Feedback Control of Grazing-Induced Chaos in the Single-Degree-of-Freedom Impact Oscillator

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yongkang Shen ◽  
Shan Yin ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Dynamical Property ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Impact Oscillator ◽  
Continuous Transition ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Existence And Stability

Based on the special dynamical property of continuous transition at certain degenerate grazing points in the single-degree-of-freedom impact oscillator, the control problem of the grazing-induced chaos is investigated in this paper. To design degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis first. Then, a discrete-in-time feedback control strategy is used to suppress the grazing-induced chaos into the 1/n impact periodic motions precisely by the desired degenerate grazing bifurcation. The feasibility of the control strategy is verified by numerical simulations.

PD Control Strategy Design and Simulation of Magnetic Bearing with Single Freedom of Degree

2013 ◽  
Vol 760-762 ◽  
pp. 1207-1211 ◽  
Author(s):  
Guang Yang ◽  
Jian Min Zhang
Keyword(s):  
Control Strategy ◽  
Magnetic Bearing ◽  
Degree Of Freedom ◽  
Pd Control ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unstable Plant ◽  
Strategy Design ◽  
The Given ◽  
Bearing System

Based on the analysis of the model of the Single-Degree-of-Freedom (SDF) magnetic bearing system, the issue of design and simulation of PD control strategy in the system is investigated. First, the plant model of the AMB (Active Magnetic Bearings) with Single-Degree-of-Freedom (SDF) is found out to be unstable plant. Then, based on the root locus theory and Routh stability criteria, the necessity of derivation action in the controller is analyzed.In addition, the PD control strategy for a particular plant is designed, the effectiveness of which is validated by the given simulation examples. The proposed approach can provide an important reference for the practical application of PD control strategy in the magnetic bearing system.

scholarly journals Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401771661 ◽  
Author(s):  
Jun Wang ◽  
Yongjun Shen ◽  
Shaopu Yang
Keyword(s):  
Periodic Motion ◽  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Dynamical Response ◽  
Restitution Coefficient ◽  
Impact Oscillator ◽  
Vibration Period ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulse Excitation

In this article, the dynamical behavior of a single degree-of-freedom impact oscillator with impulse excitation is studied, where the mass impacts at one stop and is shocked with impulse excitation at the other stop. The existing and stability conditions for periodic motion of the oscillator are established. The effects of system parameters on dynamical response are discussed under different initial velocities. It is found that smaller shock gap than impact gap could make the periodic motion more stable. The decrease in natural frequency would consume less impact energy, make the vibration frequency smaller, and reduce the vibration efficiency. Finally, the dynamical properties are further analyzed under a special case, that is, the shock gap approaches zero. It could be seen that the larger shock coefficient and impact restitution coefficient would make vibration period smaller. Based on the stability condition, there are an upper limit for the product of shock coefficient and impact restitution coefficient, so that a lower limit of corresponding vibration period exists.

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

RESONANCE CONTROL FOR A FORCED SINGLE-DEGREE-OF-FREEDOM NONLINEAR SYSTEM

2004 ◽  
Vol 14 (04) ◽  
pp. 1423-1429 ◽  
Author(s):  
ANDREW Y. T. LEUNG ◽  
JIN CHEN JI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Singularity Theory ◽  
Degree Of Freedom ◽  
Theory Approach ◽  
Nonlinear Feedback ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Resonance Control

The main characteristic of a forced single-degree-of-freedom weakly nonlinear system is determined by its primary, super- and sub-harmonic resonances. A nonlinear parametric feedback control is proposed to modify the steady-state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations that take place in the resonance responses. The nonlinear gain of the feedback control is determined by analyzing the bifurcation diagrams associated with the corresponding frequency-response equation, from the singularity theory approach. It is shown by illustrative examples that the proposed nonlinear feedback is effective for controlling three kinds of resonance responses.

Resonances of a Nonlinear Single-Degree-of-Freedom System with Time Delay in Linear Feedback Control

2010 ◽  
Vol 65 (5) ◽  
pp. 357-368 ◽  
Author(s):  
Atef F. El-Bassiouny ◽  
Salah El-Kholy
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Feedback Control ◽  
Fixed Points ◽  
Multiple Scales ◽  
Degree Of Freedom ◽  
Linear Feedback ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Subharmonic Resonances

The primary and subharmonic resonances of a nonlinear single-degree-of-freedom system under feedback control with a time delay are studied by means of an asymptotic perturbation technique. Both external (forcing) and parametric excitations are included. By means of the averaging method and multiple scales method, two slow-flow equations for the amplitude and phase of the primary and subharmonic resonances and all other parameters are obtained. The steady state (fixed points) corresponding to a periodic motion of the starting system is investigated and frequency-response curves are shown. The stability of the fixed points is examined using the variational method. The effect of the feedback gains, the time-delay, the coefficient of cubic term, and the coefficients of external and parametric excitations on the steady-state responses are investigated and the results are presented as plots of the steady-state response amplitude versus the detuning parameter. The results obtained by two methods are in excellent agreement

An Experimental Study of a Single-Degree-of-Freedom Impact Oscillator

2021 ◽  
Author(s):  
Shun Zhong ◽  
Jingyuan Tan ◽  
Zhicheng Cui ◽  
Tanghong Xu ◽  
Liqing Li
Keyword(s):  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Physical Parameters ◽  
Impact Oscillator ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Design Choice ◽  
Wide Range ◽  
Simulation Results

Purpose. Impacts appear in a wide range of mechanical systems. To study the dynamical behavior introduced by impact in practical way, a single-degree-of-freedom impact oscillator rig is designed. Originality. A simple piece-wise linear system with symmetrical flexible constraints is designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piece-wise models. The new design choice is based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness as well avoidance of the delay introduced by the structure. Meanwhile, the new design provides the possibility of the applications of the complex control algorithms. Design/methodology/approach. The design process is described in detail. The initial experimental results of the rig as well as numerical simulation results are given. In this rig, the mass driven force is generated by electromagnet, which can be adjusted and control easily. Also, most of the physical parameters can be varied in a certain range to enhance flexibility of the system allowing to observe subtle phenomena. Findings. Compared with the simulation results, the designed rig is proved to be validated. Then, the initial experimental results demonstrate potentials of this rig to study fundamental impact phenomena, which have been observed in various engineering systems. They also indicate that this rig can be a good platform for investigating nonlinear control methods.

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