Vibration Control for Parametrically Excited Coupled Nonlinear Oscillators

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Attilio Maccari
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Periodic Solutions ◽  
Parametric Excitation ◽  
Nonlinear Oscillators ◽  
Excitation Amplitude ◽  
State Feedback Control ◽  
Coupled Equations ◽  
Technical Requirements ◽  
Coupled Nonlinear Oscillators

A complex nonlinear system under state feedback control with a time delay corresponding to two coupled nonlinear oscillators with a parametric excitation is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. In the system without control, phase-locked solutions with period equal to the parametric excitation period are possible only if the oscillator amplitudes are equal, but they depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. It is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.

Time Delay Control for Two van der Pol Oscillators

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Attilio Maccari
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Periodic Solutions ◽  
Original System ◽  
Excitation Amplitude ◽  
Van Der Pol ◽  
Flow Equations ◽  
Technical Requirements ◽  
Stable Periodic ◽  
Van Der Pol Oscillators

A method for time delay vibration control of the principal and fundamental resonances of two nonlinearly coupled van der Pol oscillators is investigated Using the asymptotic perturbation method, four slow-flow equations on the amplitude and phase of the oscillators are obtained. Their fixed points correspond to a two-period quasi-periodic phase-locked motion for the original system. In the system without control, stable periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of these solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if vibration control terms are added, stable two-period quasi-periodic solutions with arbitrarily chosen amplitudes can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.

scholarly journals The Vibration reduction of a cantilever beam subjected to parametric excitation using time delay feedback

2017 ◽  
Vol 13 (2) ◽  
pp. 7186-7193
Author(s):  
Y A Amer
Keyword(s):  
Time Delay ◽  
Cantilever Beam ◽  
Parametric Excitation ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Multiple Scale ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Resonance Case

In this paper, dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay is analyzed. The method of multiple scale perturbation technique is applied to obtain the solution up to the first order approximation. We obtain equations for the amplitude and phase. We studied all resonance cases numerically. Stability of the steady state solution for the selected resonance case is studied applying Rung-Kutta fourth method and frequency response equation via Matlab 7.0 and maple 16. From the results, it can be seen that the frequency and amplitude responses for the selected resonance case can be affected by the time delayed control. Effects of different parameters of the system are studied.

Closed Form Control Gains for Zero Assignment in the Time Delayed System

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Kumar Vikram Singh ◽  
Biswa Nath Datta ◽  
Mayank Tyagi
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Closed Form ◽  
Control Strategy ◽  
Taylor Series Expansion ◽  
Small Time ◽  
State Feedback Control ◽  
Control Force ◽  
Sensors And Actuators ◽  
The Stability

Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which the dynamics of the structure are to be controlled. In recent years, dynamic absorption schemes are investigated in which control strategies that absorb a steady state motion of a desired location in the structure have been developed. Such a vibration control strategy is termed as zero assignment. Unlike conventional full-state feedback control, which requires all the states of the system to be measured, zero assignment requires least numbers of sensors and actuators (depending on the number of dynamic absorption points) for estimating the control gains and, hence, it may provide economical engineering solution. However, while applying control strategy by active zero assignment, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper, we have developed vibration control strategy by active zero assignment and obtained closed form control gains for systems with and without time delays by using truncated and full Taylor series expansion. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the active dynamic absorption and the effects of time delay on control gains. The effect of delay in the stability of the controlled system is also summarized.

Effect of parameter mismatch and time delay interaction on density-induced amplitude death in coupled nonlinear oscillators

2014 ◽  
Vol 76 (3) ◽  
pp. 1797-1806 ◽  
Author(s):  
Amit Sharma ◽  
K. Suresh ◽  
K. Thamilmaran ◽  
Awadhesh Prasad ◽  
Manish Dev Shrimali
Keyword(s):  
Time Delay ◽  
Nonlinear Oscillators ◽  
Amplitude Death ◽  
Parameter Mismatch ◽  
Coupled Nonlinear Oscillators ◽  
Delay Interaction

Vibration Control of a Cantilever Beam with Time Delay State Feedback

2006 ◽  
Vol 61 (12) ◽  
pp. 629-640 ◽  
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Cantilever Beam ◽  
State Feedback ◽  
Multiple Scales ◽  
State Feedback Control ◽  
Response Curves ◽  
Flow Equations ◽  
Equivalent Damping ◽  
The Stability

The primary and subharmonic resonance of order one-third of a cantilever beam under state feedback control with a time delay are investigated. Using the method of multiple scales, we obtain two slow flow equations for the amplitude and phase. The first-order approximate solution is derived and the effect of time delay on the resonance is investigated. The concept of an equivalent damping, related to the delay feedback, is proposed and an appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The fixed points corresponding to the periodic motion of the starting system are determined, and the frequency-response and external excitation-response curves are shown. Bifurcation analysis is conducted in order to examine the stability of the system.

The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons

2014 ◽  
Vol 24 (05) ◽  
pp. 1450069 ◽  
Author(s):  
E. B. Megam Ngouonkadi ◽  
Hilaire B. Fotsin ◽  
P. H. Louodop Fotso
Keyword(s):  
Phase Transition ◽  
Time Delay ◽  
Nonlinear Oscillators ◽  
Combined Effect ◽  
Electrical Synapses ◽  
Bursting Neurons ◽  
Coupled Nonlinear Oscillators ◽  
Binding Time ◽  
Chemical Synapses ◽  
Synaptic Parameters

In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh–Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.

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