Response Analysis and Controlling the Nonlinear Vibration of Van Der-Pol Duffing Oscillator Connected to the NIPPF Controller

E El Emam Ahmed,Y A Amer,Khadijah M Abualnaja,Y S Hamed,A T El-Sayed

doi:10.1109/access.2021.3089978

E El Emam Ahmed, Y A Amer + Show 3 more

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https://doi.org/10.1109/access.2021.3089978

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Abstract

In this paper, we introduced response analysis and controlling the nonlinear vibration of van der pol duffing oscillator subject to parametric and external excitations by connecting the nonlinear integral positive position feedback (NIPPF). The controller combines the characteristics of the positive position feedback controller (PPF) and integral resonant control (IRC) and these controllers are viewed in a blocked scheme for the closed-loop system (system under control). The analytical solution and all resonance cases are obtained by applying the multiple time scales perturbation method (MSPM). The stability analysis is studied using the frequency response equations at the supposed worst resonance case. For numerical simulation, the system is examined before and after connecting the NIPPF controller using Matlab software program (package ode45). The influences of different parameters are examined numerically for the vibrating system and controller. The approximate analysis is confirmed with numerical simulation outcomes. Finally, making a comparison with previously related published work.

Highlights

The van der- Pol Duffing oscillators have achieved a lot of attention in studying because they can use as patterns in physics, engineering, electronics, biology, neurology and many different disciplines [1]–[3]
EFFECTS OF THREE CONTROLLERS (PPF, integral resonant control (IRC), nonlinear integral positive position feedback (NIPPF)) ON THE SYSTEM Figure 2b illustrates the controlled vibration amplitude after the positive position feedback controller (PPF) controller connected to the system which reached to 0.12 with a reduced rate 89.47%
The van der pol duffing oscillator is modified by joining the NIPPF controller to reduce the vibration near the external and parametric excitations at the measured resonant case

Summary

Introduction

The van der- Pol Duffing oscillators have achieved a lot of attention in studying because they can use as patterns in physics, engineering, electronics, biology, neurology and many different disciplines [1]–[3]. Ji et al [5] investigated the response of the controlled van der Pol-Duffing oscillator at three types of additive resonance, the response of two types of different resonance [6] and the nonlinear response through non-resonant bifurcations of codimension two at primary resonance [7], respectively. Kamel [12] investigated the nonlinear performance of van der pol oscillators through parametric and harmonic excitations. Hu and Chung [13] used the delayed self-connection and the couplings of velocity and position to study the stability analysis for a pair of van der pol oscillators. The vibration of Duffing– Van der Pol oscillator is controlled in [15] using a time delay

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