The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer, Y. A.; EL-Sayed, A. T.; Abdelwahab, Ahmed; Salman, Hala F.

doi:10.21595/jve.2018.19983

Cited by 7 publications

(10 citation statements)

References 25 publications

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“…Along with Amer et al 38 and Omidi and Mahmoodi, 39 the NIPPF controller can be represented by using three degrees of freedom as shown in equations ( 33)- (35). It is worthy to notice that the NIPPF controller includes both types of controllers, PPF and IRC.…”

Section: Controller Design Via Multiple Scales Methodsmentioning

confidence: 99%

“…where AðT 1 , T 2 Þ and BðT 1 , T 2 Þ are arbitrary complex functions of T 1 , and T 2 . By using equation ( 45) and substituting equation (38), one finds…”

Section: Controller Design Via Multiple Scales Methodsmentioning

confidence: 99%

“…There are numerous ways to reduce the higher amplitude of vibrations that occur in nonlinear dynamical systems. In this regard, Amer et al 38 compared the evolution of time in three different types of control, namely, IRC, PPF, and NIPPF on their main model. They showed that the best one of them is the NIPPF controller, which reduces the vibration at larger or shorter times.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

Tian

Moatimid

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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The current study examines the hybrid Rayleigh–Van der Pol–Duffing oscillator (HRVD) with a cubic–quintic nonlinear term and an external excited force. The Poincaré–Lindstedt technique is adapted to attain an approximate bounded solution. A comparison between the approximate solution with the fourth-order Runge–Kutta method (RK4) shows a good matching. In case of the autonomous system, the linearized stability approach is employed to realize the stability performance near fixed points. The phase portraits are plotted to visualize the behavior of HRVD around their fixed points. The multiple scales method, along with a nonlinear integrated positive position feedback (NIPPF) controller, is employed to minimize the vibrations of the excited force. Optimal conditions of the operation system and frequency response curves (FRCs) are discussed at different values of the controller and the system parameters. The system is scrutinized numerically and graphically before and after providing the controller at the primary resonance case. The MATLAB program is employed to simulate the effectiveness of different parameters and the controller on the system. The calculations showed that NIPPF is the best controller. The validations of time history and FRC of the analysis as well as the numerical results are satisfied by making a comparison among them.

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Section: Controller Design Via Multiple Scales Methodsmentioning

confidence: 99%

“…where AðT 1 , T 2 Þ and BðT 1 , T 2 Þ are arbitrary complex functions of T 1 , and T 2 . By using equation ( 45) and substituting equation (38), one finds…”

Section: Controller Design Via Multiple Scales Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

Tian

Moatimid

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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show abstract

“…Also, a new novel procedure is presented [28] to overcome vibration of the nonlinear oscillatory active structures. For different resonance cases the NIPPF control is applied to reduce the vibrations of duffing oscillator system near primary and super-harmonic resonances [29], through primary and internal resonance [30] and the cracked beam via harmonic excitation [31]. EL-Sayed [32] added a couple of delays connected to PPF controllers to study the response of coupled van der pol harmonic oscillators through external excitation.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…Kumar et al [19] presented a model of the vertical dynamic excitation of structures induced by a single pedestrian walking along a straight path on flat and relatively stiff surfaces. Amer et al [20] studied a Duffing oscillator system subjected to harmonic force. They applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF).The numerical comparison between the three different control methods illustrated that NIPPF controller is the best for reducing vibration at a high rate and after a short time.…”

Section: Introductionmentioning

confidence: 99%

Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

Osama

Amer

Raslan

2021

Al-Azhar Bulletin of Science

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Vibration suppression using a positive position feedback (PPF) control for a nonlinear dynamical system which subjected to an external force is studied. The proposed model is the vertical dynamic excitation of structures induced by a single pedestrian walking along a straight path on flat and relatively stiff surfaces. The multiple scale perturbation technique was applied to derive the first order approximate solution of the system. The response equation and the stability criteria for the system were derived near the simultaneous primary and internal resonance cases. MATLAB 14.0 have been used for the numerical studying to show the time history of the main system with and without PPF controller. Also, the effect of the system parameters on the response system have been studied. A comparison between the approximate and numerical solutions is illustrated and it show a good agreement between them. It is found that (PPF) controller is very suitable for small natural frequency dynamical systems subjected to primary resonance excitations.

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The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Cited by 7 publications

References 25 publications

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

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

Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

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