Yaser Amer, Hanan Abd Elrahman, Mansour Abd El-Salamr
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 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 according to Routh–Hurwitz criterion. 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.
Positive position feedback control; Modified Duffing equation; Stability analysis
Cite this paper
Yaser Amer, Hanan Abd Elrahman, Mansour Abd El-Salamr. (2022) Study the Behaviors of the Modified Duffing Equation by PPF Control Under the Primary and Internal Resonance Case. International Journal of Control Systems and Robotics, 7, 27-35