectral diagrams.

Nonlinear Dynamics of FGM Conical Panel With Initial Imperfection in Thermal Environment

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Yan Niu ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Initial Imperfection ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

In this paper, the nonlinear dynamics of a simply supported functionally graded materials (FGM) conical panel with different forms of initial imperfections is investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin’s method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers and amplitudes on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories and phase portraits are obtained to show the dynamic response.

scholarly journals Exploitation of Nonlinear Dynamics of Buckled Beams

2016 ◽  
Author(s):  
James M. Wilson ◽  
Amit Shukla ◽  
William Olson
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Response ◽  
Maximum Amplitude ◽  
Harmonic Excitation ◽  
System Response ◽  
Optimization Approach ◽  
Response Characteristics ◽  
Buckled Beams ◽  
Integral Role ◽  
Loading Methods

Axially-loaded structures play an integral role in engineering design. Some of these structures exhibit a nonlinear response behavior under harmonic loading. Methods aimed at eliminating these behaviors are often employed in design of such structures. Our hypothesis is that the nonlinear dynamics can be used to optimize desired system response characteristics. In this paper, the dynamic response of a buckled beams under harmonic excitation is considered. An optimization approach is formulated that achieves maximum amplitude, periodic, and stable responses of the beam systems. Case studies are presented that demonstrate the utility of this optimization approach to exploit the nonlinear dynamics to achieve desired responses.

Nonlinear Dynamics and Control of Flexible Structures

1989 ◽  
Author(s):  
Francis C. Moon ◽  
Peter Gergely ◽  
James S. Thorp ◽  
John F. Abel
Keyword(s):  
Nonlinear Dynamics ◽  
Flexible Structures ◽  
Dynamics And Control ◽  
And Control ◽  
Nonlinear Dynamics And Control

scholarly journals Neighboring Optimal Guidance and Constrained Attitude Control for Accurate Orbit Injection

2021 ◽  
Author(s):  
Mauro Pontani ◽  
Fabio Celani
Keyword(s):  
Attitude Control ◽  
Initial Position ◽  
Low Earth Orbit ◽  
Guidance And Control ◽  
Optimal Guidance ◽  
Combined Use ◽  
Upper Stage ◽  
Neighboring Optimal Guidance ◽  
And Control ◽  
Guidance Technique

AbstractAccurate orbit injection represents a crucial issue in several mission scenarios, e.g., for spacecraft orbiting the Earth or for payload release from the upper stage of an ascent vehicle. This work considers a new guidance and control architecture based on the combined use of (i) the variable-time-domain neighboring optimal guidance technique (VTD-NOG), and (ii) the constrained proportional-derivative (CPD) algorithm for attitude control. More specifically, VTD-NOG & CPD is applied to two distinct injection maneuvers: (a) Hohmann-like finite-thrust transfer from a low Earth orbit to a geostationary orbit, and (b) orbit injection of the upper stage of a launch vehicle. Nonnominal flight conditions are modeled by assuming errors on the initial position, velocity, attitude, and attitude rate, as well as actuation deviations. Extensive Monte Carlo campaigns prove effectiveness and accuracy of the guidance and control methodology at hand, in the presence of realistic deviations from nominal flight conditions.

A High Gain Novel Double-Boost Converter for DC Microgrid Applications

2020 ◽  
Vol 29 (15) ◽  
pp. 2050246 ◽  
Author(s):  
B. N. Ch. V. Chakravarthi ◽  
G. V. Siva Krishna Rao
Keyword(s):  
Control Strategies ◽  
High Gain ◽  
Photovoltaic System ◽  
Solar Photovoltaic ◽  
Dc Microgrid ◽  
Boost Converters ◽  
Power Point ◽  
Solar Photovoltaic System ◽  
Conversion Stage ◽  
And Control

In solar photovoltaic (PV)-based DC microgrid systems, the voltage output of the classical DC–DC converter produces very less voltage as a result of poor voltage gain. Therefore, cascaded DC–DC boost converters are mandatory for boosting the voltage to match the DC microgrid voltage. However, the number of devices utilized in the DC–DC conversion stage becomes higher and leads to more losses. Thereby, it affects the system efficiency and increases the complication of the system and cost. In order to overcome this drawback, a novel double-boost DC–DC converter is proposed to meet the voltage in DC microgrid. Also, this paper discusses the detailed operation of maximum power point (MPP) tracking techniques in the novel double-boost DC–DC converter topology. The fundamental [Formula: see text]–[Formula: see text] and [Formula: see text]–[Formula: see text] characteristics of solar photovoltaic system, operational details of MPP execution and control strategies for double-boost DC/DC converter are described elaborately. The proposed converter operation and power injection into the DC microgrid are verified through the real-time PSCAD simulation and the validation is done through the experiment with hardware module which is indistinguishable with the simulation platform.

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