scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Global Analysis of the Double Impact Oscillator Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Global Analysis ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Real Value ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighbourhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally and the real value of the restitution coefficient is determined by this method.

scholarly journals Analysis of moored ship oscillations in waves

2020 ◽  
Author(s):  
Д.П. Ковалев ◽  
П.Д. Ковалев ◽  
А.С. Борисов
Keyword(s):  
Dynamic System ◽  
Sea Level ◽  
Order Differential Equation ◽  
External Excitation ◽  
Impact Oscillator ◽  
Mooring Lines ◽  
Sea Level Fluctuations ◽  
Port Area ◽  
Sea Level Fluctuation ◽  
The Impact

В работе рассмотрены особенности колебаний пришвартованного судна для основных портов Сахалинской области, поскольку качка судна у причала может представлять опасность и приводить к повреждению судна или швартовых линий. По данным натурных измерений морского волнения в портовых бухтах рассчитаны спектры колебаний уровня и определены периоды существующих в них волн для диапазона периодов от 2 с до 30 минут. Произведен расчет периодов собственных колебаний (качки) двух типов судов, преимущественно швартующихся в портах. С учетом полученных результатов выполнено моделирование движения судов при волнении как динамической с системы внешним возбуждающим воздействием на основе дифференциального уравнения второго порядка. Показано влияние коэффициента вязкого демпфирования и жесткости швартовых на реакцию динамической системы без удара о причал и для режима ударного осциллятора. Установлено, что в случае прихода в район порта Корсаков длинноволновой зыби движения судна могут переходить в хаотические. The paper considers the peculiarities of moored vessel oscillations for the main ports of the Sakhalin region, since the pitching of the vessel at the berth can be dangerous and lead to damages of the vessel or mooring lines. Spectra of sea level fluctuations and periods of waves in port bays were calculated using sea level fluctuation measurements obtained in the range from 2 seconds to 30 minutes. Calculations of resonance periods (pitching) of two types of vessels mainly moored in ports were done. Taking into consideration these results the simulation of the vessel movement in waves as a dynamic system with an external excitation was performed on the base of second-order differential equation. The influence of viscous damping coefficient and mooring stiffness on the response of the dynamic system is shown for two cases: for system without impact and for the impact oscillator mode. It is established that in the event of a long-wave swell coming to the Korsakov port area, the vessels movements may become chaotic.

scholarly journals Экспериментальное и теоретическое исследование осциллятора с соударениями

2020 ◽  
Vol 90 (10) ◽  
pp. 1672
Author(s):  
В.В. Нарожнов
Keyword(s):  
Theoretical Model ◽  
Equations Of Motion ◽  
Spectral Characteristics ◽  
Contact Theory ◽  
Hertz Contact ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
Fourier Filtering ◽  
Nonlinear Mechanical ◽  
The Impact

The results of a study of a nonlinear mechanical oscillator with elastic impacts are presented. The experiment was carried out using an electromechanical impact oscillator. The theoretical model is based on the equations of motion, taking into account the elastic force, which is calculated under the Hertz contact theory. It is shown that bifurcations and attractors of the “stable focus” and “limit cycle” types can occur for the impact oscillator. Fourier filtering was used to analyze the spectral characteristics of the signals.

Dynamics of Oscillator With Soft Impacts

2001 ◽  
Author(s):  
František Peterka
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Mechanical System ◽  
Linear Model ◽  
Piecewise Linear ◽  
Impact Oscillator ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
New Phenomena ◽  
The Impact

Abstract The impact oscillator is the simplest mechanical system with one degree of freedom, the periodically excited mass of which can impact on the stop. The aim of this paper is to explain the dynamics of the system, when the stiffness of the stop changes from zero to infinity. It corresponds to the transition from the linear system into strongly nonlinear system with rigid impacts. The Kelvin-Voigt and piecewise linear model of soft impact was chosen for the study. New phenomena in the dynamics of motion with soft impacts in comparison with known dynamics of motion with rigid impacts are introduced in this paper.

Comparative Study of Evolutionary Algorithms for Parameter Identification of an Impact Oscillator

2014 ◽  
Author(s):  
Amit Banerjee ◽  
Issam Abu Mahfouz
Keyword(s):  
Evolutionary Algorithms ◽  
Differential Evolution ◽  
Parameter Identification ◽  
Optimization Techniques ◽  
System Response ◽  
Impact Oscillator ◽  
Swarm Optimization ◽  
System Parameters ◽  
Highly Nonlinear ◽  
The Impact

The use of non-classical evolutionary optimization techniques such as genetic algorithms, differential evolution, swarm optimization and genetic programming to solve the inverse problem of parameter identification of dynamical systems leading to chaotic states has been gaining popularity in recent years. In this paper, three popular evolutionary algorithms — differential evolution, particle swarm optimization and the firefly algorithm are used for parameter identification of a clearance-coupled-impact oscillator system. The behavior of impacting systems is highly nonlinear exhibiting a myriad of harmonic, low order and high order sub-harmonic resonances, as well as chaotic vibrations. The time-history simulations of the single-degree-of-freedom impact oscillator were obtained by the Neumark-β numerical integration algorithm. The results are illustrated by bifurcation graphs, state space portraits and Poincare’ maps which gives valuable insights on the dynamics of the impact system. The parameter identification problem relates to finding one set of system parameters given a chaotic or periodic system response as a set of Poincaré points and a different but known set of system parameters. The three evolutionary algorithms are compared over a set of parameter identification problems. The algorithms are compared based on solution quality to evaluate the efficacy of using one algorithm over another.

Explanation of appearance and characteristics of intermittency chaos of the impact oscillator

2004 ◽  
Vol 19 (5) ◽  
pp. 1251-1259 ◽  
Author(s):  
František Peterka ◽  
Tadashi Kotera ◽  
Stanislav Čipera
Keyword(s):  
Impact Oscillator ◽  
The Impact

Application of the Harmonic Balance Method to Ground Moling Machines Operating in Periodic Regimes

2001 ◽  
Author(s):  
Ko-Choong Woo ◽  
Albert A. Rodger ◽  
Richard D. Neilson ◽  
Marian Wiercigroch
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Structural Complexity ◽  
Initial Guess ◽  
Balance Method ◽  
Operational Parameters ◽  
Impact Oscillator ◽  
Time Harmonic ◽  
Wide Range ◽  
The Impact

Abstract The paper describes current research into mathematical modelling of a novel vibro-impact ground moling system. Experimental and theoretical studies suggest periodic responses are required to achieve the optimal penetrating conditions for the ground moling process, as this results in reduced soil penetration resistance. Therefore, there is a practical need for a robust and efficient methodology to calculate periodic responses for a wide range of operational parameters. Due to the structural complexity of a real vibro-impact moling system, the dynamic response of an idealised impact oscillator has been investigated in the first instance. This paper presents a detailed study of periodic responses of the impact oscillator under harmonic forcing using alternating frequency-time harmonic balance method. Recommendations of how to effectively adapt the alternating frequency-time harmonic balance method for a stiff impacting system are given. The periodic motion is represented algebraically by a truncated Fourier series and the systematic methodology employed allows for convergence. The idea central to this procedure is that the linear oscillator is explicitly solvable analytically, and this allows for the initial set of Fourier coefficients. The clearance value is then adjusted so that contact with the secondary stiffness is slight and the nonlinearity is weak. The solution to this subsequent system is obtainable as the initial guess is close to the required solution.

Application of Double Impact Oscillator in Forming

2001 ◽  
Author(s):  
František Peterka
Keyword(s):  
Numerical Simulations ◽  
Single System ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighborhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally.

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