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

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