scholarly journals Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration

2016 ◽  
Vol 2016 ◽  
pp. 1-22 ◽  
Author(s):  
Yongjun Hou ◽  
Pan Fang
Keyword(s):  
Lagrange Equation ◽  
Transformation Method ◽  
Spring Stiffness ◽  
Balance Equations ◽  
Pendulum System ◽  
Dimensionless Equation ◽  
Coupling Relationship ◽  
The Stability ◽  
Synchronous Behavior ◽  
Laplace Transformation Method

This work is a continuation for our published literature for vibration synchronization. A new mechanism, two rotors coupled with a pendulum rod in a multi-DOF vibration system, is proposed to implement coupling synchronization, and the dynamics equation of mechanism is derived by Lagrange equation. In addition, the coupling relationship between the vibrobody and the pendulum rod is ascertained with the Laplace transformation method, based on the dimensionless equation of the dynamics system. The Poincare method is employed to study the synchronization state between the two unbalanced rotors, which is converted into that of existence and the stability of solutions for synchronization-balance equations. The obtained results are supported by computer simulations. It is demonstrated that the values of the spring stiffness coefficient, the length of the pendulum, and the angular installation of the pendulum are important parameters with respect to the synchronous behavior in the rotor-pendulum system.

Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems

2017 ◽  
Vol 232 (10) ◽  
pp. 1802-1822 ◽  
Author(s):  
Pan Fang ◽  
Yongjun Hou
Keyword(s):  
Dynamic Characteristics ◽  
Transformation Method ◽  
Stable Phase ◽  
Coupling Coefficients ◽  
Synchronous State ◽  
Rotation Direction ◽  
Pendula System ◽  
Resonant Systems ◽  
The Stability ◽  
Synchronous Behavior

The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker. To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system. In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations. Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system. Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincaré method on which stable phase difference and synchronous behavior can be ascertained. To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determined by the geometry parameters, coupling coefficients, and rotor rotation direction.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

DESIGN OF ADAPTIVE FUZZY SLIDING MODE CONTROL FOR NONLINEAR SYSTEMS

1999 ◽  
Vol 07 (05) ◽  
pp. 463-474 ◽  
Author(s):  
JEN-YANG CHEN
Keyword(s):  
Sliding Mode ◽  
Membership Functions ◽  
System Specification ◽  
Pendulum System ◽  
Control Rules ◽  
Inverted Pendulum System ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
The Stability ◽  
The Individual

In this paper, a fuzzy sliding mode controller (FSMC), which is synthesized by a collection of linguistic control rules whose membership functions of THEN-part is adapted, is proposed. Both the membership functions of IF-part and THEN-part are arranged symmetrically and distributed equally in the individual universe of discourse. In particular, the membership functions of the THEN-part can be adapted via one parameter adaptation to meet the required system specification. The proposed direct adaptive FSMC can be synthesized through the following stages. First, the control rules are constructed according to the concepts of SMC, and the fuzzy sets whose membership functions are symmetrically covered in state space. Then, the derived adaptive law is used to adjust the membership functions of the THEN-part. The FSMC is employed to approximate the equivalent control of SMC without knowing the mathematical model of the controlled system. Third, a hitting control is developed to guarantee the stability of the control system. Finally, we apply this FSMC to control a nonlinear inverted pendulum system for confirming the validity of the proposed approach.

scholarly journals ANÁLISE DA INTEGRIDADE E DA INSTABILIDADE DINÂMICA DE UM SISTEMA MECÂNICO SUJEITO A BIFURAÇÃO DO TIPO BUTTERFLY

2021 ◽  
Vol 12 (3) ◽  
pp. 14-22
Author(s):  
Michael Dowglas de Gois Silva ◽  
Fábio Roberto Chavarette ◽  
Milton Batista Ferreira Junior ◽  
Rodrigo Francisco Borges Lourenco
Keyword(s):  
Static Load ◽  
Structural Systems ◽  
Spring Stiffness ◽  
Bifurcation Diagrams ◽  
Model Uncertainties ◽  
Geometric Imperfections ◽  
Attraction Basin ◽  
Linear Buckling ◽  
Lower Load ◽  
The Stability

Slender structural systems susceptible to unstable buckling generally losestability at lower load levels than the linear buckling load of the perfect structure. This is mainly due to the geometric imperfections present in real structures. The objective of this work is to determine the integrity measures, together with the stability of the post-critical solutions of a mechanical system subject to unstable symmetrical buckling, Burtterfly-type bifurcation, using a discrete degree of freedom model. Uncertainties in the order of 10% will be considered in its deterministic parameters, to obtain lower and reliable limits for the project. The proposed uncertainty in the spring stiffness parameters does not change the type of bifurcation and the value of the critical load, only the value of the minimum post-critical of the bifurcation diagrams. The results showed the erosion of the attraction basin and the decrease of the factors of integrity, local and global, for the trivial solutions with the increase of the static load, for the investigated bifurcation.

Hybrid Optimization Technique for Enhancing the Stability of Inverted Pendulum System

2021 ◽  
Vol 12 (1) ◽  
pp. 77-97
Author(s):  
M. E. Mousa ◽  
M. A. Ebrahim ◽  
Magdy M. Zaky ◽  
E. M. Saied ◽  
S. A. Kotb
Keyword(s):  
Inverted Pendulum ◽  
Optimization Technique ◽  
Linear Quadratic Regulator ◽  
Variable Structure ◽  
Grey Wolf Optimizer ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
New Variant ◽  
The Stability

The inverted pendulum system (IPS) is considered the milestone of many robotic-based industries. In this paper, a new variant of variable structure adaptive fuzzy (VSAF) is used with new reduced linear quadratic regulator (RLQR) and feedforward gain for enhancing the stability of IPS. The optimal determining of VSAF parameters as well as Q and R matrices of RLQR are obtained by using a modified grey wolf optimizer with adaptive constants property via particle swarm optimization technique (GWO/PSO-AC). A comparison between the hybrid GWO/PSO-AC and classical GWO/PSO based on multi-objective function is provided to justify the superiority of the proposed technique. The IPS equipped with the hybrid GWO/PSO-AC-based controllers has minimum settling time, rise time, undershoot, and overshoot results for the two system outputs (cart position and pendulum angle). The system is subjected to robustness tests to ensure that the system can cope with small as well as significant disturbances.

Fuzzy Control of an Inverted Pendulum

1996 ◽  
Author(s):  
Tuna Balkan ◽  
Mehmet Emin Ari
Keyword(s):  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Angular Position ◽  
Upright Position ◽  
Control Signal ◽  
Position Measurement ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
And Performance ◽  
The Stability

Abstract An inverted pendulum system has been designed and constructed as a physical model of inherently unstable mechanical systems. The vertical upright position of a pendulum is controlled by changing the horizontal position of a cart to which the pendulum is hinged. The stability of the system has been investigated when a fuzzy controller is used to produce the control signal, while making a single measurement. It has been shown that by using simple fuzzy rules to allow real time computation with a single angular position measurement, the system can not be made absolutely stable. However, the stability and performance of the system have been considerably improved by shrinking the membership functions of angular position, computed angular velocity and control signal when inverted pendulum is very close to the vertical upright position.

Advanced modeling and optimal control of a cart-double pendulum system

2019 ◽  
Author(s):  
◽  
Cecil Jr. Shy
Keyword(s):  
Optimal Control ◽  
Lagrange Equation ◽  
Control Technique ◽  
Tuning Parameter ◽  
Microgravity Environment ◽  
Double Pendulum ◽  
Overhead Crane ◽  
Material Transport ◽  
Pendulum System ◽  
Industry Standards

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The Overhead Crane has evolved in scope since its inception in the late 1800's. Its early use as a hoist for material transport is now proceeded by new found applications, such as in the Active Response Gravity Offload System (ARGOS) at the NASA Johnson Space Center. ARGOS is an astronaut training facility designed to simulate reduced gravity environments such as Lunar, Martian, or microgravity. By industry standards, it is essentially a repurposed Overhead Crane; in academia it can be conceptualized as a cart-double pendulum system. Anti-sway control of cart-pendulum systems has been heavily researched; however, these methods are not typically designed for space simulation. The goal of this research is to design a controller that provides both energy and error minimization for the cart-pendulum, so that its payload moves as if it were floating freely in a microgravity environment (according to Newton's 1st law). The Euler-Lagrange equation is used to model the system and an optimal control technique called the [alpha]-shift is used to control the system. Most treatments on optimal linear control do not include the [alpha]-shift, but its addition allows one to stabilize the system faster and provides an extra tuning parameter while maintaining the simplicity of the solution. Numerical experiments show that the [alpha]-shift method significantly improves the cart-pendulum's ability to control its payload; especially for payloads in the cart-double-pendulum case.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

2019 ◽  
Vol 28 (04) ◽  
pp. 1950068 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Stability Margin ◽  
Transformation Method ◽  
Second Order ◽  
Approximation Accuracy ◽  
Parameter Transformation ◽  
Practical Applications ◽  
Compensator Design ◽  
Novel Method ◽  
Design Idea ◽  
The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050282
Author(s):  
Asıf Yokuş ◽  
Doğan Kaya
Keyword(s):  
Traveling Wave ◽  
Numerical Solutions ◽  
Traveling Wave Solutions ◽  
Transformation Method ◽  
Mkdv Equation ◽  
Traveling Wave Solution ◽  
Von Neumann ◽  
Wave Solutions ◽  
De Vries ◽  
The Stability

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

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