Determination of optimal positive position feedback parameters by using nonsmooth H∞ synthesis

E, Bin; Shan, Jinjun; Khushnood, Muhammad Atif; Wang, Xiaogang; Cui, Naigang

doi:10.1177/1077546320943794

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…The results are presented in graphical forms as steady-state vibration amplitudes (a 1 & a 2 ) against the detuning parameter σ 1 or the excitation amplitude f . In addition, the stability of the obtained solution is investigated according to the condition given by Equation (26). In all obtained response curves, the solid line refers to the stable solution, while the dotted line represents the unstable one.…”

Section: Response Curves and Numerical Validationsmentioning

confidence: 99%

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Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

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The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

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Section: Response Curves and Numerical Validationsmentioning

confidence: 99%

“…The authors showed that the fractional-order controller is more efficient in suppressing both the periodic and random vibration responses. Also, the optimal design of the positive position feedback controller parameters is introduced using the H 2 and H ∞ optimization techniques [25,26].…”

Section: Introductionmentioning

confidence: 99%

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

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Tuned Positive Position Feedback Control of an Active Magnetic Bearings System With 16-Poles and Constant Stiffness

Kandil

Hamed

2021

IEEE Access

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This paper presents a tuned positive position feedback controller (TPPF) to overcome the dual high peaks of the classical PPF. This control signal is merged with a proportional-derivative (PD) control signal to suppress the vibrations of a constant-stiffness 16-poles rotor active magnetic bearings (AMBs) system. Another benefit of the applied TPPF is turning the rotor's quasiperiodic unstable motion into a periodic stable motion by eliminating both saddle-node and Hopf points. The whole group equations of motion are derived and their approximate solutions are sought with the aid of the multiple scales method. Different response curves are plotted to clarify the difference between the rotor's vibratory behaviors before and after PPF and also with TPPF.

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Determination of optimal positive position feedback parameters by using nonsmooth H∞ synthesis

Cited by 2 publications

References 26 publications

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Tuned Positive Position Feedback Control of an Active Magnetic Bearings System With 16-Poles and Constant Stiffness

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